Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(327))\).
|
Total |
New |
Old |
| Modular forms
| 237 |
127 |
110 |
| Cusp forms
| 21 |
21 |
0 |
| Eisenstein series
| 216 |
106 |
110 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(327))\)
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 |
| 327.1.b |
\(\chi_{327}(110, \cdot)\) |
None |
0 |
1 |
| 327.1.d |
\(\chi_{327}(326, \cdot)\) |
327.1.d.a |
1 |
1 |
| 327.1.d.b |
1 |
| 327.1.d.c |
1 |
| 327.1.d.d |
2 |
| 327.1.g |
\(\chi_{327}(76, \cdot)\) |
None |
0 |
2 |
| 327.1.i |
\(\chi_{327}(263, \cdot)\) |
327.1.i.a |
2 |
2 |
| 327.1.j |
\(\chi_{327}(155, \cdot)\) |
327.1.j.a |
2 |
2 |
| 327.1.l |
\(\chi_{327}(226, \cdot)\) |
None |
0 |
4 |
| 327.1.n |
\(\chi_{327}(71, \cdot)\) |
327.1.n.a |
6 |
6 |
| 327.1.o |
\(\chi_{327}(38, \cdot)\) |
327.1.o.a |
6 |
6 |
| 327.1.r |
\(\chi_{327}(19, \cdot)\) |
None |
0 |
12 |
| 327.1.t |
\(\chi_{327}(20, \cdot)\) |
None |
0 |
18 |
| 327.1.v |
\(\chi_{327}(5, \cdot)\) |
None |
0 |
18 |
| 327.1.x |
\(\chi_{327}(10, \cdot)\) |
None |
0 |
36 |
