Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(583))\).
|
Total |
New |
Old |
| Modular forms
| 547 |
485 |
62 |
| Cusp forms
| 27 |
27 |
0 |
| Eisenstein series
| 520 |
458 |
62 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(583))\)
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 |
| 583.1.c |
\(\chi_{583}(54, \cdot)\) |
None |
0 |
1 |
| 583.1.d |
\(\chi_{583}(582, \cdot)\) |
583.1.d.a |
1 |
1 |
| 583.1.d.b |
2 |
| 583.1.e |
\(\chi_{583}(23, \cdot)\) |
None |
0 |
2 |
| 583.1.h |
\(\chi_{583}(52, \cdot)\) |
None |
0 |
4 |
| 583.1.i |
\(\chi_{583}(107, \cdot)\) |
None |
0 |
4 |
| 583.1.m |
\(\chi_{583}(136, \cdot)\) |
None |
0 |
8 |
| 583.1.n |
\(\chi_{583}(43, \cdot)\) |
583.1.n.a |
12 |
12 |
| 583.1.o |
\(\chi_{583}(10, \cdot)\) |
583.1.o.a |
12 |
12 |
| 583.1.r |
\(\chi_{583}(12, \cdot)\) |
None |
0 |
24 |
| 583.1.u |
\(\chi_{583}(13, \cdot)\) |
None |
0 |
48 |
| 583.1.v |
\(\chi_{583}(6, \cdot)\) |
None |
0 |
48 |
| 583.1.w |
\(\chi_{583}(3, \cdot)\) |
None |
0 |
96 |
