Defining parameters
| Level: | \( N \) | \(=\) | \( 35280 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 35280.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 251 \) | ||
| Sturm bound: | \(16128\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(35280))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8256 | 410 | 7846 |
| Cusp forms | 7873 | 410 | 7463 |
| 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 | ||||||||
| \(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(504\) | \(20\) | \(484\) | \(481\) | \(20\) | \(461\) | \(23\) | \(0\) | \(23\) | |||
| \(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(524\) | \(21\) | \(503\) | \(500\) | \(21\) | \(479\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(520\) | \(20\) | \(500\) | \(496\) | \(20\) | \(476\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(516\) | \(21\) | \(495\) | \(492\) | \(21\) | \(471\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(520\) | \(31\) | \(489\) | \(496\) | \(31\) | \(465\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(512\) | \(30\) | \(482\) | \(488\) | \(30\) | \(458\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(520\) | \(29\) | \(491\) | \(496\) | \(29\) | \(467\) | \(24\) | \(0\) | \(24\) | |||
| \(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(512\) | \(33\) | \(479\) | \(488\) | \(33\) | \(455\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(528\) | \(20\) | \(508\) | \(504\) | \(20\) | \(484\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(508\) | \(21\) | \(487\) | \(484\) | \(21\) | \(463\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(512\) | \(20\) | \(492\) | \(488\) | \(20\) | \(468\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(516\) | \(21\) | \(495\) | \(492\) | \(21\) | \(471\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(512\) | \(29\) | \(483\) | \(488\) | \(29\) | \(459\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(520\) | \(33\) | \(487\) | \(496\) | \(33\) | \(463\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(512\) | \(31\) | \(481\) | \(488\) | \(31\) | \(457\) | \(24\) | \(0\) | \(24\) | |||
| \(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(520\) | \(30\) | \(490\) | \(496\) | \(30\) | \(466\) | \(24\) | \(0\) | \(24\) | |||
| Plus space | \(+\) | \(4104\) | \(200\) | \(3904\) | \(3913\) | \(200\) | \(3713\) | \(191\) | \(0\) | \(191\) | ||||||
| Minus space | \(-\) | \(4152\) | \(210\) | \(3942\) | \(3960\) | \(210\) | \(3750\) | \(192\) | \(0\) | \(192\) | ||||||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(35280))\) 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 | |||||||
| 35280.2.a.a | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q-q^{5}-6q^{11}-3q^{13}+4q^{17}-q^{19}+\cdots\) | |
| 35280.2.a.b | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}-6q^{11}-2q^{13}+2q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.c | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-6q^{11}+6q^{17}+4q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.d | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-6q^{11}+2q^{13}+4q^{17}+8q^{19}+\cdots\) | |
| 35280.2.a.e | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-6q^{11}+4q^{13}+2q^{19}-3q^{23}+\cdots\) | |
| 35280.2.a.f | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}-6q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\) | |
| 35280.2.a.g | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-5q^{11}-7q^{13}-3q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.h | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q-q^{5}-5q^{11}-5q^{13}+4q^{17}+7q^{19}+\cdots\) | |
| 35280.2.a.i | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-5q^{11}-q^{13}+3q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.j | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-5q^{11}+3q^{13}-q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.k | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-4q^{11}-7q^{13}-6q^{17}+3q^{19}+\cdots\) | |
| 35280.2.a.l | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}-4q^{11}-6q^{13}+4q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.m | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}-4q^{11}-4q^{13}-2q^{17}-4q^{23}+\cdots\) | |
| 35280.2.a.n | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{23}+\cdots\) | |
| 35280.2.a.o | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-4q^{11}+2q^{13}-8q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.p | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-4q^{11}+2q^{13}-6q^{17}-8q^{23}+\cdots\) | |
| 35280.2.a.q | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-4q^{11}+6q^{13}-2q^{17}-8q^{19}+\cdots\) | |
| 35280.2.a.r | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-3q^{11}-5q^{13}+3q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.s | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{11}-4q^{13}+6q^{19}+3q^{23}+\cdots\) | |
| 35280.2.a.t | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{11}-2q^{13}-2q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.u | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{11}-q^{13}+3q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.v | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{11}-4q^{17}-6q^{19}+3q^{23}+\cdots\) | |
| 35280.2.a.w | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q-q^{5}-2q^{11}+q^{13}+4q^{17}+q^{19}+\cdots\) | |
