Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5776))\).
|
Total |
New |
Old |
| Modular forms
| 1046736 |
583693 |
463043 |
| Cusp forms
| 1032625 |
579476 |
453149 |
| Eisenstein series
| 14111 |
4217 |
9894 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5776))\)
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 the newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 5776.2.a |
\(\chi_{5776}(1, \cdot)\) |
5776.2.a.a |
1 |
1 |
| 5776.2.a.b |
1 |
| 5776.2.a.c |
1 |
| 5776.2.a.d |
1 |
| 5776.2.a.e |
1 |
| 5776.2.a.f |
1 |
| 5776.2.a.g |
1 |
| 5776.2.a.h |
1 |
| 5776.2.a.i |
1 |
| 5776.2.a.j |
1 |
| 5776.2.a.k |
1 |
| 5776.2.a.l |
1 |
| 5776.2.a.m |
1 |
| 5776.2.a.n |
1 |
| 5776.2.a.o |
1 |
| 5776.2.a.p |
1 |
| 5776.2.a.q |
1 |
| 5776.2.a.r |
2 |
| 5776.2.a.s |
2 |
| 5776.2.a.t |
2 |
| 5776.2.a.u |
2 |
| 5776.2.a.v |
2 |
| 5776.2.a.w |
2 |
| 5776.2.a.x |
2 |
| 5776.2.a.y |
2 |
| 5776.2.a.z |
2 |
| 5776.2.a.ba |
2 |
| 5776.2.a.bb |
2 |
| 5776.2.a.bc |
2 |
| 5776.2.a.bd |
2 |
| 5776.2.a.be |
2 |
| 5776.2.a.bf |
2 |
| 5776.2.a.bg |
2 |
| 5776.2.a.bh |
2 |
| 5776.2.a.bi |
3 |
| 5776.2.a.bj |
3 |
| 5776.2.a.bk |
3 |
| 5776.2.a.bl |
3 |
| 5776.2.a.bm |
3 |
| 5776.2.a.bn |
3 |
| 5776.2.a.bo |
3 |
| 5776.2.a.bp |
3 |
| 5776.2.a.bq |
3 |
| 5776.2.a.br |
3 |
| 5776.2.a.bs |
3 |
| 5776.2.a.bt |
4 |
| 5776.2.a.bu |
4 |
| 5776.2.a.bv |
4 |
| 5776.2.a.bw |
6 |
| 5776.2.a.bx |
6 |
| 5776.2.a.by |
6 |
| 5776.2.a.bz |
6 |
| 5776.2.a.ca |
8 |
| 5776.2.a.cb |
8 |
| 5776.2.a.cc |
8 |
| 5776.2.a.cd |
9 |
| 5776.2.a.ce |
9 |
| 5776.2.b |
\(\chi_{5776}(2887, \cdot)\) |
None |
0 |
1 |
| 5776.2.c |
\(\chi_{5776}(2889, \cdot)\) |
None |
0 |
1 |
| 5776.2.h |
\(\chi_{5776}(5775, \cdot)\) |
n/a |
170 |
1 |
| 5776.2.i |
\(\chi_{5776}(1873, \cdot)\) |
n/a |
324 |
2 |
| 5776.2.k |
\(\chi_{5776}(1445, \cdot)\) |
n/a |
1330 |
2 |
| 5776.2.m |
\(\chi_{5776}(1443, \cdot)\) |
n/a |
1328 |
2 |
| 5776.2.n |
\(\chi_{5776}(3679, \cdot)\) |
n/a |
340 |
2 |
| 5776.2.s |
\(\chi_{5776}(791, \cdot)\) |
None |
0 |
2 |
| 5776.2.t |
\(\chi_{5776}(4761, \cdot)\) |
None |
0 |
2 |
| 5776.2.u |
\(\chi_{5776}(1137, \cdot)\) |
n/a |
972 |
6 |
| 5776.2.v |
\(\chi_{5776}(429, \cdot)\) |
n/a |
2656 |
4 |
| 5776.2.x |
\(\chi_{5776}(2235, \cdot)\) |
n/a |
2656 |
4 |
| 5776.2.bb |
\(\chi_{5776}(1145, \cdot)\) |
None |
0 |
6 |
| 5776.2.bd |
\(\chi_{5776}(1751, \cdot)\) |
None |
0 |
6 |
| 5776.2.be |
\(\chi_{5776}(127, \cdot)\) |
n/a |
1020 |
6 |
| 5776.2.bg |
\(\chi_{5776}(305, \cdot)\) |
n/a |
3402 |
18 |
| 5776.2.bh |
\(\chi_{5776}(299, \cdot)\) |
n/a |
7968 |
12 |
| 5776.2.bj |
\(\chi_{5776}(245, \cdot)\) |
n/a |
7968 |
12 |
| 5776.2.bl |
\(\chi_{5776}(303, \cdot)\) |
n/a |
3420 |
18 |
| 5776.2.bq |
\(\chi_{5776}(153, \cdot)\) |
None |
0 |
18 |
| 5776.2.br |
\(\chi_{5776}(151, \cdot)\) |
None |
0 |
18 |
| 5776.2.bs |
\(\chi_{5776}(49, \cdot)\) |
n/a |
6804 |
36 |
| 5776.2.bt |
\(\chi_{5776}(75, \cdot)\) |
n/a |
27288 |
36 |
| 5776.2.bv |
\(\chi_{5776}(77, \cdot)\) |
n/a |
27288 |
36 |
| 5776.2.bx |
\(\chi_{5776}(121, \cdot)\) |
None |
0 |
36 |
| 5776.2.by |
\(\chi_{5776}(103, \cdot)\) |
None |
0 |
36 |
| 5776.2.cd |
\(\chi_{5776}(31, \cdot)\) |
n/a |
6840 |
36 |
| 5776.2.ce |
\(\chi_{5776}(17, \cdot)\) |
n/a |
20412 |
108 |
| 5776.2.cg |
\(\chi_{5776}(27, \cdot)\) |
n/a |
54576 |
72 |
| 5776.2.ci |
\(\chi_{5776}(45, \cdot)\) |
n/a |
54576 |
72 |
| 5776.2.ck |
\(\chi_{5776}(15, \cdot)\) |
n/a |
20520 |
108 |
| 5776.2.cl |
\(\chi_{5776}(71, \cdot)\) |
None |
0 |
108 |
| 5776.2.cn |
\(\chi_{5776}(9, \cdot)\) |
None |
0 |
108 |
| 5776.2.cr |
\(\chi_{5776}(5, \cdot)\) |
n/a |
163728 |
216 |
| 5776.2.ct |
\(\chi_{5776}(3, \cdot)\) |
n/a |
163728 |
216 |
"n/a" means that newforms for that character have not been added to the database yet
