Defining parameters
Level: | \( N \) | \(=\) | \( 10944 = 2^{6} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10944.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 112 \) | ||
Sturm bound: | \(3840\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(10944))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1968 | 180 | 1788 |
Cusp forms | 1873 | 180 | 1693 |
Eisenstein series | 95 | 0 | 95 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(16\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(22\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(28\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(25\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(20\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(14\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(26\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(29\) |
Plus space | \(+\) | \(81\) | ||
Minus space | \(-\) | \(99\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(10944))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 19 | |||||||
10944.2.a.a | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-4\) | \(-3\) | $-$ | $-$ | $+$ | \(q-4q^{5}-3q^{7}-2q^{11}+q^{13}-3q^{17}+\cdots\) | |
10944.2.a.b | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $-$ | $+$ | $+$ | \(q-4q^{5}-6q^{11}-2q^{13}+4q^{17}-q^{19}+\cdots\) | |
10944.2.a.c | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | $+$ | $+$ | $-$ | \(q-4q^{5}+6q^{11}-2q^{13}+4q^{17}+q^{19}+\cdots\) | |
10944.2.a.d | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-4\) | \(3\) | $+$ | $-$ | $-$ | \(q-4q^{5}+3q^{7}+2q^{11}+q^{13}-3q^{17}+\cdots\) | |
10944.2.a.e | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(-5\) | $+$ | $-$ | $-$ | \(q-3q^{5}-5q^{7}+q^{11}-2q^{13}+q^{17}+\cdots\) | |
10944.2.a.f | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(-3\) | $+$ | $-$ | $+$ | \(q-3q^{5}-3q^{7}-q^{11}+2q^{13}+5q^{17}+\cdots\) | |
10944.2.a.g | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(-1\) | $-$ | $-$ | $-$ | \(q-3q^{5}-q^{7}+5q^{11}+6q^{13}+5q^{17}+\cdots\) | |
10944.2.a.h | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(1\) | $+$ | $-$ | $+$ | \(q-3q^{5}+q^{7}-5q^{11}+6q^{13}+5q^{17}+\cdots\) | |
10944.2.a.i | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(3\) | $-$ | $-$ | $-$ | \(q-3q^{5}+3q^{7}+q^{11}+2q^{13}+5q^{17}+\cdots\) | |
10944.2.a.j | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(5\) | $-$ | $-$ | $+$ | \(q-3q^{5}+5q^{7}-q^{11}-2q^{13}+q^{17}+\cdots\) | |
10944.2.a.k | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(-4\) | $+$ | $+$ | $+$ | \(q-2q^{5}-4q^{7}-6q^{11}+4q^{13}-q^{19}+\cdots\) | |
10944.2.a.l | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(-4\) | $+$ | $-$ | $-$ | \(q-2q^{5}-4q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\) | |
10944.2.a.m | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $+$ | $-$ | \(q-2q^{5}-2q^{11}+4q^{13}+q^{19}+8q^{23}+\cdots\) | |
10944.2.a.n | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $-$ | $+$ | \(q-2q^{5}-6q^{13}+6q^{17}-q^{19}+4q^{23}+\cdots\) | |
10944.2.a.o | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $+$ | $-$ | $-$ | \(q-2q^{5}-6q^{13}+6q^{17}+q^{19}-4q^{23}+\cdots\) | |