| 35280.2.a.x | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.y | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.z | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+2q^{13}+6q^{17}+6q^{23}+\cdots\) | |
| 35280.2.a.ba | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+6q^{13}-4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.bb | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+6q^{13}+2q^{17}-9q^{23}+\cdots\) | |
| 35280.2.a.bc | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{11}+6q^{13}+6q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.bd | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q-q^{5}-q^{11}-5q^{13}+4q^{17}-5q^{19}+\cdots\) | |
| 35280.2.a.be | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-q^{11}-q^{13}-3q^{19}+7q^{23}+\cdots\) | |
| 35280.2.a.bf | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-q^{11}+3q^{13}-2q^{17}-5q^{19}+\cdots\) | |
| 35280.2.a.bg | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-q^{11}+5q^{13}+q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.bh | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q-q^{5}-q^{11}+7q^{13}+4q^{17}-q^{19}+\cdots\) | |
| 35280.2.a.bi | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-6q^{13}-2q^{17}+4q^{19}+4q^{23}+\cdots\) | |
| 35280.2.a.bj | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}-6q^{17}-4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.bk | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.bl | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}-2q^{13}+2q^{19}+q^{25}-6q^{29}+\cdots\) | |
| 35280.2.a.bm | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}+2q^{17}-6q^{19}-6q^{23}+\cdots\) | |
| 35280.2.a.bn | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}+2q^{17}-2q^{19}-2q^{23}+\cdots\) | |
| 35280.2.a.bo | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}+2q^{17}+4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.bp | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{13}+6q^{17}-4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.bq | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q-q^{5}-q^{13}-2q^{17}-3q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.br | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+q^{13}+6q^{17}+5q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.bs | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{13}+6q^{17}-4q^{19}+4q^{23}+\cdots\) | |
| 35280.2.a.bt | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+4q^{13}-6q^{17}+2q^{19}-6q^{23}+\cdots\) | |
| 35280.2.a.bu | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+6q^{13}-2q^{17}+4q^{19}-8q^{23}+\cdots\) | |
| 35280.2.a.bv | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+q^{11}-3q^{13}-3q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.bw | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-6q^{13}+6q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.bx | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-5q^{13}+4q^{17}+3q^{19}+\cdots\) | |
| 35280.2.a.by | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-4q^{13}-2q^{17}+2q^{23}+\cdots\) | |
| 35280.2.a.bz | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-4q^{13}-2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.ca | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-4q^{13}+6q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.cb | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.cc | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.cd | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{11}+4q^{17}-2q^{19}+q^{23}+\cdots\) | |
| 35280.2.a.ce | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}+2q^{13}-2q^{17}-8q^{19}+\cdots\) | |
| 35280.2.a.cf | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}+2q^{13}-2q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.cg | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+2q^{11}+2q^{13}+4q^{17}+8q^{23}+\cdots\) | |
| 35280.2.a.ch | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+2q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.ci | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+3q^{11}-5q^{13}+5q^{19}-9q^{23}+\cdots\) | |
| 35280.2.a.cj | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+3q^{11}-5q^{13}+6q^{17}-q^{19}+\cdots\) | |
| 35280.2.a.ck | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+3q^{11}-q^{13}-7q^{19}-5q^{23}+\cdots\) | |
| 35280.2.a.cl | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $+$ | \(q-q^{5}+3q^{11}-q^{13}+6q^{17}+q^{19}+\cdots\) | |
| 35280.2.a.cm | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+3q^{11}+q^{13}+5q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.cn | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+4q^{11}-6q^{13}-6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.co | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+4q^{11}-6q^{13}-4q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.cp | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $+$ | \(q-q^{5}+4q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots\) | |
| 35280.2.a.cq | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+2q^{17}-6q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.cr | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.cs | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+2q^{13}-6q^{17}+q^{25}+\cdots\) | |
| 35280.2.a.ct | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $-$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+2q^{13}-2q^{19}-4q^{23}+\cdots\) | |
| 35280.2.a.cu | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+4q^{13}-2q^{17}+4q^{23}+\cdots\) | |
