Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1045))\).
|
Total |
New |
Old |
Modular forms
| 1528 |
984 |
544 |
Cusp forms
| 88 |
64 |
24 |
Eisenstein series
| 1440 |
920 |
520 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1045))\)
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 |
1045.1.c |
\(\chi_{1045}(56, \cdot)\) |
None |
0 |
1 |
1045.1.d |
\(\chi_{1045}(571, \cdot)\) |
None |
0 |
1 |
1045.1.g |
\(\chi_{1045}(989, \cdot)\) |
None |
0 |
1 |
1045.1.h |
\(\chi_{1045}(474, \cdot)\) |
None |
0 |
1 |
1045.1.k |
\(\chi_{1045}(208, \cdot)\) |
1045.1.k.a |
2 |
2 |
1045.1.k.b |
2 |
1045.1.k.c |
2 |
1045.1.k.d |
2 |
1045.1.l |
\(\chi_{1045}(628, \cdot)\) |
None |
0 |
2 |
1045.1.o |
\(\chi_{1045}(639, \cdot)\) |
None |
0 |
2 |
1045.1.q |
\(\chi_{1045}(714, \cdot)\) |
None |
0 |
2 |
1045.1.r |
\(\chi_{1045}(296, \cdot)\) |
None |
0 |
2 |
1045.1.u |
\(\chi_{1045}(221, \cdot)\) |
None |
0 |
2 |
1045.1.w |
\(\chi_{1045}(284, \cdot)\) |
1045.1.w.a |
4 |
4 |
1045.1.w.b |
4 |
1045.1.w.c |
4 |
1045.1.w.d |
4 |
1045.1.w.e |
8 |
1045.1.w.f |
16 |
1045.1.x |
\(\chi_{1045}(39, \cdot)\) |
None |
0 |
4 |
1045.1.ba |
\(\chi_{1045}(96, \cdot)\) |
None |
0 |
4 |
1045.1.bb |
\(\chi_{1045}(246, \cdot)\) |
None |
0 |
4 |
1045.1.be |
\(\chi_{1045}(353, \cdot)\) |
None |
0 |
4 |
1045.1.bf |
\(\chi_{1045}(373, \cdot)\) |
None |
0 |
4 |
1045.1.bi |
\(\chi_{1045}(54, \cdot)\) |
None |
0 |
6 |
1045.1.bk |
\(\chi_{1045}(166, \cdot)\) |
None |
0 |
6 |
1045.1.bl |
\(\chi_{1045}(34, \cdot)\) |
None |
0 |
6 |
1045.1.bn |
\(\chi_{1045}(131, \cdot)\) |
None |
0 |
6 |
1045.1.bq |
\(\chi_{1045}(58, \cdot)\) |
None |
0 |
8 |
1045.1.br |
\(\chi_{1045}(18, \cdot)\) |
1045.1.br.a |
8 |
8 |
1045.1.br.b |
8 |
1045.1.bt |
\(\chi_{1045}(31, \cdot)\) |
None |
0 |
8 |
1045.1.bw |
\(\chi_{1045}(106, \cdot)\) |
None |
0 |
8 |
1045.1.bx |
\(\chi_{1045}(239, \cdot)\) |
None |
0 |
8 |
1045.1.bz |
\(\chi_{1045}(69, \cdot)\) |
None |
0 |
8 |
1045.1.ca |
\(\chi_{1045}(23, \cdot)\) |
None |
0 |
12 |
1045.1.cd |
\(\chi_{1045}(32, \cdot)\) |
None |
0 |
12 |
1045.1.cg |
\(\chi_{1045}(8, \cdot)\) |
None |
0 |
16 |
1045.1.ch |
\(\chi_{1045}(102, \cdot)\) |
None |
0 |
16 |
1045.1.cj |
\(\chi_{1045}(6, \cdot)\) |
None |
0 |
24 |
1045.1.cl |
\(\chi_{1045}(14, \cdot)\) |
None |
0 |
24 |
1045.1.co |
\(\chi_{1045}(71, \cdot)\) |
None |
0 |
24 |
1045.1.cp |
\(\chi_{1045}(24, \cdot)\) |
None |
0 |
24 |
1045.1.cq |
\(\chi_{1045}(2, \cdot)\) |
None |
0 |
48 |
1045.1.ct |
\(\chi_{1045}(42, \cdot)\) |
None |
0 |
48 |