Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(192))\).
|
Total |
New |
Old |
| Modular forms
| 146 |
24 |
122 |
| Cusp forms
| 2 |
2 |
0 |
| Eisenstein series
| 144 |
22 |
122 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)
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 |
| 192.1.b |
\(\chi_{192}(31, \cdot)\) |
None |
0 |
1 |
| 192.1.e |
\(\chi_{192}(65, \cdot)\) |
None |
0 |
1 |
| 192.1.g |
\(\chi_{192}(127, \cdot)\) |
None |
0 |
1 |
| 192.1.h |
\(\chi_{192}(161, \cdot)\) |
192.1.h.a |
2 |
1 |
| 192.1.i |
\(\chi_{192}(17, \cdot)\) |
None |
0 |
2 |
| 192.1.l |
\(\chi_{192}(79, \cdot)\) |
None |
0 |
2 |
| 192.1.m |
\(\chi_{192}(7, \cdot)\) |
None |
0 |
4 |
| 192.1.p |
\(\chi_{192}(41, \cdot)\) |
None |
0 |
4 |
| 192.1.q |
\(\chi_{192}(5, \cdot)\) |
None |
0 |
8 |
| 192.1.t |
\(\chi_{192}(19, \cdot)\) |
None |
0 |
8 |
