Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(936))\).
|
Total |
New |
Old |
Modular forms
| 1320 |
224 |
1096 |
Cusp forms
| 168 |
26 |
142 |
Eisenstein series
| 1152 |
198 |
954 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(936))\)
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 |
936.1.b |
\(\chi_{936}(701, \cdot)\) |
None |
0 |
1 |
936.1.e |
\(\chi_{936}(235, \cdot)\) |
None |
0 |
1 |
936.1.f |
\(\chi_{936}(521, \cdot)\) |
None |
0 |
1 |
936.1.i |
\(\chi_{936}(415, \cdot)\) |
None |
0 |
1 |
936.1.k |
\(\chi_{936}(703, \cdot)\) |
None |
0 |
1 |
936.1.l |
\(\chi_{936}(233, \cdot)\) |
None |
0 |
1 |
936.1.o |
\(\chi_{936}(883, \cdot)\) |
936.1.o.a |
1 |
1 |
936.1.o.b |
1 |
936.1.o.c |
4 |
936.1.p |
\(\chi_{936}(53, \cdot)\) |
None |
0 |
1 |
936.1.u |
\(\chi_{936}(109, \cdot)\) |
None |
0 |
2 |
936.1.v |
\(\chi_{936}(73, \cdot)\) |
None |
0 |
2 |
936.1.y |
\(\chi_{936}(359, \cdot)\) |
None |
0 |
2 |
936.1.z |
\(\chi_{936}(395, \cdot)\) |
None |
0 |
2 |
936.1.bc |
\(\chi_{936}(127, \cdot)\) |
None |
0 |
2 |
936.1.bf |
\(\chi_{936}(737, \cdot)\) |
None |
0 |
2 |
936.1.bg |
\(\chi_{936}(451, \cdot)\) |
None |
0 |
2 |
936.1.bj |
\(\chi_{936}(413, \cdot)\) |
None |
0 |
2 |
936.1.bl |
\(\chi_{936}(257, \cdot)\) |
None |
0 |
2 |
936.1.bm |
\(\chi_{936}(295, \cdot)\) |
None |
0 |
2 |
936.1.bo |
\(\chi_{936}(355, \cdot)\) |
None |
0 |
2 |
936.1.bq |
\(\chi_{936}(365, \cdot)\) |
None |
0 |
2 |
936.1.bs |
\(\chi_{936}(259, \cdot)\) |
936.1.bs.a |
6 |
2 |
936.1.bs.b |
6 |
936.1.bt |
\(\chi_{936}(29, \cdot)\) |
None |
0 |
2 |
936.1.bu |
\(\chi_{936}(367, \cdot)\) |
None |
0 |
2 |
936.1.bw |
\(\chi_{936}(545, \cdot)\) |
None |
0 |
2 |
936.1.bz |
\(\chi_{936}(79, \cdot)\) |
None |
0 |
2 |
936.1.cb |
\(\chi_{936}(329, \cdot)\) |
None |
0 |
2 |
936.1.cc |
\(\chi_{936}(653, \cdot)\) |
None |
0 |
2 |
936.1.cd |
\(\chi_{936}(43, \cdot)\) |
None |
0 |
2 |
936.1.cf |
\(\chi_{936}(211, \cdot)\) |
None |
0 |
2 |
936.1.ci |
\(\chi_{936}(173, \cdot)\) |
None |
0 |
2 |
936.1.ck |
\(\chi_{936}(113, \cdot)\) |
None |
0 |
2 |
936.1.cm |
\(\chi_{936}(103, \cdot)\) |
None |
0 |
2 |
936.1.cn |
\(\chi_{936}(209, \cdot)\) |
None |
0 |
2 |
936.1.cp |
\(\chi_{936}(439, \cdot)\) |
None |
0 |
2 |
936.1.cs |
\(\chi_{936}(101, \cdot)\) |
None |
0 |
2 |
936.1.cu |
\(\chi_{936}(547, \cdot)\) |
None |
0 |
2 |
936.1.cv |
\(\chi_{936}(77, \cdot)\) |
None |
0 |
2 |
936.1.cx |
\(\chi_{936}(139, \cdot)\) |
None |
0 |
2 |
936.1.cz |
\(\chi_{936}(511, \cdot)\) |
None |
0 |
2 |
936.1.dc |
\(\chi_{936}(185, \cdot)\) |
None |
0 |
2 |
936.1.dd |
\(\chi_{936}(269, \cdot)\) |
None |
0 |
2 |
936.1.de |
\(\chi_{936}(595, \cdot)\) |
None |
0 |
2 |
936.1.dh |
\(\chi_{936}(17, \cdot)\) |
None |
0 |
2 |
936.1.di |
\(\chi_{936}(55, \cdot)\) |
None |
0 |
2 |
936.1.dm |
\(\chi_{936}(265, \cdot)\) |
936.1.dm.a |
4 |
4 |
936.1.dm.b |
4 |
936.1.dn |
\(\chi_{936}(229, \cdot)\) |
None |
0 |
4 |
936.1.do |
\(\chi_{936}(227, \cdot)\) |
None |
0 |
4 |
936.1.dp |
\(\chi_{936}(167, \cdot)\) |
None |
0 |
4 |
936.1.du |
\(\chi_{936}(323, \cdot)\) |
None |
0 |
4 |
936.1.dv |
\(\chi_{936}(71, \cdot)\) |
None |
0 |
4 |
936.1.dw |
\(\chi_{936}(119, \cdot)\) |
None |
0 |
4 |
936.1.dx |
\(\chi_{936}(11, \cdot)\) |
None |
0 |
4 |
936.1.ea |
\(\chi_{936}(97, \cdot)\) |
None |
0 |
4 |
936.1.eb |
\(\chi_{936}(301, \cdot)\) |
None |
0 |
4 |
936.1.eg |
\(\chi_{936}(145, \cdot)\) |
None |
0 |
4 |
936.1.eh |
\(\chi_{936}(37, \cdot)\) |
None |
0 |
4 |
936.1.ei |
\(\chi_{936}(85, \cdot)\) |
None |
0 |
4 |
936.1.ej |
\(\chi_{936}(409, \cdot)\) |
None |
0 |
4 |
936.1.eo |
\(\chi_{936}(83, \cdot)\) |
None |
0 |
4 |
936.1.ep |
\(\chi_{936}(47, \cdot)\) |
None |
0 |
4 |