Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(80))\).
|
Total |
New |
Old |
| Modular forms
| 57 |
15 |
42 |
| Cusp forms
| 1 |
1 |
0 |
| Eisenstein series
| 56 |
14 |
42 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)
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 |
| 80.1.b |
\(\chi_{80}(31, \cdot)\) |
None |
0 |
1 |
| 80.1.e |
\(\chi_{80}(39, \cdot)\) |
None |
0 |
1 |
| 80.1.g |
\(\chi_{80}(71, \cdot)\) |
None |
0 |
1 |
| 80.1.h |
\(\chi_{80}(79, \cdot)\) |
80.1.h.a |
1 |
1 |
| 80.1.i |
\(\chi_{80}(13, \cdot)\) |
None |
0 |
2 |
| 80.1.k |
\(\chi_{80}(19, \cdot)\) |
None |
0 |
2 |
| 80.1.m |
\(\chi_{80}(57, \cdot)\) |
None |
0 |
2 |
| 80.1.p |
\(\chi_{80}(17, \cdot)\) |
None |
0 |
2 |
| 80.1.r |
\(\chi_{80}(11, \cdot)\) |
None |
0 |
2 |
| 80.1.t |
\(\chi_{80}(53, \cdot)\) |
None |
0 |
2 |
