Defining parameters
| Level: | \( N \) | \(=\) | \( 47040 = 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 47040.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 344 \) | ||
| Sturm bound: | \(21504\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(47040))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10944 | 656 | 10288 |
| Cusp forms | 10561 | 656 | 9905 |
| Eisenstein series | 383 | 0 | 383 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(3\) | \(5\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| All | New | Old | All | New | Old | All | New | Old | ||||||||
| \(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(668\) | \(39\) | \(629\) | \(645\) | \(39\) | \(606\) | \(23\) | \(0\) | \(23\) | |||
| \(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(696\) | \(42\) | \(654\) | \(672\) | \(42\) | \(630\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(700\) | \(43\) | \(657\) | \(676\) | \(43\) | \(633\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(672\) | \(39\) | \(633\) | \(648\) | \(39\) | \(609\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(684\) | \(41\) | \(643\) | \(660\) | \(41\) | \(619\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(680\) | \(42\) | \(638\) | \(656\) | \(42\) | \(614\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(684\) | \(37\) | \(647\) | \(660\) | \(37\) | \(623\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(688\) | \(45\) | \(643\) | \(664\) | \(45\) | \(619\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(692\) | \(41\) | \(651\) | \(668\) | \(41\) | \(627\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(680\) | \(42\) | \(638\) | \(656\) | \(42\) | \(614\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(676\) | \(37\) | \(639\) | \(652\) | \(37\) | \(615\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(688\) | \(45\) | \(643\) | \(664\) | \(45\) | \(619\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(692\) | \(39\) | \(653\) | \(668\) | \(39\) | \(629\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(680\) | \(42\) | \(638\) | \(656\) | \(42\) | \(614\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(676\) | \(43\) | \(633\) | \(652\) | \(43\) | \(609\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(688\) | \(39\) | \(649\) | \(664\) | \(39\) | \(625\) | \(24\) | \(0\) | \(24\) | |||
| Plus space | \(+\) | \(5440\) | \(314\) | \(5126\) | \(5249\) | \(314\) | \(4935\) | \(191\) | \(0\) | \(191\) | ||||||
| Minus space | \(-\) | \(5504\) | \(342\) | \(5162\) | \(5312\) | \(342\) | \(4970\) | \(192\) | \(0\) | \(192\) | ||||||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(47040))\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 5 | 7 | |||||||
| 47040.2.a.a | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-6q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.b | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-6q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.c | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}-5q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.d | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.e | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.f | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.g | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.h | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.i | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.j | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.k | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.l | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.m | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}-2q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.n | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.o | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-2q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.p | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}-q^{11}+5q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.q | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-6q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.r | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.s | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.t | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}+q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.u | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.v | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.w | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.x | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.y | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.z | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.ba | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+6q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.bb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}+q^{11}-7q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.bc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.bd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.be | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.bf | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.bg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.bh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.bi | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.bj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+3q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.bk | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.bl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.bm | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.bn | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.bo | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.bp | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.bq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+4q^{11}+7q^{13}+\cdots\) | |
| 47040.2.a.br | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.bs | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+6q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.bt | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+6q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.bu | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{3}-q^{5}+q^{9}+6q^{11}+q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.bv | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $+$ | \(q-q^{3}-q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\) | |
| 47040.2.a.bw | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\) | |
| 47040.2.a.bx | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-6q^{11}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.by | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.bz | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.ca | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.cb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-7q^{13}+\cdots\) | |
| 47040.2.a.cc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.cd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.ce | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.cf | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.cg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.ch | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.ci | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.cj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.ck | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.cl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.cm | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.cn | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}-2q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.co | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.cp | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.cq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.cr | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-q^{11}+7q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.cs | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.ct | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.cu | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.cv | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.cw | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}-q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.cx | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}+q^{13}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.cy | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.cz | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.da | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.db | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.dc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+q^{11}-5q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.dd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}+2q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.de | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.df | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.dg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.dh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.di | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.dj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $+$ | \(q-q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.dk | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.dl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.dm | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.dn | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.do | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.dp | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.dq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+5q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.dr | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+6q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.ds | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q-q^{3}+q^{5}+q^{9}+6q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.dt | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-6q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.du | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-6q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.dv | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-6q^{11}-q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.dw | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\) | |
