Defining parameters
| Level: | \( N \) | = | \( 435 = 3 \cdot 5 \cdot 29 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(13440\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(435))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 464 | 168 | 296 |
| Cusp forms | 16 | 4 | 12 |
| Eisenstein series | 448 | 164 | 284 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(435))\)
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 |
|---|---|---|---|---|
| 435.1.b | \(\chi_{435}(434, \cdot)\) | 435.1.b.a | 4 | 1 |
| 435.1.e | \(\chi_{435}(146, \cdot)\) | None | 0 | 1 |
| 435.1.g | \(\chi_{435}(59, \cdot)\) | None | 0 | 1 |
| 435.1.h | \(\chi_{435}(86, \cdot)\) | None | 0 | 1 |
| 435.1.i | \(\chi_{435}(17, \cdot)\) | None | 0 | 2 |
| 435.1.k | \(\chi_{435}(244, \cdot)\) | None | 0 | 2 |
| 435.1.n | \(\chi_{435}(28, \cdot)\) | None | 0 | 2 |
| 435.1.o | \(\chi_{435}(88, \cdot)\) | None | 0 | 2 |
| 435.1.r | \(\chi_{435}(46, \cdot)\) | None | 0 | 2 |
| 435.1.t | \(\chi_{435}(278, \cdot)\) | None | 0 | 2 |
| 435.1.v | \(\chi_{435}(71, \cdot)\) | None | 0 | 6 |
| 435.1.w | \(\chi_{435}(74, \cdot)\) | None | 0 | 6 |
| 435.1.y | \(\chi_{435}(161, \cdot)\) | None | 0 | 6 |
| 435.1.bb | \(\chi_{435}(149, \cdot)\) | None | 0 | 6 |
| 435.1.bc | \(\chi_{435}(47, \cdot)\) | None | 0 | 12 |
| 435.1.be | \(\chi_{435}(31, \cdot)\) | None | 0 | 12 |
| 435.1.bh | \(\chi_{435}(7, \cdot)\) | None | 0 | 12 |
| 435.1.bi | \(\chi_{435}(13, \cdot)\) | None | 0 | 12 |
| 435.1.bl | \(\chi_{435}(19, \cdot)\) | None | 0 | 12 |
| 435.1.bn | \(\chi_{435}(2, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(435)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)