Defining parameters
| Level: | \( N \) | = | \( 204 = 2^{2} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(2304\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(204))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 168 | 34 | 134 |
| Cusp forms | 8 | 2 | 6 |
| Eisenstein series | 160 | 32 | 128 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)
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 |
|---|---|---|---|---|
| 204.1.d | \(\chi_{204}(137, \cdot)\) | None | 0 | 1 |
| 204.1.e | \(\chi_{204}(67, \cdot)\) | None | 0 | 1 |
| 204.1.f | \(\chi_{204}(103, \cdot)\) | None | 0 | 1 |
| 204.1.g | \(\chi_{204}(101, \cdot)\) | 204.1.g.a | 1 | 1 |
| 204.1.g.b | 1 | |||
| 204.1.i | \(\chi_{204}(89, \cdot)\) | None | 0 | 2 |
| 204.1.k | \(\chi_{204}(55, \cdot)\) | None | 0 | 2 |
| 204.1.m | \(\chi_{204}(53, \cdot)\) | None | 0 | 4 |
| 204.1.n | \(\chi_{204}(19, \cdot)\) | None | 0 | 4 |
| 204.1.s | \(\chi_{204}(37, \cdot)\) | None | 0 | 8 |
| 204.1.t | \(\chi_{204}(11, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(204))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(204)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)