Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(244))\).
|
Total |
New |
Old |
| Modular forms
| 166 |
74 |
92 |
| Cusp forms
| 16 |
16 |
0 |
| Eisenstein series
| 150 |
58 |
92 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(244))\)
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 |
| 244.1.b |
\(\chi_{244}(123, \cdot)\) |
None |
0 |
1 |
| 244.1.c |
\(\chi_{244}(243, \cdot)\) |
244.1.c.a |
1 |
1 |
| 244.1.c.b |
1 |
| 244.1.f |
\(\chi_{244}(133, \cdot)\) |
None |
0 |
2 |
| 244.1.i |
\(\chi_{244}(75, \cdot)\) |
None |
0 |
2 |
| 244.1.j |
\(\chi_{244}(47, \cdot)\) |
244.1.j.a |
2 |
2 |
| 244.1.m |
\(\chi_{244}(3, \cdot)\) |
None |
0 |
4 |
| 244.1.n |
\(\chi_{244}(95, \cdot)\) |
244.1.n.a |
4 |
4 |
| 244.1.o |
\(\chi_{244}(21, \cdot)\) |
None |
0 |
4 |
| 244.1.s |
\(\chi_{244}(33, \cdot)\) |
None |
0 |
8 |
| 244.1.u |
\(\chi_{244}(15, \cdot)\) |
244.1.u.a |
8 |
8 |
| 244.1.v |
\(\chi_{244}(19, \cdot)\) |
None |
0 |
8 |
| 244.1.x |
\(\chi_{244}(17, \cdot)\) |
None |
0 |
16 |
