Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7742))\).
|
Total |
New |
Old |
| Modular forms
| 1843920 |
586630 |
1257290 |
| Cusp forms
| 1825201 |
586630 |
1238571 |
| Eisenstein series
| 18719 |
0 |
18719 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7742))\)
We only show spaces with even 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 |
| 7742.2.a |
\(\chi_{7742}(1, \cdot)\) |
7742.2.a.a |
1 |
1 |
| 7742.2.a.b |
1 |
| 7742.2.a.c |
1 |
| 7742.2.a.d |
1 |
| 7742.2.a.e |
1 |
| 7742.2.a.f |
1 |
| 7742.2.a.g |
1 |
| 7742.2.a.h |
1 |
| 7742.2.a.i |
1 |
| 7742.2.a.j |
1 |
| 7742.2.a.k |
1 |
| 7742.2.a.l |
1 |
| 7742.2.a.m |
1 |
| 7742.2.a.n |
1 |
| 7742.2.a.o |
2 |
| 7742.2.a.p |
2 |
| 7742.2.a.q |
2 |
| 7742.2.a.r |
2 |
| 7742.2.a.s |
2 |
| 7742.2.a.t |
2 |
| 7742.2.a.u |
3 |
| 7742.2.a.v |
3 |
| 7742.2.a.w |
3 |
| 7742.2.a.x |
4 |
| 7742.2.a.y |
4 |
| 7742.2.a.z |
4 |
| 7742.2.a.ba |
4 |
| 7742.2.a.bb |
6 |
| 7742.2.a.bc |
6 |
| 7742.2.a.bd |
6 |
| 7742.2.a.be |
7 |
| 7742.2.a.bf |
7 |
| 7742.2.a.bg |
8 |
| 7742.2.a.bh |
8 |
| 7742.2.a.bi |
8 |
| 7742.2.a.bj |
9 |
| 7742.2.a.bk |
12 |
| 7742.2.a.bl |
12 |
| 7742.2.a.bm |
12 |
| 7742.2.a.bn |
12 |
| 7742.2.a.bo |
12 |
| 7742.2.a.bp |
12 |
| 7742.2.a.bq |
12 |
| 7742.2.a.br |
13 |
| 7742.2.a.bs |
13 |
| 7742.2.a.bt |
16 |
| 7742.2.a.bu |
24 |
| 7742.2.d |
\(\chi_{7742}(7741, \cdot)\) |
n/a |
264 |
1 |
| 7742.2.e |
\(\chi_{7742}(687, \cdot)\) |
n/a |
548 |
2 |
| 7742.2.f |
\(\chi_{7742}(949, \cdot)\) |
n/a |
520 |
2 |
| 7742.2.g |
\(\chi_{7742}(1635, \cdot)\) |
n/a |
532 |
2 |
| 7742.2.h |
\(\chi_{7742}(655, \cdot)\) |
n/a |
532 |
2 |
| 7742.2.k |
\(\chi_{7742}(5213, \cdot)\) |
n/a |
536 |
2 |
| 7742.2.l |
\(\chi_{7742}(293, \cdot)\) |
n/a |
536 |
2 |
| 7742.2.m |
\(\chi_{7742}(5507, \cdot)\) |
n/a |
532 |
2 |
| 7742.2.t |
\(\chi_{7742}(4527, \cdot)\) |
n/a |
532 |
2 |
| 7742.2.u |
\(\chi_{7742}(1107, \cdot)\) |
n/a |
2184 |
6 |
| 7742.2.v |
\(\chi_{7742}(1079, \cdot)\) |
n/a |
3264 |
12 |
| 7742.2.w |
\(\chi_{7742}(1105, \cdot)\) |
n/a |
2256 |
6 |
| 7742.2.z |
\(\chi_{7742}(1003, \cdot)\) |
n/a |
4488 |
12 |
| 7742.2.ba |
\(\chi_{7742}(23, \cdot)\) |
n/a |
4488 |
12 |
| 7742.2.bb |
\(\chi_{7742}(317, \cdot)\) |
n/a |
4368 |
12 |
| 7742.2.bc |
\(\chi_{7742}(813, \cdot)\) |
n/a |
4464 |
12 |
| 7742.2.bd |
\(\chi_{7742}(489, \cdot)\) |
n/a |
3168 |
12 |
| 7742.2.bg |
\(\chi_{7742}(263, \cdot)\) |
n/a |
6384 |
24 |
| 7742.2.bh |
\(\chi_{7742}(177, \cdot)\) |
n/a |
6384 |
24 |
| 7742.2.bi |
\(\chi_{7742}(67, \cdot)\) |
n/a |
6432 |
24 |
| 7742.2.bj |
\(\chi_{7742}(99, \cdot)\) |
n/a |
6576 |
24 |
| 7742.2.bk |
\(\chi_{7742}(103, \cdot)\) |
n/a |
4488 |
12 |
| 7742.2.br |
\(\chi_{7742}(577, \cdot)\) |
n/a |
4488 |
12 |
| 7742.2.bs |
\(\chi_{7742}(419, \cdot)\) |
n/a |
4464 |
12 |
| 7742.2.bt |
\(\chi_{7742}(157, \cdot)\) |
n/a |
4464 |
12 |
| 7742.2.bw |
\(\chi_{7742}(509, \cdot)\) |
n/a |
6384 |
24 |
| 7742.2.cd |
\(\chi_{7742}(423, \cdot)\) |
n/a |
6384 |
24 |
| 7742.2.ce |
\(\chi_{7742}(195, \cdot)\) |
n/a |
6432 |
24 |
| 7742.2.cf |
\(\chi_{7742}(215, \cdot)\) |
n/a |
6432 |
24 |
| 7742.2.ci |
\(\chi_{7742}(141, \cdot)\) |
n/a |
27072 |
72 |
| 7742.2.cl |
\(\chi_{7742}(27, \cdot)\) |
n/a |
27072 |
72 |
| 7742.2.cm |
\(\chi_{7742}(155, \cdot)\) |
n/a |
53568 |
144 |
| 7742.2.cn |
\(\chi_{7742}(65, \cdot)\) |
n/a |
53568 |
144 |
| 7742.2.co |
\(\chi_{7742}(9, \cdot)\) |
n/a |
53856 |
144 |
| 7742.2.cp |
\(\chi_{7742}(11, \cdot)\) |
n/a |
53856 |
144 |
| 7742.2.cs |
\(\chi_{7742}(17, \cdot)\) |
n/a |
53568 |
144 |
| 7742.2.ct |
\(\chi_{7742}(139, \cdot)\) |
n/a |
53568 |
144 |
| 7742.2.cu |
\(\chi_{7742}(3, \cdot)\) |
n/a |
53856 |
144 |
| 7742.2.db |
\(\chi_{7742}(145, \cdot)\) |
n/a |
53856 |
144 |
"n/a" means that newforms for that character have not been added to the database yet
