Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(777))\).
|
Total |
New |
Old |
| Modular forms
| 1000 |
440 |
560 |
| Cusp forms
| 136 |
88 |
48 |
| Eisenstein series
| 864 |
352 |
512 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(777))\)
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 |
| 777.1.b |
\(\chi_{777}(260, \cdot)\) |
None |
0 |
1 |
| 777.1.e |
\(\chi_{777}(517, \cdot)\) |
None |
0 |
1 |
| 777.1.g |
\(\chi_{777}(223, \cdot)\) |
None |
0 |
1 |
| 777.1.h |
\(\chi_{777}(554, \cdot)\) |
None |
0 |
1 |
| 777.1.n |
\(\chi_{777}(524, \cdot)\) |
777.1.n.a |
2 |
2 |
| 777.1.n.b |
2 |
| 777.1.n.c |
2 |
| 777.1.n.d |
2 |
| 777.1.o |
\(\chi_{777}(43, \cdot)\) |
None |
0 |
2 |
| 777.1.q |
\(\chi_{777}(418, \cdot)\) |
None |
0 |
2 |
| 777.1.t |
\(\chi_{777}(158, \cdot)\) |
777.1.t.a |
4 |
2 |
| 777.1.u |
\(\chi_{777}(565, \cdot)\) |
None |
0 |
2 |
| 777.1.w |
\(\chi_{777}(221, \cdot)\) |
777.1.w.a |
2 |
2 |
| 777.1.w.b |
2 |
| 777.1.w.c |
4 |
| 777.1.w.d |
8 |
| 777.1.x |
\(\chi_{777}(323, \cdot)\) |
None |
0 |
2 |
| 777.1.z |
\(\chi_{777}(433, \cdot)\) |
None |
0 |
2 |
| 777.1.ba |
\(\chi_{777}(334, \cdot)\) |
None |
0 |
2 |
| 777.1.bc |
\(\chi_{777}(11, \cdot)\) |
None |
0 |
2 |
| 777.1.be |
\(\chi_{777}(137, \cdot)\) |
777.1.be.a |
4 |
2 |
| 777.1.bg |
\(\chi_{777}(286, \cdot)\) |
None |
0 |
2 |
| 777.1.bh |
\(\chi_{777}(73, \cdot)\) |
None |
0 |
2 |
| 777.1.bk |
\(\chi_{777}(149, \cdot)\) |
None |
0 |
2 |
| 777.1.bl |
\(\chi_{777}(470, \cdot)\) |
None |
0 |
2 |
| 777.1.bn |
\(\chi_{777}(397, \cdot)\) |
None |
0 |
2 |
| 777.1.bp |
\(\chi_{777}(233, \cdot)\) |
None |
0 |
2 |
| 777.1.bq |
\(\chi_{777}(10, \cdot)\) |
None |
0 |
2 |
| 777.1.bw |
\(\chi_{777}(88, \cdot)\) |
None |
0 |
4 |
| 777.1.bx |
\(\chi_{777}(341, \cdot)\) |
None |
0 |
4 |
| 777.1.ca |
\(\chi_{777}(125, \cdot)\) |
777.1.ca.a |
4 |
4 |
| 777.1.ca.b |
4 |
| 777.1.cd |
\(\chi_{777}(193, \cdot)\) |
None |
0 |
4 |
| 777.1.ce |
\(\chi_{777}(142, \cdot)\) |
None |
0 |
4 |
| 777.1.cf |
\(\chi_{777}(236, \cdot)\) |
None |
0 |
4 |
| 777.1.cg |
\(\chi_{777}(68, \cdot)\) |
None |
0 |
4 |
| 777.1.cj |
\(\chi_{777}(421, \cdot)\) |
None |
0 |
4 |
| 777.1.cl |
\(\chi_{777}(271, \cdot)\) |
None |
0 |
6 |
| 777.1.cn |
\(\chi_{777}(95, \cdot)\) |
777.1.cn.a |
6 |
6 |
| 777.1.co |
\(\chi_{777}(176, \cdot)\) |
None |
0 |
6 |
| 777.1.cq |
\(\chi_{777}(34, \cdot)\) |
None |
0 |
6 |
| 777.1.cs |
\(\chi_{777}(145, \cdot)\) |
None |
0 |
6 |
| 777.1.ct |
\(\chi_{777}(65, \cdot)\) |
777.1.ct.a |
6 |
6 |
| 777.1.cu |
\(\chi_{777}(115, \cdot)\) |
None |
0 |
6 |
| 777.1.cw |
\(\chi_{777}(44, \cdot)\) |
777.1.cw.a |
6 |
6 |
| 777.1.cy |
\(\chi_{777}(71, \cdot)\) |
None |
0 |
6 |
| 777.1.db |
\(\chi_{777}(139, \cdot)\) |
None |
0 |
6 |
| 777.1.dd |
\(\chi_{777}(40, \cdot)\) |
None |
0 |
6 |
| 777.1.df |
\(\chi_{777}(86, \cdot)\) |
777.1.df.a |
6 |
6 |
| 777.1.dg |
\(\chi_{777}(89, \cdot)\) |
777.1.dg.a |
12 |
12 |
| 777.1.di |
\(\chi_{777}(79, \cdot)\) |
None |
0 |
12 |
| 777.1.dk |
\(\chi_{777}(22, \cdot)\) |
None |
0 |
12 |
| 777.1.dn |
\(\chi_{777}(20, \cdot)\) |
None |
0 |
12 |
| 777.1.dp |
\(\chi_{777}(5, \cdot)\) |
777.1.dp.a |
12 |
12 |
| 777.1.dr |
\(\chi_{777}(130, \cdot)\) |
None |
0 |
12 |