| 35280.2.a.cv | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+4q^{11}+6q^{13}+2q^{17}+q^{25}+\cdots\) | |
| 35280.2.a.cw | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+6q^{11}-2q^{13}-6q^{17}+8q^{19}+\cdots\) | |
| 35280.2.a.cx | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $+$ | $+$ | $+$ | $-$ | \(q-q^{5}+6q^{11}+2q^{13}+2q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.cy | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+6q^{11}+4q^{13}+6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.cz | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | $-$ | $-$ | $+$ | $-$ | \(q-q^{5}+6q^{11}+6q^{13}+4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.da | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-6q^{11}-4q^{13}-2q^{19}-3q^{23}+\cdots\) | |
| 35280.2.a.db | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-6q^{11}-2q^{13}-4q^{17}-8q^{19}+\cdots\) | |
| 35280.2.a.dc | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-6q^{11}-6q^{17}-4q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.dd | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-6q^{11}+2q^{13}-2q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.de | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-6q^{11}+3q^{13}-4q^{17}+q^{19}+\cdots\) | |
| 35280.2.a.df | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-5q^{11}+5q^{13}-7q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.dg | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-5q^{11}+5q^{13}-4q^{17}-7q^{19}+\cdots\) | |
| 35280.2.a.dh | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-5q^{11}+7q^{13}+3q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.di | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots\) | |
| 35280.2.a.dj | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-4q^{11}-6q^{13}+4q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.dk | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-4q^{11}-2q^{13}+8q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.dl | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-4q^{11}-2q^{17}-6q^{19}-6q^{23}+\cdots\) | |
| 35280.2.a.dm | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\) | |
| 35280.2.a.dn | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.do | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.dp | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-4q^{11}+4q^{13}+2q^{17}-4q^{23}+\cdots\) | |
| 35280.2.a.dq | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-4q^{11}+7q^{13}+6q^{17}-3q^{19}+\cdots\) | |
| 35280.2.a.dr | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-6q^{13}-6q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.ds | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-2q^{11}-6q^{13}-2q^{17}-9q^{23}+\cdots\) | |
| 35280.2.a.dt | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-6q^{13}+4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.du | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.dv | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.dw | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.dx | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.dy | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-2q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\) | |
| 35280.2.a.dz | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-2q^{11}+4q^{17}+6q^{19}+3q^{23}+\cdots\) | |
| 35280.2.a.ea | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}-2q^{11}+q^{13}-3q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.eb | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\) | |
| 35280.2.a.ec | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}+2q^{13}+2q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.ed | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}-2q^{11}+4q^{13}-6q^{19}+3q^{23}+\cdots\) | |
| 35280.2.a.ee | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{11}+6q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.ef | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-q^{11}-7q^{13}-4q^{17}+q^{19}+\cdots\) | |
| 35280.2.a.eg | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-q^{11}-5q^{13}-q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.eh | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}-q^{11}-3q^{13}+2q^{17}+5q^{19}+\cdots\) | |
| 35280.2.a.ei | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-q^{11}+q^{13}+3q^{19}+7q^{23}+\cdots\) | |
| 35280.2.a.ej | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-q^{11}+5q^{13}-4q^{17}+5q^{19}+\cdots\) | |
| 35280.2.a.ek | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}-2q^{13}-6q^{17}+8q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.el | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}-2q^{13}+2q^{19}+q^{25}+6q^{29}+\cdots\) | |
| 35280.2.a.em | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}-2q^{13}+2q^{17}+q^{25}-6q^{29}+\cdots\) | |
| 35280.2.a.en | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}-q^{13}-6q^{17}-5q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.eo | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+q^{13}+2q^{17}+3q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.ep | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+2q^{13}-2q^{17}+2q^{19}-2q^{23}+\cdots\) | |
| 35280.2.a.eq | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+2q^{13}-2q^{17}+6q^{19}-6q^{23}+\cdots\) | |
| 35280.2.a.er | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}+4q^{13}+6q^{17}+2q^{19}+6q^{23}+\cdots\) | |
