Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(120))\).
|
Total |
New |
Old |
| Modular forms
| 98 |
14 |
84 |
| Cusp forms
| 2 |
2 |
0 |
| Eisenstein series
| 96 |
12 |
84 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)
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 |
| 120.1.c |
\(\chi_{120}(89, \cdot)\) |
None |
0 |
1 |
| 120.1.e |
\(\chi_{120}(31, \cdot)\) |
None |
0 |
1 |
| 120.1.g |
\(\chi_{120}(91, \cdot)\) |
None |
0 |
1 |
| 120.1.i |
\(\chi_{120}(29, \cdot)\) |
120.1.i.a |
2 |
1 |
| 120.1.j |
\(\chi_{120}(79, \cdot)\) |
None |
0 |
1 |
| 120.1.l |
\(\chi_{120}(41, \cdot)\) |
None |
0 |
1 |
| 120.1.n |
\(\chi_{120}(101, \cdot)\) |
None |
0 |
1 |
| 120.1.p |
\(\chi_{120}(19, \cdot)\) |
None |
0 |
1 |
| 120.1.q |
\(\chi_{120}(83, \cdot)\) |
None |
0 |
2 |
| 120.1.t |
\(\chi_{120}(13, \cdot)\) |
None |
0 |
2 |
| 120.1.u |
\(\chi_{120}(73, \cdot)\) |
None |
0 |
2 |
| 120.1.x |
\(\chi_{120}(23, \cdot)\) |
None |
0 |
2 |
