Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(741))\).
|
Total |
New |
Old |
| Modular forms
| 938 |
440 |
498 |
| Cusp forms
| 74 |
64 |
10 |
| Eisenstein series
| 864 |
376 |
488 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(741))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 741.1.c |
\(\chi_{741}(248, \cdot)\) |
None |
0 |
1 |
| 741.1.e |
\(\chi_{741}(664, \cdot)\) |
None |
0 |
1 |
| 741.1.f |
\(\chi_{741}(493, \cdot)\) |
None |
0 |
1 |
| 741.1.h |
\(\chi_{741}(77, \cdot)\) |
None |
0 |
1 |
| 741.1.n |
\(\chi_{741}(229, \cdot)\) |
None |
0 |
2 |
| 741.1.p |
\(\chi_{741}(398, \cdot)\) |
741.1.p.a |
2 |
2 |
| 741.1.p.b |
2 |
| 741.1.q |
\(\chi_{741}(373, \cdot)\) |
None |
0 |
2 |
| 741.1.s |
\(\chi_{741}(68, \cdot)\) |
None |
0 |
2 |
| 741.1.v |
\(\chi_{741}(322, \cdot)\) |
None |
0 |
2 |
| 741.1.w |
\(\chi_{741}(311, \cdot)\) |
741.1.w.a |
2 |
2 |
| 741.1.w.b |
2 |
| 741.1.x |
\(\chi_{741}(140, \cdot)\) |
None |
0 |
2 |
| 741.1.y |
\(\chi_{741}(103, \cdot)\) |
None |
0 |
2 |
| 741.1.ba |
\(\chi_{741}(88, \cdot)\) |
None |
0 |
2 |
| 741.1.bc |
\(\chi_{741}(134, \cdot)\) |
None |
0 |
2 |
| 741.1.bd |
\(\chi_{741}(191, \cdot)\) |
None |
0 |
2 |
| 741.1.bg |
\(\chi_{741}(217, \cdot)\) |
None |
0 |
2 |
| 741.1.bi |
\(\chi_{741}(274, \cdot)\) |
None |
0 |
2 |
| 741.1.bk |
\(\chi_{741}(581, \cdot)\) |
None |
0 |
2 |
| 741.1.bm |
\(\chi_{741}(482, \cdot)\) |
None |
0 |
2 |
| 741.1.bn |
\(\chi_{741}(94, \cdot)\) |
None |
0 |
2 |
| 741.1.bp |
\(\chi_{741}(296, \cdot)\) |
None |
0 |
2 |
| 741.1.br |
\(\chi_{741}(316, \cdot)\) |
None |
0 |
2 |
| 741.1.bv |
\(\chi_{741}(236, \cdot)\) |
None |
0 |
4 |
| 741.1.bx |
\(\chi_{741}(7, \cdot)\) |
None |
0 |
4 |
| 741.1.bz |
\(\chi_{741}(163, \cdot)\) |
None |
0 |
4 |
| 741.1.cc |
\(\chi_{741}(8, \cdot)\) |
741.1.cc.a |
4 |
4 |
| 741.1.cc.b |
4 |
| 741.1.ce |
\(\chi_{741}(227, \cdot)\) |
None |
0 |
4 |
| 741.1.cg |
\(\chi_{741}(463, \cdot)\) |
None |
0 |
4 |
| 741.1.ci |
\(\chi_{741}(58, \cdot)\) |
None |
0 |
4 |
| 741.1.cj |
\(\chi_{741}(50, \cdot)\) |
None |
0 |
4 |
| 741.1.cl |
\(\chi_{741}(166, \cdot)\) |
None |
0 |
6 |
| 741.1.cm |
\(\chi_{741}(62, \cdot)\) |
741.1.cm.a |
6 |
6 |
| 741.1.cr |
\(\chi_{741}(22, \cdot)\) |
None |
0 |
6 |
| 741.1.cs |
\(\chi_{741}(40, \cdot)\) |
None |
0 |
6 |
| 741.1.ct |
\(\chi_{741}(92, \cdot)\) |
None |
0 |
6 |
| 741.1.cu |
\(\chi_{741}(35, \cdot)\) |
741.1.cu.a |
6 |
6 |
| 741.1.cv |
\(\chi_{741}(17, \cdot)\) |
741.1.cv.a |
6 |
6 |
| 741.1.cw |
\(\chi_{741}(194, \cdot)\) |
None |
0 |
6 |
| 741.1.cx |
\(\chi_{741}(181, \cdot)\) |
None |
0 |
6 |
| 741.1.cy |
\(\chi_{741}(10, \cdot)\) |
None |
0 |
6 |
| 741.1.de |
\(\chi_{741}(263, \cdot)\) |
741.1.de.a |
6 |
6 |
| 741.1.df |
\(\chi_{741}(211, \cdot)\) |
None |
0 |
6 |
| 741.1.di |
\(\chi_{741}(2, \cdot)\) |
741.1.di.a |
12 |
12 |
| 741.1.dj |
\(\chi_{741}(85, \cdot)\) |
None |
0 |
12 |
| 741.1.dk |
\(\chi_{741}(73, \cdot)\) |
None |
0 |
12 |
| 741.1.dl |
\(\chi_{741}(86, \cdot)\) |
None |
0 |
12 |
| 741.1.do |
\(\chi_{741}(28, \cdot)\) |
None |
0 |
12 |
| 741.1.dp |
\(\chi_{741}(59, \cdot)\) |
741.1.dp.a |
12 |
12 |
