Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(180))\).
|
Total |
New |
Old |
| Modular forms
| 170 |
36 |
134 |
| Cusp forms
| 10 |
10 |
0 |
| Eisenstein series
| 160 |
26 |
134 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)
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 |
| 180.1.b |
\(\chi_{180}(89, \cdot)\) |
None |
0 |
1 |
| 180.1.c |
\(\chi_{180}(91, \cdot)\) |
None |
0 |
1 |
| 180.1.f |
\(\chi_{180}(19, \cdot)\) |
180.1.f.a |
2 |
1 |
| 180.1.g |
\(\chi_{180}(161, \cdot)\) |
None |
0 |
1 |
| 180.1.l |
\(\chi_{180}(37, \cdot)\) |
None |
0 |
2 |
| 180.1.m |
\(\chi_{180}(107, \cdot)\) |
180.1.m.a |
4 |
2 |
| 180.1.o |
\(\chi_{180}(41, \cdot)\) |
None |
0 |
2 |
| 180.1.p |
\(\chi_{180}(79, \cdot)\) |
180.1.p.a |
2 |
2 |
| 180.1.p.b |
2 |
| 180.1.s |
\(\chi_{180}(31, \cdot)\) |
None |
0 |
2 |
| 180.1.t |
\(\chi_{180}(29, \cdot)\) |
None |
0 |
2 |
| 180.1.u |
\(\chi_{180}(13, \cdot)\) |
None |
0 |
4 |
| 180.1.v |
\(\chi_{180}(23, \cdot)\) |
None |
0 |
4 |