10944.2.a.p | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | \(q-2q^{5}+2q^{11}+4q^{13}-q^{19}-8q^{23}+\cdots\) | |
10944.2.a.q | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(4\) | $+$ | $-$ | $+$ | \(q-2q^{5}+4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\) | |
10944.2.a.r | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-2\) | \(4\) | $+$ | $+$ | $-$ | \(q-2q^{5}+4q^{7}+6q^{11}+4q^{13}+q^{19}+\cdots\) | |
10944.2.a.s | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-3\) | $+$ | $-$ | $-$ | \(q-q^{5}-3q^{7}-3q^{11}+4q^{13}-5q^{17}+\cdots\) | |
10944.2.a.t | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-3\) | $+$ | $-$ | $-$ | \(q-q^{5}-3q^{7}+5q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.u | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-1\) | $+$ | $-$ | $+$ | \(q-q^{5}-q^{7}-5q^{11}-4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.v | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-1\) | $-$ | $-$ | $+$ | \(q-q^{5}-q^{7}+3q^{11}+7q^{17}-q^{19}+\cdots\) | |
10944.2.a.w | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-1\) | $+$ | $-$ | $+$ | \(q-q^{5}-q^{7}+3q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.x | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(1\) | $-$ | $-$ | $-$ | \(q-q^{5}+q^{7}-3q^{11}+7q^{17}+q^{19}+\cdots\) | |
10944.2.a.y | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(1\) | $+$ | $-$ | $-$ | \(q-q^{5}+q^{7}-3q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.z | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(1\) | $+$ | $-$ | $-$ | \(q-q^{5}+q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.ba | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(3\) | $-$ | $-$ | $+$ | \(q-q^{5}+3q^{7}-5q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.bb | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(3\) | $-$ | $-$ | $+$ | \(q-q^{5}+3q^{7}+3q^{11}+4q^{13}-5q^{17}+\cdots\) | |
10944.2.a.bc | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | $-$ | $-$ | $-$ | \(q-4q^{7}-4q^{11}+2q^{17}+q^{19}-2q^{23}+\cdots\) | |
10944.2.a.bd | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | $+$ | $-$ | $+$ | \(q-4q^{7}+4q^{13}-6q^{17}-q^{19}+6q^{23}+\cdots\) | |
10944.2.a.be | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-3\) | $-$ | $-$ | $-$ | \(q-3q^{7}-2q^{11}-q^{13}+5q^{17}+q^{19}+\cdots\) | |
10944.2.a.bf | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-1\) | $+$ | $-$ | $+$ | \(q-q^{7}-6q^{11}-5q^{13}-3q^{17}-q^{19}+\cdots\) | |
10944.2.a.bg | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-1\) | $-$ | $-$ | $-$ | \(q-q^{7}+2q^{11}+q^{13}-3q^{17}+q^{19}+\cdots\) | |
10944.2.a.bh | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | $-$ | \(q-2q^{11}+2q^{13}-4q^{17}+q^{19}+2q^{23}+\cdots\) | |
10944.2.a.bi | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $+$ | $+$ | \(q-2q^{11}+2q^{13}+4q^{17}-q^{19}+2q^{23}+\cdots\) | |
10944.2.a.bj | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $-$ | $+$ | \(q+2q^{17}-q^{19}-6q^{23}-5q^{25}+10q^{29}+\cdots\) | |
