Defining parameters
| Level: | \( N \) | = | \( 408 = 2^{3} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(9216\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(408))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 434 | 80 | 354 |
| Cusp forms | 50 | 20 | 30 |
| Eisenstein series | 384 | 60 | 324 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 16 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(408))\)
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 |
|---|---|---|---|---|
| 408.1.b | \(\chi_{408}(101, \cdot)\) | None | 0 | 1 |
| 408.1.d | \(\chi_{408}(307, \cdot)\) | None | 0 | 1 |
| 408.1.g | \(\chi_{408}(137, \cdot)\) | None | 0 | 1 |
| 408.1.i | \(\chi_{408}(271, \cdot)\) | None | 0 | 1 |
| 408.1.k | \(\chi_{408}(103, \cdot)\) | None | 0 | 1 |
| 408.1.m | \(\chi_{408}(305, \cdot)\) | None | 0 | 1 |
| 408.1.n | \(\chi_{408}(67, \cdot)\) | None | 0 | 1 |
| 408.1.p | \(\chi_{408}(341, \cdot)\) | None | 0 | 1 |
| 408.1.r | \(\chi_{408}(115, \cdot)\) | None | 0 | 2 |
| 408.1.t | \(\chi_{408}(149, \cdot)\) | None | 0 | 2 |
| 408.1.u | \(\chi_{408}(89, \cdot)\) | 408.1.u.a | 4 | 2 |
| 408.1.w | \(\chi_{408}(55, \cdot)\) | None | 0 | 2 |
| 408.1.y | \(\chi_{408}(161, \cdot)\) | None | 0 | 4 |
| 408.1.z | \(\chi_{408}(127, \cdot)\) | None | 0 | 4 |
| 408.1.be | \(\chi_{408}(53, \cdot)\) | None | 0 | 4 |
| 408.1.bf | \(\chi_{408}(19, \cdot)\) | None | 0 | 4 |
| 408.1.bg | \(\chi_{408}(11, \cdot)\) | 408.1.bg.a | 8 | 8 |
| 408.1.bg.b | 8 | |||
| 408.1.bj | \(\chi_{408}(37, \cdot)\) | None | 0 | 8 |
| 408.1.bk | \(\chi_{408}(73, \cdot)\) | None | 0 | 8 |
| 408.1.bn | \(\chi_{408}(23, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(408))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(408)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)