Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(133))\).
|
Total |
New |
Old |
| Modular forms
| 114 |
90 |
24 |
| Cusp forms
| 6 |
6 |
0 |
| Eisenstein series
| 108 |
84 |
24 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)
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 |
| 133.1.b |
\(\chi_{133}(113, \cdot)\) |
None |
0 |
1 |
| 133.1.d |
\(\chi_{133}(20, \cdot)\) |
None |
0 |
1 |
| 133.1.j |
\(\chi_{133}(46, \cdot)\) |
None |
0 |
2 |
| 133.1.k |
\(\chi_{133}(45, \cdot)\) |
None |
0 |
2 |
| 133.1.l |
\(\chi_{133}(96, \cdot)\) |
None |
0 |
2 |
| 133.1.m |
\(\chi_{133}(83, \cdot)\) |
133.1.m.a |
4 |
2 |
| 133.1.n |
\(\chi_{133}(65, \cdot)\) |
None |
0 |
2 |
| 133.1.q |
\(\chi_{133}(8, \cdot)\) |
None |
0 |
2 |
| 133.1.r |
\(\chi_{133}(18, \cdot)\) |
133.1.r.a |
2 |
2 |
| 133.1.t |
\(\chi_{133}(26, \cdot)\) |
None |
0 |
2 |
| 133.1.x |
\(\chi_{133}(17, \cdot)\) |
None |
0 |
6 |
| 133.1.y |
\(\chi_{133}(6, \cdot)\) |
None |
0 |
6 |
| 133.1.z |
\(\chi_{133}(5, \cdot)\) |
None |
0 |
6 |
| 133.1.bc |
\(\chi_{133}(15, \cdot)\) |
None |
0 |
6 |
| 133.1.bd |
\(\chi_{133}(51, \cdot)\) |
None |
0 |
6 |
| 133.1.be |
\(\chi_{133}(2, \cdot)\) |
None |
0 |
6 |
