Defining parameters
| Level: | \( N \) | = | \( 304 = 2^{4} \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(5760\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(304))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 276 | 78 | 198 |
| Cusp forms | 24 | 1 | 23 |
| Eisenstein series | 252 | 77 | 175 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)
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 |
|---|---|---|---|---|
| 304.1.d | \(\chi_{304}(191, \cdot)\) | None | 0 | 1 |
| 304.1.e | \(\chi_{304}(113, \cdot)\) | 304.1.e.a | 1 | 1 |
| 304.1.f | \(\chi_{304}(39, \cdot)\) | None | 0 | 1 |
| 304.1.g | \(\chi_{304}(265, \cdot)\) | None | 0 | 1 |
| 304.1.j | \(\chi_{304}(37, \cdot)\) | None | 0 | 2 |
| 304.1.l | \(\chi_{304}(115, \cdot)\) | None | 0 | 2 |
| 304.1.o | \(\chi_{304}(7, \cdot)\) | None | 0 | 2 |
| 304.1.p | \(\chi_{304}(217, \cdot)\) | None | 0 | 2 |
| 304.1.q | \(\chi_{304}(159, \cdot)\) | None | 0 | 2 |
| 304.1.r | \(\chi_{304}(65, \cdot)\) | None | 0 | 2 |
| 304.1.w | \(\chi_{304}(69, \cdot)\) | None | 0 | 4 |
| 304.1.y | \(\chi_{304}(11, \cdot)\) | None | 0 | 4 |
| 304.1.z | \(\chi_{304}(33, \cdot)\) | None | 0 | 6 |
| 304.1.ba | \(\chi_{304}(41, \cdot)\) | None | 0 | 6 |
| 304.1.bc | \(\chi_{304}(23, \cdot)\) | None | 0 | 6 |
| 304.1.bf | \(\chi_{304}(47, \cdot)\) | None | 0 | 6 |
| 304.1.bh | \(\chi_{304}(35, \cdot)\) | None | 0 | 12 |
| 304.1.bj | \(\chi_{304}(13, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)