Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1404))\).
|
Total |
New |
Old |
Modular forms
| 1995 |
388 |
1607 |
Cusp forms
| 195 |
36 |
159 |
Eisenstein series
| 1800 |
352 |
1448 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1404))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1404.1.d |
\(\chi_{1404}(53, \cdot)\) |
None |
0 |
1 |
1404.1.e |
\(\chi_{1404}(1351, \cdot)\) |
1404.1.e.a |
2 |
1 |
1404.1.e.b |
2 |
1404.1.e.c |
4 |
1404.1.f |
\(\chi_{1404}(703, \cdot)\) |
None |
0 |
1 |
1404.1.g |
\(\chi_{1404}(701, \cdot)\) |
1404.1.g.a |
2 |
1 |
1404.1.m |
\(\chi_{1404}(109, \cdot)\) |
1404.1.m.a |
4 |
2 |
1404.1.o |
\(\chi_{1404}(863, \cdot)\) |
None |
0 |
2 |
1404.1.q |
\(\chi_{1404}(595, \cdot)\) |
1404.1.q.a |
2 |
2 |
1404.1.q.b |
2 |
1404.1.r |
\(\chi_{1404}(269, \cdot)\) |
1404.1.r.a |
2 |
2 |
1404.1.u |
\(\chi_{1404}(881, \cdot)\) |
None |
0 |
2 |
1404.1.v |
\(\chi_{1404}(451, \cdot)\) |
1404.1.v.a |
4 |
2 |
1404.1.y |
\(\chi_{1404}(991, \cdot)\) |
1404.1.y.a |
4 |
2 |
1404.1.z |
\(\chi_{1404}(233, \cdot)\) |
1404.1.z.a |
2 |
2 |
1404.1.ba |
\(\chi_{1404}(235, \cdot)\) |
None |
0 |
2 |
1404.1.bb |
\(\chi_{1404}(17, \cdot)\) |
None |
0 |
2 |
1404.1.bf |
\(\chi_{1404}(1205, \cdot)\) |
None |
0 |
2 |
1404.1.bg |
\(\chi_{1404}(415, \cdot)\) |
None |
0 |
2 |
1404.1.bh |
\(\chi_{1404}(521, \cdot)\) |
None |
0 |
2 |
1404.1.bi |
\(\chi_{1404}(127, \cdot)\) |
None |
0 |
2 |
1404.1.bn |
\(\chi_{1404}(667, \cdot)\) |
None |
0 |
2 |
1404.1.bo |
\(\chi_{1404}(341, \cdot)\) |
None |
0 |
2 |
1404.1.bq |
\(\chi_{1404}(485, \cdot)\) |
1404.1.bq.a |
2 |
2 |
1404.1.br |
\(\chi_{1404}(55, \cdot)\) |
None |
0 |
2 |
1404.1.bw |
\(\chi_{1404}(73, \cdot)\) |
None |
0 |
4 |
1404.1.bx |
\(\chi_{1404}(683, \cdot)\) |
None |
0 |
4 |
1404.1.ca |
\(\chi_{1404}(215, \cdot)\) |
None |
0 |
4 |
1404.1.cb |
\(\chi_{1404}(71, \cdot)\) |
None |
0 |
4 |
1404.1.cd |
\(\chi_{1404}(37, \cdot)\) |
None |
0 |
4 |
1404.1.cg |
\(\chi_{1404}(865, \cdot)\) |
1404.1.cg.a |
4 |
4 |
1404.1.ch |
\(\chi_{1404}(253, \cdot)\) |
None |
0 |
4 |
1404.1.ck |
\(\chi_{1404}(359, \cdot)\) |
None |
0 |
4 |
1404.1.cm |
\(\chi_{1404}(29, \cdot)\) |
None |
0 |
6 |
1404.1.co |
\(\chi_{1404}(101, \cdot)\) |
None |
0 |
6 |
1404.1.cp |
\(\chi_{1404}(211, \cdot)\) |
None |
0 |
6 |
1404.1.cr |
\(\chi_{1404}(103, \cdot)\) |
None |
0 |
6 |
1404.1.ct |
\(\chi_{1404}(79, \cdot)\) |
None |
0 |
6 |
1404.1.cu |
\(\chi_{1404}(43, \cdot)\) |
None |
0 |
6 |
1404.1.cv |
\(\chi_{1404}(173, \cdot)\) |
None |
0 |
6 |
1404.1.cy |
\(\chi_{1404}(209, \cdot)\) |
None |
0 |
6 |
1404.1.da |
\(\chi_{1404}(77, \cdot)\) |
None |
0 |
6 |
1404.1.db |
\(\chi_{1404}(185, \cdot)\) |
None |
0 |
6 |
1404.1.dd |
\(\chi_{1404}(355, \cdot)\) |
None |
0 |
6 |
1404.1.df |
\(\chi_{1404}(139, \cdot)\) |
None |
0 |
6 |
1404.1.dg |
\(\chi_{1404}(85, \cdot)\) |
None |
0 |
12 |
1404.1.dj |
\(\chi_{1404}(47, \cdot)\) |
None |
0 |
12 |
1404.1.dl |
\(\chi_{1404}(167, \cdot)\) |
None |
0 |
12 |
1404.1.dn |
\(\chi_{1404}(229, \cdot)\) |
None |
0 |
12 |
1404.1.dp |
\(\chi_{1404}(97, \cdot)\) |
None |
0 |
12 |
1404.1.dq |
\(\chi_{1404}(11, \cdot)\) |
None |
0 |
12 |