10944.2.a.bk | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $-$ | $-$ | \(q+2q^{17}+q^{19}+6q^{23}-5q^{25}+10q^{29}+\cdots\) | |
10944.2.a.bl | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $+$ | $+$ | \(q+2q^{11}+2q^{13}-4q^{17}-q^{19}-2q^{23}+\cdots\) | |
10944.2.a.bm | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | $-$ | \(q+2q^{11}+2q^{13}+4q^{17}+q^{19}-2q^{23}+\cdots\) | |
10944.2.a.bn | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(1\) | $-$ | $-$ | $+$ | \(q+q^{7}-2q^{11}+q^{13}-3q^{17}-q^{19}+\cdots\) | |
10944.2.a.bo | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(1\) | $-$ | $-$ | $-$ | \(q+q^{7}+6q^{11}-5q^{13}-3q^{17}+q^{19}+\cdots\) | |
10944.2.a.bp | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(3\) | $+$ | $-$ | $+$ | \(q+3q^{7}+2q^{11}-q^{13}+5q^{17}-q^{19}+\cdots\) | |
10944.2.a.bq | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(4\) | $-$ | $-$ | $-$ | \(q+4q^{7}+4q^{13}-6q^{17}+q^{19}-6q^{23}+\cdots\) | |
10944.2.a.br | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(4\) | $+$ | $-$ | $+$ | \(q+4q^{7}+4q^{11}+2q^{17}-q^{19}+2q^{23}+\cdots\) | |
10944.2.a.bs | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-3\) | $+$ | $-$ | $+$ | \(q+q^{5}-3q^{7}-5q^{11}+2q^{13}+q^{17}+\cdots\) | |
10944.2.a.bt | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-3\) | $-$ | $-$ | $+$ | \(q+q^{5}-3q^{7}+3q^{11}+6q^{13}-3q^{17}+\cdots\) | |
10944.2.a.bu | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(3\) | $+$ | $-$ | $-$ | \(q+q^{5}+3q^{7}-3q^{11}+6q^{13}-3q^{17}+\cdots\) | |
10944.2.a.bv | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(3\) | $-$ | $-$ | $-$ | \(q+q^{5}+3q^{7}+5q^{11}+2q^{13}+q^{17}+\cdots\) | |
10944.2.a.bw | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(-4\) | $-$ | $-$ | $-$ | \(q+2q^{5}-4q^{7}+6q^{11}+2q^{13}-6q^{17}+\cdots\) | |
10944.2.a.bx | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(-4\) | $+$ | $+$ | $+$ | \(q+2q^{5}-4q^{7}+6q^{11}+4q^{13}-q^{19}+\cdots\) | |
10944.2.a.by | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | \(q+2q^{5}-4q^{11}-2q^{13}+6q^{17}+q^{19}+\cdots\) | |
10944.2.a.bz | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $+$ | \(q+2q^{5}-2q^{11}-2q^{13}-6q^{17}-q^{19}+\cdots\) | |
10944.2.a.ca | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $+$ | \(q+2q^{5}-2q^{11}+4q^{13}-q^{19}+8q^{23}+\cdots\) | |
10944.2.a.cb | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $+$ | \(q+2q^{5}-2q^{13}-2q^{17}-q^{19}-q^{25}+\cdots\) | |
10944.2.a.cc | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | \(q+2q^{5}-2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots\) | |
10944.2.a.cd | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $-$ | $-$ | \(q+2q^{5}+2q^{11}-2q^{13}-6q^{17}+q^{19}+\cdots\) | |
10944.2.a.ce | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | \(q+2q^{5}+2q^{11}+4q^{13}+q^{19}-8q^{23}+\cdots\) | |
10944.2.a.cf | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $-$ | $+$ | \(q+2q^{5}+4q^{11}-2q^{13}+6q^{17}-q^{19}+\cdots\) | |
10944.2.a.cg | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(4\) | $-$ | $-$ | $+$ | \(q+2q^{5}+4q^{7}-6q^{11}+2q^{13}-6q^{17}+\cdots\) | |
