Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(175))\).
|
Total |
New |
Old |
| Modular forms
| 172 |
107 |
65 |
| Cusp forms
| 4 |
4 |
0 |
| Eisenstein series
| 168 |
103 |
65 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)
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 |
| 175.1.c |
\(\chi_{175}(174, \cdot)\) |
175.1.c.a |
2 |
1 |
| 175.1.d |
\(\chi_{175}(76, \cdot)\) |
175.1.d.a |
1 |
1 |
| 175.1.d.b |
1 |
| 175.1.g |
\(\chi_{175}(43, \cdot)\) |
None |
0 |
2 |
| 175.1.i |
\(\chi_{175}(26, \cdot)\) |
None |
0 |
2 |
| 175.1.j |
\(\chi_{175}(24, \cdot)\) |
None |
0 |
2 |
| 175.1.l |
\(\chi_{175}(6, \cdot)\) |
None |
0 |
4 |
| 175.1.m |
\(\chi_{175}(34, \cdot)\) |
None |
0 |
4 |
| 175.1.p |
\(\chi_{175}(18, \cdot)\) |
None |
0 |
4 |
| 175.1.r |
\(\chi_{175}(8, \cdot)\) |
None |
0 |
8 |
| 175.1.u |
\(\chi_{175}(19, \cdot)\) |
None |
0 |
8 |
| 175.1.v |
\(\chi_{175}(31, \cdot)\) |
None |
0 |
8 |
| 175.1.w |
\(\chi_{175}(2, \cdot)\) |
None |
0 |
16 |
