Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1260))\).
|
Total |
New |
Old |
Modular forms
| 2106 |
358 |
1748 |
Cusp forms
| 186 |
86 |
100 |
Eisenstein series
| 1920 |
272 |
1648 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1260))\)
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 |
1260.1.b |
\(\chi_{1260}(379, \cdot)\) |
None |
0 |
1 |
1260.1.e |
\(\chi_{1260}(449, \cdot)\) |
None |
0 |
1 |
1260.1.g |
\(\chi_{1260}(701, \cdot)\) |
None |
0 |
1 |
1260.1.h |
\(\chi_{1260}(631, \cdot)\) |
None |
0 |
1 |
1260.1.j |
\(\chi_{1260}(181, \cdot)\) |
None |
0 |
1 |
1260.1.m |
\(\chi_{1260}(251, \cdot)\) |
None |
0 |
1 |
1260.1.o |
\(\chi_{1260}(1259, \cdot)\) |
None |
0 |
1 |
1260.1.p |
\(\chi_{1260}(1189, \cdot)\) |
1260.1.p.a |
1 |
1 |
1260.1.p.b |
1 |
1260.1.u |
\(\chi_{1260}(307, \cdot)\) |
1260.1.u.a |
4 |
2 |
1260.1.u.b |
4 |
1260.1.x |
\(\chi_{1260}(377, \cdot)\) |
None |
0 |
2 |
1260.1.y |
\(\chi_{1260}(253, \cdot)\) |
None |
0 |
2 |
1260.1.bb |
\(\chi_{1260}(323, \cdot)\) |
None |
0 |
2 |
1260.1.bd |
\(\chi_{1260}(331, \cdot)\) |
None |
0 |
2 |
1260.1.be |
\(\chi_{1260}(221, \cdot)\) |
None |
0 |
2 |
1260.1.bg |
\(\chi_{1260}(569, \cdot)\) |
None |
0 |
2 |
1260.1.bj |
\(\chi_{1260}(79, \cdot)\) |
1260.1.bj.a |
2 |
2 |
1260.1.bj.b |
2 |
1260.1.bj.c |
2 |
1260.1.bj.d |
2 |
1260.1.bk |
\(\chi_{1260}(971, \cdot)\) |
None |
0 |
2 |
1260.1.bn |
\(\chi_{1260}(901, \cdot)\) |
None |
0 |
2 |
1260.1.bp |
\(\chi_{1260}(419, \cdot)\) |
1260.1.bp.a |
4 |
2 |
1260.1.bp.b |
4 |
1260.1.bq |
\(\chi_{1260}(229, \cdot)\) |
None |
0 |
2 |
1260.1.br |
\(\chi_{1260}(479, \cdot)\) |
1260.1.br.a |
4 |
2 |
1260.1.br.b |
4 |
1260.1.bt |
\(\chi_{1260}(349, \cdot)\) |
1260.1.bt.a |
2 |
2 |
1260.1.bt.b |
2 |
1260.1.bt.c |
2 |
1260.1.bt.d |
2 |
1260.1.bu |
\(\chi_{1260}(601, \cdot)\) |
None |
0 |
2 |
1260.1.bw |
\(\chi_{1260}(131, \cdot)\) |
None |
0 |
2 |
1260.1.bz |
\(\chi_{1260}(241, \cdot)\) |
None |
0 |
2 |
1260.1.cb |
\(\chi_{1260}(671, \cdot)\) |
None |
0 |
2 |
1260.1.cc |
\(\chi_{1260}(649, \cdot)\) |
None |
0 |
2 |
1260.1.cd |
\(\chi_{1260}(719, \cdot)\) |
None |
0 |
2 |
1260.1.cf |
\(\chi_{1260}(809, \cdot)\) |
1260.1.cf.a |
8 |
2 |
1260.1.ci |
\(\chi_{1260}(739, \cdot)\) |
1260.1.ci.a |
2 |
2 |
1260.1.ci.b |
2 |
1260.1.ck |
\(\chi_{1260}(281, \cdot)\) |
None |
0 |
2 |
1260.1.cm |
\(\chi_{1260}(151, \cdot)\) |
None |
0 |
2 |
1260.1.cn |
\(\chi_{1260}(401, \cdot)\) |
None |
0 |
2 |
1260.1.cp |
\(\chi_{1260}(211, \cdot)\) |
None |
0 |
2 |
1260.1.cr |
\(\chi_{1260}(799, \cdot)\) |
None |
0 |
2 |
1260.1.ct |
\(\chi_{1260}(149, \cdot)\) |
None |
0 |
2 |
1260.1.cw |
\(\chi_{1260}(499, \cdot)\) |
1260.1.cw.a |
2 |
2 |
1260.1.cw.b |
2 |
1260.1.cw.c |
2 |
1260.1.cw.d |
2 |
1260.1.cy |
\(\chi_{1260}(29, \cdot)\) |
None |
0 |
2 |
1260.1.da |
\(\chi_{1260}(991, \cdot)\) |
None |
0 |
2 |
1260.1.db |
\(\chi_{1260}(1061, \cdot)\) |
None |
0 |
2 |
1260.1.dd |
\(\chi_{1260}(409, \cdot)\) |
None |
0 |
2 |
1260.1.de |
\(\chi_{1260}(59, \cdot)\) |
1260.1.de.a |
4 |
2 |
1260.1.de.b |
4 |
1260.1.dg |
\(\chi_{1260}(311, \cdot)\) |
None |
0 |
2 |
1260.1.dj |
\(\chi_{1260}(61, \cdot)\) |
None |
0 |
2 |
1260.1.dk |
\(\chi_{1260}(173, \cdot)\) |
None |
0 |
4 |
1260.1.dn |
\(\chi_{1260}(187, \cdot)\) |
None |
0 |
4 |
1260.1.dp |
\(\chi_{1260}(337, \cdot)\) |
None |
0 |
4 |
1260.1.dr |
\(\chi_{1260}(23, \cdot)\) |
None |
0 |
4 |
1260.1.dt |
\(\chi_{1260}(107, \cdot)\) |
None |
0 |
4 |
1260.1.du |
\(\chi_{1260}(37, \cdot)\) |
None |
0 |
4 |
1260.1.dw |
\(\chi_{1260}(277, \cdot)\) |
None |
0 |
4 |
1260.1.dy |
\(\chi_{1260}(407, \cdot)\) |
None |
0 |
4 |
1260.1.eb |
\(\chi_{1260}(223, \cdot)\) |
1260.1.eb.a |
8 |
4 |
1260.1.eb.b |
8 |
1260.1.ed |
\(\chi_{1260}(257, \cdot)\) |
None |
0 |
4 |
1260.1.ef |
\(\chi_{1260}(17, \cdot)\) |
None |
0 |
4 |
1260.1.eg |
\(\chi_{1260}(523, \cdot)\) |
None |
0 |
4 |
1260.1.ei |
\(\chi_{1260}(103, \cdot)\) |
None |
0 |
4 |
1260.1.ek |
\(\chi_{1260}(293, \cdot)\) |
None |
0 |
4 |
1260.1.em |
\(\chi_{1260}(347, \cdot)\) |
None |
0 |
4 |
1260.1.ep |
\(\chi_{1260}(193, \cdot)\) |
None |
0 |
4 |