| 47040.2.a.dx | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-5q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.dy | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.dz | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.ea | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.eb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.ec | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.ed | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.ee | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-4q^{11}+7q^{13}+\cdots\) | |
| 47040.2.a.ef | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.eg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.eh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.ei | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.ej | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.ek | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.el | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.em | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}-q^{11}-7q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.en | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.eo | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-6q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.ep | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.eq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.er | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.es | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.et | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.eu | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.ev | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.ew | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.ex | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.ey | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.ez | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}+q^{11}+5q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.fa | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}+2q^{11}-q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.fb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.fc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+2q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.fd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.fe | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}-q^{15}+\cdots\) | |
| 47040.2.a.ff | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.fg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.fh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fi | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.fk | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.fl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.fm | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q+q^{3}-q^{5}+q^{9}+5q^{11}+5q^{13}+\cdots\) | |
| 47040.2.a.fn | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+6q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.fo | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q+q^{3}-q^{5}+q^{9}+6q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fp | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-6q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.fq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-6q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.fr | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-5q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.fs | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.ft | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\) | |
| 47040.2.a.fu | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fv | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fw | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.fx | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.fy | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.fz | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.ga | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}-2q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.gb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.gc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.gd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.ge | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.gf | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-q^{11}-5q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.gg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.gh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.gi | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.gj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.gk | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}-q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.gl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+q^{13}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.gm | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}-6q^{17}+\cdots\) | |
| 47040.2.a.gn | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}-2q^{17}+\cdots\) | |
| 47040.2.a.go | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+2q^{17}+\cdots\) | |
| 47040.2.a.gp | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.gq | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.gr | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+q^{11}+7q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.gs | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\) | |
| 47040.2.a.gt | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.gu | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+2q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.gv | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.gw | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.gx | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+3q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.gy | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-7q^{13}+\cdots\) | |
| 47040.2.a.gz | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-5q^{13}+\cdots\) | |
| 47040.2.a.ha | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.hb | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.hc | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.hd | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.he | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\) | |
| 47040.2.a.hf | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\) | |
| 47040.2.a.hg | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\) | |
| 47040.2.a.hh | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{3}+q^{5}+q^{9}+5q^{11}-q^{13}+q^{15}+\cdots\) | |
| 47040.2.a.hi | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\) | |
| 47040.2.a.hj | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+6q^{11}+q^{15}+6q^{17}+\cdots\) | |
| 47040.2.a.hk | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.hl | $1$ | $375.616$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{3}+q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\) | |
| 47040.2.a.hm | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.hn | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ho | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hp | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hq | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.hr | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hs | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.ht | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hu | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hv | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hw | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.hx | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.hy | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.hz | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ia | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ib | $2$ | $375.616$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ic | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.id | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ie | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.if | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ig | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.ih | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ii | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.ij | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.ik | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.il | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.im | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.in | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.io | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.ip | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.iq | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ir | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.is | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.it | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.iu | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.iv | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.iw | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.ix | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.iy | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.iz | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.ja | $2$ | $375.616$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jb | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jc | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jd | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.je | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jf | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jg | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jh | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.ji | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jj | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jk | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jl | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jm | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jn | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.jo | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.jp | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.jq | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.jr | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.js | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.jt | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.ju | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.jv | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.jw | $2$ | $375.616$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.jx | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.jy | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.jz | $2$ | $375.616$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.ka | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.kb | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.kc | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.kd | $2$ | $375.616$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.ke | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.kf | $2$ | $375.616$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.kg | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.kh | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.ki | $3$ | $375.616$ | 3.3.3132.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.kj | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.kk | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.kl | $3$ | $375.616$ | 3.3.3576.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.km | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.kn | $3$ | $375.616$ | 3.3.1524.1 | None | \(0\) | \(-3\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.ko | $3$ | $375.616$ | 3.3.1524.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.kp | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.kq | $3$ | $375.616$ | 3.3.3576.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.kr | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.ks | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.kt | $3$ | $375.616$ | 3.3.3132.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ku | $3$ | $375.616$ | 3.3.148.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.kv | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.kw | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(-3\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.kx | $3$ | $375.616$ | 3.3.1524.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.ky | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.kz | $3$ | $375.616$ | 3.3.3576.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.la | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.lb | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.lc | $3$ | $375.616$ | 3.3.3132.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.ld | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.le | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.lf | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.lg | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.lh | $3$ | $375.616$ | 3.3.148.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.li | $3$ | $375.616$ | 3.3.3132.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.lj | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.lk | $3$ | $375.616$ | 3.3.229.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.ll | $3$ | $375.616$ | 3.3.3576.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.lm | $3$ | $375.616$ | 3.3.404.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.ln | $3$ | $375.616$ | 3.3.1524.1 | None | \(0\) | \(3\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.lo | $4$ | $375.616$ | 4.4.22592.1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.lp | $4$ | $375.616$ | 4.4.29268.1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.lq | $4$ | $375.616$ | \(\Q(\zeta_{16})^+\) | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.lr | $4$ | $375.616$ | 4.4.20308.1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.ls | $4$ | $375.616$ | 4.4.10304.1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.lt | $4$ | $375.616$ | 4.4.4352.1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.lu | $4$ | $375.616$ | 4.4.4352.1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.lv | $4$ | $375.616$ | 4.4.10304.1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.lw | $4$ | $375.616$ | 4.4.20308.1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.lx | $4$ | $375.616$ | \(\Q(\zeta_{16})^+\) | None | \(0\) | \(-4\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ly | $4$ | $375.616$ | 4.4.29268.1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.lz | $4$ | $375.616$ | 4.4.22592.1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ma | $4$ | $375.616$ | 4.4.4352.1 | None | \(0\) | \(4\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.mb | $4$ | $375.616$ | 4.4.10304.1 | None | \(0\) | \(4\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.mc | $4$ | $375.616$ | 4.4.20308.1 | None | \(0\) | \(4\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.md | $4$ | $375.616$ | \(\Q(\zeta_{16})^+\) | None | \(0\) | \(4\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.me | $4$ | $375.616$ | 4.4.29268.1 | None | \(0\) | \(4\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.mf | $4$ | $375.616$ | 4.4.22592.1 | None | \(0\) | \(4\) | \(-4\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.mg | $4$ | $375.616$ | 4.4.22592.1 | None | \(0\) | \(4\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.mh | $4$ | $375.616$ | 4.4.29268.1 | None | \(0\) | \(4\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.mi | $4$ | $375.616$ | \(\Q(\zeta_{16})^+\) | None | \(0\) | \(4\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.mj | $4$ | $375.616$ | 4.4.20308.1 | None | \(0\) | \(4\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.mk | $4$ | $375.616$ | 4.4.10304.1 | None | \(0\) | \(4\) | \(4\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.ml | $4$ | $375.616$ | 4.4.4352.1 | None | \(0\) | \(4\) | \(4\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.mm | $5$ | $375.616$ | 5.5.3561732.1 | None | \(0\) | \(-5\) | \(-5\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.mn | $5$ | $375.616$ | 5.5.22775940.1 | None | \(0\) | \(-5\) | \(-5\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 47040.2.a.mo | $5$ | $375.616$ | 5.5.22775940.1 | None | \(0\) | \(-5\) | \(5\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.mp | $5$ | $375.616$ | 5.5.3561732.1 | None | \(0\) | \(-5\) | \(5\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 47040.2.a.mq | $5$ | $375.616$ | 5.5.22775940.1 | None | \(0\) | \(5\) | \(-5\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 47040.2.a.mr | $5$ | $375.616$ | 5.5.3561732.1 | None | \(0\) | \(5\) | \(-5\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.ms | $5$ | $375.616$ | 5.5.3561732.1 | None | \(0\) | \(5\) | \(5\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 47040.2.a.mt | $5$ | $375.616$ | 5.5.22775940.1 | None | \(0\) | \(5\) | \(5\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.mu | $6$ | $375.616$ | 6.6.59148288.1 | None | \(0\) | \(-6\) | \(-6\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.mv | $6$ | $375.616$ | 6.6.41781248.1 | None | \(0\) | \(-6\) | \(-6\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.mw | $6$ | $375.616$ | 6.6.41781248.1 | None | \(0\) | \(-6\) | \(6\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.mx | $6$ | $375.616$ | 6.6.59148288.1 | None | \(0\) | \(-6\) | \(6\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.my | $6$ | $375.616$ | 6.6.41781248.1 | None | \(0\) | \(6\) | \(-6\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.mz | $6$ | $375.616$ | 6.6.59148288.1 | None | \(0\) | \(6\) | \(-6\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.na | $6$ | $375.616$ | 6.6.59148288.1 | None | \(0\) | \(6\) | \(6\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.nb | $6$ | $375.616$ | 6.6.41781248.1 | None | \(0\) | \(6\) | \(6\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 47040.2.a.nc | $8$ | $375.616$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-8\) | \(-8\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 47040.2.a.nd | $8$ | $375.616$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-8\) | \(8\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 47040.2.a.ne | $8$ | $375.616$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(8\) | \(-8\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 47040.2.a.nf | $8$ | $375.616$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(8\) | \(8\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(47040))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(47040)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3920))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(7840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(9408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11760))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23520))\)\(^{\oplus 2}\)