Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1312))\).
|
Total |
New |
Old |
Modular forms
| 1472 |
437 |
1035 |
Cusp forms
| 192 |
47 |
145 |
Eisenstein series
| 1280 |
390 |
890 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1312))\)
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 |
1312.1.c |
\(\chi_{1312}(655, \cdot)\) |
1312.1.c.a |
1 |
1 |
1312.1.e |
\(\chi_{1312}(575, \cdot)\) |
None |
0 |
1 |
1312.1.f |
\(\chi_{1312}(1231, \cdot)\) |
None |
0 |
1 |
1312.1.h |
\(\chi_{1312}(1311, \cdot)\) |
None |
0 |
1 |
1312.1.j |
\(\chi_{1312}(583, \cdot)\) |
None |
0 |
2 |
1312.1.k |
\(\chi_{1312}(255, \cdot)\) |
None |
0 |
2 |
1312.1.m |
\(\chi_{1312}(327, \cdot)\) |
None |
0 |
2 |
1312.1.p |
\(\chi_{1312}(247, \cdot)\) |
None |
0 |
2 |
1312.1.q |
\(\chi_{1312}(911, \cdot)\) |
1312.1.q.a |
2 |
2 |
1312.1.s |
\(\chi_{1312}(647, \cdot)\) |
None |
0 |
2 |
1312.1.w |
\(\chi_{1312}(85, \cdot)\) |
None |
0 |
4 |
1312.1.y |
\(\chi_{1312}(137, \cdot)\) |
None |
0 |
4 |
1312.1.z |
\(\chi_{1312}(155, \cdot)\) |
None |
0 |
4 |
1312.1.bb |
\(\chi_{1312}(437, \cdot)\) |
None |
0 |
4 |
1312.1.bd |
\(\chi_{1312}(413, \cdot)\) |
None |
0 |
4 |
1312.1.bg |
\(\chi_{1312}(163, \cdot)\) |
1312.1.bg.a |
4 |
4 |
1312.1.bh |
\(\chi_{1312}(273, \cdot)\) |
1312.1.bh.a |
4 |
4 |
1312.1.bi |
\(\chi_{1312}(161, \cdot)\) |
1312.1.bi.a |
4 |
4 |
1312.1.bl |
\(\chi_{1312}(83, \cdot)\) |
None |
0 |
4 |
1312.1.bn |
\(\chi_{1312}(91, \cdot)\) |
None |
0 |
4 |
1312.1.bq |
\(\chi_{1312}(489, \cdot)\) |
None |
0 |
4 |
1312.1.br |
\(\chi_{1312}(301, \cdot)\) |
None |
0 |
4 |
1312.1.bt |
\(\chi_{1312}(223, \cdot)\) |
None |
0 |
4 |
1312.1.bv |
\(\chi_{1312}(271, \cdot)\) |
1312.1.bv.a |
4 |
4 |
1312.1.bx |
\(\chi_{1312}(31, \cdot)\) |
None |
0 |
4 |
1312.1.bz |
\(\chi_{1312}(303, \cdot)\) |
1312.1.bz.a |
4 |
4 |
1312.1.ca |
\(\chi_{1312}(39, \cdot)\) |
None |
0 |
8 |
1312.1.cd |
\(\chi_{1312}(143, \cdot)\) |
1312.1.cd.a |
8 |
8 |
1312.1.ce |
\(\chi_{1312}(119, \cdot)\) |
None |
0 |
8 |
1312.1.ch |
\(\chi_{1312}(23, \cdot)\) |
None |
0 |
8 |
1312.1.cj |
\(\chi_{1312}(159, \cdot)\) |
None |
0 |
8 |
1312.1.cl |
\(\chi_{1312}(87, \cdot)\) |
None |
0 |
8 |
1312.1.cm |
\(\chi_{1312}(69, \cdot)\) |
None |
0 |
16 |
1312.1.co |
\(\chi_{1312}(233, \cdot)\) |
None |
0 |
16 |
1312.1.cr |
\(\chi_{1312}(115, \cdot)\) |
None |
0 |
16 |
1312.1.ct |
\(\chi_{1312}(29, \cdot)\) |
None |
0 |
16 |
1312.1.cv |
\(\chi_{1312}(13, \cdot)\) |
None |
0 |
16 |
1312.1.cx |
\(\chi_{1312}(51, \cdot)\) |
None |
0 |
16 |
1312.1.da |
\(\chi_{1312}(65, \cdot)\) |
1312.1.da.a |
16 |
16 |
1312.1.db |
\(\chi_{1312}(17, \cdot)\) |
None |
0 |
16 |
1312.1.dc |
\(\chi_{1312}(107, \cdot)\) |
None |
0 |
16 |
1312.1.df |
\(\chi_{1312}(43, \cdot)\) |
None |
0 |
16 |
1312.1.dg |
\(\chi_{1312}(89, \cdot)\) |
None |
0 |
16 |
1312.1.dj |
\(\chi_{1312}(53, \cdot)\) |
None |
0 |
16 |