| 35280.2.a.es | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+6q^{13}+2q^{17}-8q^{19}+8q^{23}+\cdots\) | |
| 35280.2.a.et | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+q^{11}+3q^{13}+3q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.eu | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.ev | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+2q^{11}-2q^{13}-4q^{17}+8q^{23}+\cdots\) | |
| 35280.2.a.ew | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}+2q^{11}-2q^{13}+2q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.ex | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}+2q^{11}-4q^{17}+2q^{19}+q^{23}+\cdots\) | |
| 35280.2.a.ey | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}+2q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.ez | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}+2q^{11}+2q^{13}-6q^{17}-6q^{23}+\cdots\) | |
| 35280.2.a.fa | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}+2q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.fb | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+2q^{11}+4q^{13}+2q^{17}+2q^{23}+\cdots\) | |
| 35280.2.a.fc | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}+2q^{11}+5q^{13}-4q^{17}-3q^{19}+\cdots\) | |
| 35280.2.a.fd | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}+2q^{11}+6q^{13}-6q^{17}+6q^{19}+\cdots\) | |
| 35280.2.a.fe | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+3q^{11}-q^{13}-5q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.ff | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+3q^{11}+q^{13}-6q^{17}-q^{19}+\cdots\) | |
| 35280.2.a.fg | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+3q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.fh | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $+$ | \(q+q^{5}+3q^{11}+q^{13}+7q^{19}-5q^{23}+\cdots\) | |
| 35280.2.a.fi | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}+3q^{11}+5q^{13}-6q^{17}+q^{19}+\cdots\) | |
| 35280.2.a.fj | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}+3q^{11}+5q^{13}-5q^{19}-9q^{23}+\cdots\) | |
| 35280.2.a.fk | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}+4q^{11}-6q^{13}-4q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.fl | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}+4q^{11}-4q^{13}+2q^{17}+4q^{23}+\cdots\) | |
| 35280.2.a.fm | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}-2q^{13}+2q^{19}-4q^{23}+\cdots\) | |
| 35280.2.a.fn | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\) | |
| 35280.2.a.fo | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.fp | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\) | |
| 35280.2.a.fq | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.fr | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\) | |
| 35280.2.a.fs | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+5q^{13}+6q^{17}-5q^{19}+\cdots\) | |
| 35280.2.a.ft | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | $-$ | \(q+q^{5}+4q^{11}+6q^{13}+6q^{17}-2q^{19}+\cdots\) | |
| 35280.2.a.fu | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $-$ | \(q+q^{5}+6q^{11}-6q^{13}-4q^{19}+q^{25}+\cdots\) | |
| 35280.2.a.fv | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $+$ | $+$ | $-$ | $-$ | \(q+q^{5}+6q^{11}-2q^{13}-2q^{17}-6q^{19}+\cdots\) | |
| 35280.2.a.fw | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{5}+6q^{11}+2q^{13}+6q^{17}-8q^{19}+\cdots\) | |
| 35280.2.a.fx | $1$ | $281.712$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{5}+6q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\) | |
| 35280.2.a.fy | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.fz | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.ga | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.gb | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.gc | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.gd | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.ge | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gf | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.gg | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gh | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gi | $2$ | $281.712$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.gj | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gk | $2$ | $281.712$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gl | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.gm | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gn | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.go | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gp | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gq | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.gr | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gs | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gt | $2$ | $281.712$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.gu | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gv | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.gw | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.gx | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.gy | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.gz | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.ha | $2$ | $281.712$ | \(\Q(\sqrt{33}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.hb | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hc | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hd | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.he | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hf | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hg | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.hh | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.hi | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.hj | $2$ | $281.712$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hk | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hl | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hm | $2$ | $281.712$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hn | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.ho | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hp | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hq | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hr | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hs | $2$ | $281.712$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.ht | $2$ | $281.712$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.hu | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hv | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.hw | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.hx | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.hy | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.hz | $2$ | $281.712$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.ia | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.ib | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.ic | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.id | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.ie | $2$ | $281.712$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.if | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.ig | $3$ | $281.712$ | 3.3.3132.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $-$ | ||
| 35280.2.a.ih | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.ii | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.ij | $3$ | $281.712$ | 3.3.3576.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.ik | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.il | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.im | $3$ | $281.712$ | 3.3.1944.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.in | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(-3\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.io | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.ip | $3$ | $281.712$ | 3.3.3132.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.iq | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.ir | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.is | $3$ | $281.712$ | 3.3.3576.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.it | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.iu | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.iv | $3$ | $281.712$ | 3.3.1944.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $+$ | $-$ | $-$ | $-$ | ||
| 35280.2.a.iw | $3$ | $281.712$ | 3.3.404.1 | None | \(0\) | \(0\) | \(3\) | \(0\) | $-$ | $+$ | $-$ | $-$ | ||
| 35280.2.a.ix | $4$ | $281.712$ | \(\Q(\sqrt{11 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.iy | $4$ | $281.712$ | \(\Q(\zeta_{24})^+\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.iz | $4$ | $281.712$ | \(\Q(\sqrt{2}, \sqrt{5})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $-$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.ja | $4$ | $281.712$ | \(\Q(\sqrt{17 +4 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.jb | $4$ | $281.712$ | \(\Q(\sqrt{17 +8 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.jc | $4$ | $281.712$ | \(\Q(\sqrt{19 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.jd | $4$ | $281.712$ | \(\Q(\sqrt{10 +4 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $-$ | $-$ | $+$ | $+$ | ||
| 35280.2.a.je | $4$ | $281.712$ | \(\Q(\sqrt{11 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.jf | $4$ | $281.712$ | \(\Q(\sqrt{11 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.jg | $4$ | $281.712$ | \(\Q(\sqrt{2}, \sqrt{5})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.jh | $4$ | $281.712$ | \(\Q(\zeta_{24})^+\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $-$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.ji | $4$ | $281.712$ | \(\Q(\sqrt{17 +4 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.jj | $4$ | $281.712$ | \(\Q(\sqrt{19 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.jk | $4$ | $281.712$ | \(\Q(\sqrt{17 +8 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.jl | $4$ | $281.712$ | \(\Q(\sqrt{11 +2 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.jm | $4$ | $281.712$ | \(\Q(\sqrt{10 +4 \sqrt{2}})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $-$ | $-$ | $-$ | $+$ | ||
| 35280.2.a.jn | $5$ | $281.712$ | 5.5.85384368.1 | None | \(0\) | \(0\) | \(-5\) | \(0\) | $+$ | $+$ | $+$ | $-$ | ||
| 35280.2.a.jo | $5$ | $281.712$ | 5.5.85384368.1 | None | \(0\) | \(0\) | \(-5\) | \(0\) | $+$ | $+$ | $+$ | $+$ | ||
| 35280.2.a.jp | $5$ | $281.712$ | 5.5.85384368.1 | None | \(0\) | \(0\) | \(5\) | \(0\) | $+$ | $+$ | $-$ | $+$ | ||
| 35280.2.a.jq | $5$ | $281.712$ | 5.5.85384368.1 | None | \(0\) | \(0\) | \(5\) | \(0\) | $+$ | $+$ | $-$ | $-$ | ||
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(35280))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(35280)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3920))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8820))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17640))\)\(^{\oplus 2}\)