Defining parameters
| Level: | \( N \) | = | \( 368 = 2^{4} \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(8448\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(368))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 326 | 102 | 224 |
| Cusp forms | 18 | 7 | 11 |
| Eisenstein series | 308 | 95 | 213 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(368))\)
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 |
|---|---|---|---|---|
| 368.1.d | \(\chi_{368}(47, \cdot)\) | None | 0 | 1 |
| 368.1.e | \(\chi_{368}(137, \cdot)\) | None | 0 | 1 |
| 368.1.f | \(\chi_{368}(321, \cdot)\) | 368.1.f.a | 1 | 1 |
| 368.1.g | \(\chi_{368}(231, \cdot)\) | None | 0 | 1 |
| 368.1.k | \(\chi_{368}(45, \cdot)\) | 368.1.k.a | 2 | 2 |
| 368.1.k.b | 4 | |||
| 368.1.l | \(\chi_{368}(139, \cdot)\) | None | 0 | 2 |
| 368.1.o | \(\chi_{368}(39, \cdot)\) | None | 0 | 10 |
| 368.1.p | \(\chi_{368}(17, \cdot)\) | None | 0 | 10 |
| 368.1.q | \(\chi_{368}(57, \cdot)\) | None | 0 | 10 |
| 368.1.r | \(\chi_{368}(31, \cdot)\) | None | 0 | 10 |
| 368.1.u | \(\chi_{368}(3, \cdot)\) | None | 0 | 20 |
| 368.1.v | \(\chi_{368}(5, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)