Defining parameters
| Level: | \( N \) | = | \( 405 = 3^{4} \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(11664\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(405))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 440 | 172 | 268 |
| Cusp forms | 8 | 4 | 4 |
| Eisenstein series | 432 | 168 | 264 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(405))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 405.1.c | \(\chi_{405}(161, \cdot)\) | None | 0 | 1 |
| 405.1.d | \(\chi_{405}(404, \cdot)\) | None | 0 | 1 |
| 405.1.g | \(\chi_{405}(82, \cdot)\) | None | 0 | 2 |
| 405.1.h | \(\chi_{405}(134, \cdot)\) | 405.1.h.a | 2 | 2 |
| 405.1.h.b | 2 | |||
| 405.1.i | \(\chi_{405}(26, \cdot)\) | None | 0 | 2 |
| 405.1.l | \(\chi_{405}(28, \cdot)\) | None | 0 | 4 |
| 405.1.n | \(\chi_{405}(44, \cdot)\) | None | 0 | 6 |
| 405.1.o | \(\chi_{405}(71, \cdot)\) | None | 0 | 6 |
| 405.1.s | \(\chi_{405}(37, \cdot)\) | None | 0 | 12 |
| 405.1.u | \(\chi_{405}(11, \cdot)\) | None | 0 | 18 |
| 405.1.v | \(\chi_{405}(14, \cdot)\) | None | 0 | 18 |
| 405.1.w | \(\chi_{405}(7, \cdot)\) | None | 0 | 36 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(405)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)