Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(63))\).
|
Total |
New |
Old |
| Modular forms
| 49 |
24 |
25 |
| Cusp forms
| 1 |
1 |
0 |
| Eisenstein series
| 48 |
23 |
25 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)
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 |
| 63.1.b |
\(\chi_{63}(8, \cdot)\) |
None |
0 |
1 |
| 63.1.d |
\(\chi_{63}(55, \cdot)\) |
63.1.d.a |
1 |
1 |
| 63.1.j |
\(\chi_{63}(11, \cdot)\) |
None |
0 |
2 |
| 63.1.k |
\(\chi_{63}(31, \cdot)\) |
None |
0 |
2 |
| 63.1.l |
\(\chi_{63}(13, \cdot)\) |
None |
0 |
2 |
| 63.1.m |
\(\chi_{63}(10, \cdot)\) |
None |
0 |
2 |
| 63.1.n |
\(\chi_{63}(2, \cdot)\) |
None |
0 |
2 |
| 63.1.q |
\(\chi_{63}(44, \cdot)\) |
None |
0 |
2 |
| 63.1.r |
\(\chi_{63}(29, \cdot)\) |
None |
0 |
2 |
| 63.1.t |
\(\chi_{63}(40, \cdot)\) |
None |
0 |
2 |
