Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(867))\).
|
Total |
New |
Old |
| Modular forms
| 816 |
385 |
431 |
| Cusp forms
| 16 |
16 |
0 |
| Eisenstein series
| 800 |
369 |
431 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(867))\)
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 |
| 867.1.b |
\(\chi_{867}(290, \cdot)\) |
867.1.b.a |
1 |
1 |
| 867.1.b.b |
1 |
| 867.1.c |
\(\chi_{867}(866, \cdot)\) |
867.1.c.a |
2 |
1 |
| 867.1.f |
\(\chi_{867}(38, \cdot)\) |
867.1.f.a |
4 |
2 |
| 867.1.g |
\(\chi_{867}(110, \cdot)\) |
867.1.g.a |
8 |
4 |
| 867.1.j |
\(\chi_{867}(40, \cdot)\) |
None |
0 |
8 |
| 867.1.m |
\(\chi_{867}(50, \cdot)\) |
None |
0 |
16 |
| 867.1.n |
\(\chi_{867}(35, \cdot)\) |
None |
0 |
16 |
| 867.1.o |
\(\chi_{867}(47, \cdot)\) |
None |
0 |
32 |
| 867.1.r |
\(\chi_{867}(2, \cdot)\) |
None |
0 |
64 |
| 867.1.s |
\(\chi_{867}(7, \cdot)\) |
None |
0 |
128 |
