Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(663))\).
|
Total |
New |
Old |
Modular forms
| 784 |
346 |
438 |
Cusp forms
| 16 |
14 |
2 |
Eisenstein series
| 768 |
332 |
436 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(663))\)
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 |
663.1.c |
\(\chi_{663}(443, \cdot)\) |
None |
0 |
1 |
663.1.d |
\(\chi_{663}(560, \cdot)\) |
None |
0 |
1 |
663.1.g |
\(\chi_{663}(662, \cdot)\) |
663.1.g.a |
1 |
1 |
663.1.g.b |
1 |
663.1.g.c |
2 |
663.1.g.d |
2 |
663.1.h |
\(\chi_{663}(545, \cdot)\) |
None |
0 |
1 |
663.1.k |
\(\chi_{663}(38, \cdot)\) |
None |
0 |
2 |
663.1.l |
\(\chi_{663}(268, \cdot)\) |
None |
0 |
2 |
663.1.o |
\(\chi_{663}(307, \cdot)\) |
None |
0 |
2 |
663.1.p |
\(\chi_{663}(424, \cdot)\) |
None |
0 |
2 |
663.1.s |
\(\chi_{663}(421, \cdot)\) |
None |
0 |
2 |
663.1.t |
\(\chi_{663}(404, \cdot)\) |
None |
0 |
2 |
663.1.v |
\(\chi_{663}(101, \cdot)\) |
663.1.v.a |
2 |
2 |
663.1.v.b |
2 |
663.1.x |
\(\chi_{663}(290, \cdot)\) |
None |
0 |
2 |
663.1.y |
\(\chi_{663}(35, \cdot)\) |
None |
0 |
2 |
663.1.bb |
\(\chi_{663}(152, \cdot)\) |
663.1.bb.a |
2 |
2 |
663.1.bb.b |
2 |
663.1.bc |
\(\chi_{663}(151, \cdot)\) |
None |
0 |
4 |
663.1.be |
\(\chi_{663}(77, \cdot)\) |
None |
0 |
4 |
663.1.bf |
\(\chi_{663}(53, \cdot)\) |
None |
0 |
4 |
663.1.bj |
\(\chi_{663}(70, \cdot)\) |
None |
0 |
4 |
663.1.bl |
\(\chi_{663}(191, \cdot)\) |
None |
0 |
4 |
663.1.bn |
\(\chi_{663}(106, \cdot)\) |
None |
0 |
4 |
663.1.bo |
\(\chi_{663}(67, \cdot)\) |
None |
0 |
4 |
663.1.br |
\(\chi_{663}(154, \cdot)\) |
None |
0 |
4 |
663.1.bs |
\(\chi_{663}(310, \cdot)\) |
None |
0 |
4 |
663.1.bu |
\(\chi_{663}(140, \cdot)\) |
None |
0 |
4 |
663.1.bw |
\(\chi_{663}(44, \cdot)\) |
None |
0 |
8 |
663.1.bz |
\(\chi_{663}(5, \cdot)\) |
None |
0 |
8 |
663.1.cb |
\(\chi_{663}(40, \cdot)\) |
None |
0 |
8 |
663.1.cc |
\(\chi_{663}(142, \cdot)\) |
None |
0 |
8 |
663.1.ce |
\(\chi_{663}(19, \cdot)\) |
None |
0 |
8 |
663.1.ci |
\(\chi_{663}(134, \cdot)\) |
None |
0 |
8 |
663.1.cj |
\(\chi_{663}(185, \cdot)\) |
None |
0 |
8 |
663.1.cl |
\(\chi_{663}(145, \cdot)\) |
None |
0 |
8 |
663.1.cn |
\(\chi_{663}(10, \cdot)\) |
None |
0 |
16 |
663.1.co |
\(\chi_{663}(22, \cdot)\) |
None |
0 |
16 |
663.1.cq |
\(\chi_{663}(20, \cdot)\) |
None |
0 |
16 |
663.1.ct |
\(\chi_{663}(11, \cdot)\) |
None |
0 |
16 |