Defining parameters
| Level: | \( N \) | = | \( 285 = 3 \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(5760\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(285))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 314 | 120 | 194 |
| Cusp forms | 26 | 16 | 10 |
| Eisenstein series | 288 | 104 | 184 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(285))\)
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 |
|---|---|---|---|---|
| 285.1.d | \(\chi_{285}(191, \cdot)\) | None | 0 | 1 |
| 285.1.e | \(\chi_{285}(151, \cdot)\) | None | 0 | 1 |
| 285.1.f | \(\chi_{285}(134, \cdot)\) | None | 0 | 1 |
| 285.1.g | \(\chi_{285}(94, \cdot)\) | None | 0 | 1 |
| 285.1.j | \(\chi_{285}(113, \cdot)\) | None | 0 | 2 |
| 285.1.l | \(\chi_{285}(58, \cdot)\) | None | 0 | 2 |
| 285.1.n | \(\chi_{285}(239, \cdot)\) | 285.1.n.a | 2 | 2 |
| 285.1.n.b | 2 | |||
| 285.1.o | \(\chi_{285}(259, \cdot)\) | None | 0 | 2 |
| 285.1.s | \(\chi_{285}(11, \cdot)\) | None | 0 | 2 |
| 285.1.t | \(\chi_{285}(31, \cdot)\) | None | 0 | 2 |
| 285.1.w | \(\chi_{285}(8, \cdot)\) | None | 0 | 4 |
| 285.1.y | \(\chi_{285}(7, \cdot)\) | None | 0 | 4 |
| 285.1.ba | \(\chi_{285}(91, \cdot)\) | None | 0 | 6 |
| 285.1.bb | \(\chi_{285}(101, \cdot)\) | None | 0 | 6 |
| 285.1.bc | \(\chi_{285}(34, \cdot)\) | None | 0 | 6 |
| 285.1.bd | \(\chi_{285}(44, \cdot)\) | 285.1.bd.a | 6 | 6 |
| 285.1.bd.b | 6 | |||
| 285.1.bg | \(\chi_{285}(28, \cdot)\) | None | 0 | 12 |
| 285.1.bj | \(\chi_{285}(2, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(285))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(285)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)