10944.2.a.ch | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(2\) | \(4\) | $+$ | $+$ | $-$ | \(q+2q^{5}+4q^{7}-6q^{11}+4q^{13}+q^{19}+\cdots\) | |
10944.2.a.ci | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(-5\) | $-$ | $-$ | $+$ | \(q+3q^{5}-5q^{7}-5q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.cj | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(-3\) | $+$ | $-$ | $-$ | \(q+3q^{5}-3q^{7}-3q^{11}-q^{17}+q^{19}+\cdots\) | |
10944.2.a.ck | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(-1\) | $+$ | $-$ | $+$ | \(q+3q^{5}-q^{7}+3q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.cl | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(1\) | $-$ | $-$ | $-$ | \(q+3q^{5}+q^{7}-3q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.cm | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(3\) | $+$ | $-$ | $+$ | \(q+3q^{5}+3q^{7}+3q^{11}-q^{17}-q^{19}+\cdots\) | |
10944.2.a.cn | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(3\) | \(5\) | $-$ | $-$ | $-$ | \(q+3q^{5}+5q^{7}+5q^{11}+4q^{13}+3q^{17}+\cdots\) | |
10944.2.a.co | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(-4\) | $-$ | $-$ | $-$ | \(q+4q^{5}-4q^{7}+4q^{11}+4q^{13}-6q^{17}+\cdots\) | |
10944.2.a.cp | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $+$ | $+$ | $-$ | \(q+4q^{5}-6q^{11}-2q^{13}-4q^{17}+q^{19}+\cdots\) | |
10944.2.a.cq | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(0\) | $-$ | $+$ | $+$ | \(q+4q^{5}+6q^{11}-2q^{13}-4q^{17}-q^{19}+\cdots\) | |
10944.2.a.cr | $1$ | $87.388$ | \(\Q\) | None | \(0\) | \(0\) | \(4\) | \(4\) | $+$ | $-$ | $+$ | \(q+4q^{5}+4q^{7}-4q^{11}+4q^{13}-6q^{17}+\cdots\) | |
10944.2.a.cs | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-3\) | \(-1\) | $-$ | $-$ | $+$ | ||
10944.2.a.ct | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-3\) | \(-1\) | $+$ | $-$ | $+$ | ||
10944.2.a.cu | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-3\) | \(1\) | $+$ | $-$ | $-$ | ||
10944.2.a.cv | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-3\) | \(1\) | $-$ | $-$ | $-$ | ||
10944.2.a.cw | $2$ | $87.388$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $+$ | ||
10944.2.a.cx | $2$ | $87.388$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | $-$ | $+$ | $-$ | ||
10944.2.a.cy | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-1\) | \(-6\) | $-$ | $-$ | $-$ | ||
10944.2.a.cz | $2$ | $87.388$ | \(\Q(\sqrt{41}) \) | None | \(0\) | \(0\) | \(-1\) | \(-3\) | $+$ | $-$ | $+$ | ||
10944.2.a.da | $2$ | $87.388$ | \(\Q(\sqrt{33}) \) | None | \(0\) | \(0\) | \(-1\) | \(-1\) | $+$ | $-$ | $+$ | ||
10944.2.a.db | $2$ | $87.388$ | \(\Q(\sqrt{33}) \) | None | \(0\) | \(0\) | \(-1\) | \(1\) | $+$ | $-$ | $-$ | ||
10944.2.a.dc | $2$ | $87.388$ | \(\Q(\sqrt{41}) \) | None | \(0\) | \(0\) | \(-1\) | \(3\) | $-$ | $-$ | $-$ | ||
10944.2.a.dd | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(-1\) | \(6\) | $-$ | $-$ | $+$ | ||
10944.2.a.de | $2$ | $87.388$ | \(\Q(\sqrt{7}) \) | not computed | \(0\) | \(0\) | \(0\) | \(-6\) | $-$ | $+$ | $+$ | ||
10944.2.a.df | $2$ | $87.388$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | $-$ | $+$ | $-$ | ||
