Defining parameters
| Level: | \( N \) | = | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(12672\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(460))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 468 | 150 | 318 |
| Cusp forms | 28 | 22 | 6 |
| Eisenstein series | 440 | 128 | 312 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 22 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(460))\)
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 |
|---|---|---|---|---|
| 460.1.b | \(\chi_{460}(231, \cdot)\) | None | 0 | 1 |
| 460.1.d | \(\chi_{460}(229, \cdot)\) | 460.1.d.a | 1 | 1 |
| 460.1.d.b | 1 | |||
| 460.1.f | \(\chi_{460}(321, \cdot)\) | None | 0 | 1 |
| 460.1.h | \(\chi_{460}(139, \cdot)\) | None | 0 | 1 |
| 460.1.k | \(\chi_{460}(183, \cdot)\) | None | 0 | 2 |
| 460.1.l | \(\chi_{460}(93, \cdot)\) | None | 0 | 2 |
| 460.1.n | \(\chi_{460}(39, \cdot)\) | 460.1.n.a | 10 | 10 |
| 460.1.n.b | 10 | |||
| 460.1.p | \(\chi_{460}(21, \cdot)\) | None | 0 | 10 |
| 460.1.r | \(\chi_{460}(89, \cdot)\) | None | 0 | 10 |
| 460.1.t | \(\chi_{460}(31, \cdot)\) | None | 0 | 10 |
| 460.1.u | \(\chi_{460}(13, \cdot)\) | None | 0 | 20 |
| 460.1.v | \(\chi_{460}(7, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(460))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(460)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)