Defining parameters
| Level: | \( N \) | = | \( 195 = 3 \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(2688\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(195))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 198 | 72 | 126 |
| Cusp forms | 6 | 4 | 2 |
| Eisenstein series | 192 | 68 | 124 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(195))\)
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 |
|---|---|---|---|---|
| 195.1.d | \(\chi_{195}(131, \cdot)\) | None | 0 | 1 |
| 195.1.e | \(\chi_{195}(194, \cdot)\) | 195.1.e.a | 4 | 1 |
| 195.1.f | \(\chi_{195}(14, \cdot)\) | None | 0 | 1 |
| 195.1.g | \(\chi_{195}(116, \cdot)\) | None | 0 | 1 |
| 195.1.j | \(\chi_{195}(8, \cdot)\) | None | 0 | 2 |
| 195.1.l | \(\chi_{195}(103, \cdot)\) | None | 0 | 2 |
| 195.1.p | \(\chi_{195}(31, \cdot)\) | None | 0 | 2 |
| 195.1.q | \(\chi_{195}(34, \cdot)\) | None | 0 | 2 |
| 195.1.r | \(\chi_{195}(118, \cdot)\) | None | 0 | 2 |
| 195.1.u | \(\chi_{195}(47, \cdot)\) | None | 0 | 2 |
| 195.1.w | \(\chi_{195}(56, \cdot)\) | None | 0 | 2 |
| 195.1.x | \(\chi_{195}(29, \cdot)\) | None | 0 | 2 |
| 195.1.y | \(\chi_{195}(134, \cdot)\) | None | 0 | 2 |
| 195.1.z | \(\chi_{195}(146, \cdot)\) | None | 0 | 2 |
| 195.1.bc | \(\chi_{195}(137, \cdot)\) | None | 0 | 4 |
| 195.1.be | \(\chi_{195}(22, \cdot)\) | None | 0 | 4 |
| 195.1.bi | \(\chi_{195}(19, \cdot)\) | None | 0 | 4 |
| 195.1.bj | \(\chi_{195}(46, \cdot)\) | None | 0 | 4 |
| 195.1.bk | \(\chi_{195}(43, \cdot)\) | None | 0 | 4 |
| 195.1.bn | \(\chi_{195}(2, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(195))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(195)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)