Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2563))\).
|
Total |
New |
Old |
| Modular forms
| 2334 |
2092 |
242 |
| Cusp forms
| 14 |
14 |
0 |
| Eisenstein series
| 2320 |
2078 |
242 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2563))\)
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 |
| 2563.1.b |
\(\chi_{2563}(2562, \cdot)\) |
2563.1.b.a |
1 |
1 |
| 2563.1.b.b |
1 |
| 2563.1.b.c |
2 |
| 2563.1.b.d |
2 |
| 2563.1.c |
\(\chi_{2563}(2331, \cdot)\) |
None |
0 |
1 |
| 2563.1.e |
\(\chi_{2563}(2419, \cdot)\) |
2563.1.e.a |
4 |
2 |
| 2563.1.e.b |
4 |
| 2563.1.i |
\(\chi_{2563}(12, \cdot)\) |
None |
0 |
4 |
| 2563.1.k |
\(\chi_{2563}(700, \cdot)\) |
None |
0 |
4 |
| 2563.1.l |
\(\chi_{2563}(931, \cdot)\) |
None |
0 |
4 |
| 2563.1.n |
\(\chi_{2563}(788, \cdot)\) |
None |
0 |
8 |
| 2563.1.p |
\(\chi_{2563}(97, \cdot)\) |
None |
0 |
16 |
| 2563.1.s |
\(\chi_{2563}(32, \cdot)\) |
None |
0 |
28 |
| 2563.1.t |
\(\chi_{2563}(98, \cdot)\) |
None |
0 |
28 |
| 2563.1.v |
\(\chi_{2563}(109, \cdot)\) |
None |
0 |
56 |
| 2563.1.x |
\(\chi_{2563}(34, \cdot)\) |
None |
0 |
112 |
| 2563.1.z |
\(\chi_{2563}(29, \cdot)\) |
None |
0 |
112 |
| 2563.1.ba |
\(\chi_{2563}(2, \cdot)\) |
None |
0 |
112 |
| 2563.1.bc |
\(\chi_{2563}(7, \cdot)\) |
None |
0 |
224 |
| 2563.1.bf |
\(\chi_{2563}(3, \cdot)\) |
None |
0 |
448 |
