Defining parameters
| Level: | \( N \) | = | \( 464 = 2^{4} \cdot 29 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(13440\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(464))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 425 | 131 | 294 |
| Cusp forms | 33 | 9 | 24 |
| Eisenstein series | 392 | 122 | 270 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 9 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(464))\)
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 |
|---|---|---|---|---|
| 464.1.b | \(\chi_{464}(231, \cdot)\) | None | 0 | 1 |
| 464.1.d | \(\chi_{464}(175, \cdot)\) | None | 0 | 1 |
| 464.1.f | \(\chi_{464}(407, \cdot)\) | None | 0 | 1 |
| 464.1.h | \(\chi_{464}(463, \cdot)\) | 464.1.h.a | 1 | 1 |
| 464.1.h.b | 2 | |||
| 464.1.i | \(\chi_{464}(133, \cdot)\) | None | 0 | 2 |
| 464.1.l | \(\chi_{464}(17, \cdot)\) | None | 0 | 2 |
| 464.1.o | \(\chi_{464}(59, \cdot)\) | None | 0 | 2 |
| 464.1.p | \(\chi_{464}(115, \cdot)\) | None | 0 | 2 |
| 464.1.r | \(\chi_{464}(41, \cdot)\) | None | 0 | 2 |
| 464.1.s | \(\chi_{464}(365, \cdot)\) | None | 0 | 2 |
| 464.1.v | \(\chi_{464}(63, \cdot)\) | 464.1.v.a | 6 | 6 |
| 464.1.x | \(\chi_{464}(7, \cdot)\) | None | 0 | 6 |
| 464.1.z | \(\chi_{464}(111, \cdot)\) | None | 0 | 6 |
| 464.1.bb | \(\chi_{464}(71, \cdot)\) | None | 0 | 6 |
| 464.1.bd | \(\chi_{464}(37, \cdot)\) | None | 0 | 12 |
| 464.1.be | \(\chi_{464}(73, \cdot)\) | None | 0 | 12 |
| 464.1.bg | \(\chi_{464}(35, \cdot)\) | None | 0 | 12 |
| 464.1.bh | \(\chi_{464}(83, \cdot)\) | None | 0 | 12 |
| 464.1.bk | \(\chi_{464}(97, \cdot)\) | None | 0 | 12 |
| 464.1.bn | \(\chi_{464}(21, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(464)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)