10944.2.a.dg | $2$ | $87.388$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | $-$ | $+$ | $-$ | ||
10944.2.a.dh | $2$ | $87.388$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | $-$ | $+$ | $+$ | ||
10944.2.a.di | $2$ | $87.388$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | $-$ | $+$ | $+$ | ||
10944.2.a.dj | $2$ | $87.388$ | \(\Q(\sqrt{7}) \) | not computed | \(0\) | \(0\) | \(0\) | \(6\) | $+$ | $+$ | $-$ | ||
10944.2.a.dk | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(1\) | \(-1\) | $-$ | $-$ | $-$ | ||
10944.2.a.dl | $2$ | $87.388$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(0\) | \(1\) | \(1\) | $+$ | $-$ | $+$ | ||
10944.2.a.dm | $2$ | $87.388$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $+$ | ||
10944.2.a.dn | $2$ | $87.388$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | $-$ | $+$ | $-$ | ||
10944.2.a.do | $2$ | $87.388$ | \(\Q(\sqrt{33}) \) | None | \(0\) | \(0\) | \(3\) | \(-1\) | $-$ | $-$ | $-$ | ||
10944.2.a.dp | $2$ | $87.388$ | \(\Q(\sqrt{33}) \) | None | \(0\) | \(0\) | \(3\) | \(1\) | $+$ | $-$ | $+$ | ||
10944.2.a.dq | $3$ | $87.388$ | 3.3.469.1 | None | \(0\) | \(0\) | \(-3\) | \(-5\) | $-$ | $-$ | $+$ | ||
10944.2.a.dr | $3$ | $87.388$ | 3.3.469.1 | None | \(0\) | \(0\) | \(-3\) | \(5\) | $-$ | $-$ | $-$ | ||
10944.2.a.ds | $3$ | $87.388$ | 3.3.892.1 | None | \(0\) | \(0\) | \(-2\) | \(-2\) | $+$ | $+$ | $-$ | ||
10944.2.a.dt | $3$ | $87.388$ | 3.3.892.1 | None | \(0\) | \(0\) | \(-2\) | \(2\) | $-$ | $+$ | $+$ | ||
10944.2.a.du | $3$ | $87.388$ | 3.3.961.1 | None | \(0\) | \(0\) | \(1\) | \(-4\) | $-$ | $-$ | $+$ | ||
10944.2.a.dv | $3$ | $87.388$ | 3.3.961.1 | None | \(0\) | \(0\) | \(1\) | \(4\) | $+$ | $-$ | $-$ | ||
10944.2.a.dw | $3$ | $87.388$ | 3.3.892.1 | None | \(0\) | \(0\) | \(2\) | \(-2\) | $+$ | $+$ | $-$ | ||
10944.2.a.dx | $3$ | $87.388$ | 3.3.892.1 | None | \(0\) | \(0\) | \(2\) | \(2\) | $-$ | $+$ | $+$ | ||
10944.2.a.dy | $3$ | $87.388$ | 3.3.229.1 | None | \(0\) | \(0\) | \(5\) | \(-1\) | $-$ | $-$ | $+$ | ||
10944.2.a.dz | $3$ | $87.388$ | 3.3.229.1 | None | \(0\) | \(0\) | \(5\) | \(1\) | $-$ | $-$ | $-$ | ||
10944.2.a.ea | $4$ | $87.388$ | 4.4.19664.1 | None | \(0\) | \(0\) | \(-4\) | \(-2\) | $+$ | $+$ | $-$ | ||
10944.2.a.eb | $4$ | $87.388$ | 4.4.19664.1 | None | \(0\) | \(0\) | \(-4\) | \(2\) | $+$ | $+$ | $+$ | ||
10944.2.a.ec | $4$ | $87.388$ | 4.4.13068.1 | not computed | \(0\) | \(0\) | \(0\) | \(-2\) | $-$ | $+$ | $-$ | ||
10944.2.a.ed | $4$ | $87.388$ | 4.4.13068.1 | not computed | \(0\) | \(0\) | \(0\) | \(2\) | $+$ | $+$ | $+$ | ||
10944.2.a.ee | $4$ | $87.388$ | 4.4.15317.1 | None | \(0\) | \(0\) | \(1\) | \(-1\) | $+$ | $-$ | $+$ | ||
10944.2.a.ef | $4$ | $87.388$ | 4.4.15317.1 | None | \(0\) | \(0\) | \(1\) | \(1\) | $+$ | $-$ | $-$ | ||
10944.2.a.eg | $4$ | $87.388$ | 4.4.19664.1 | None | \(0\) | \(0\) | \(4\) | \(-2\) | $+$ | $+$ | $-$ | ||
10944.2.a.eh | $4$ | $87.388$ | 4.4.19664.1 | None | \(0\) | \(0\) | \(4\) | \(2\) | $+$ | $+$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(10944))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(10944)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5472))\)\(^{\oplus 2}\)