Defining parameters
| Level: | \( N \) | = | \( 1328 = 2^{4} \cdot 83 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(110208\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1328))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1254 | 369 | 885 |
| Cusp forms | 106 | 4 | 102 |
| Eisenstein series | 1148 | 365 | 783 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(1328))\)
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 |
|---|---|---|---|---|
| 1328.1.d | \(\chi_{1328}(831, \cdot)\) | None | 0 | 1 |
| 1328.1.e | \(\chi_{1328}(1161, \cdot)\) | None | 0 | 1 |
| 1328.1.f | \(\chi_{1328}(167, \cdot)\) | None | 0 | 1 |
| 1328.1.g | \(\chi_{1328}(497, \cdot)\) | 1328.1.g.a | 1 | 1 |
| 1328.1.g.b | 3 | |||
| 1328.1.i | \(\chi_{1328}(165, \cdot)\) | None | 0 | 2 |
| 1328.1.k | \(\chi_{1328}(499, \cdot)\) | None | 0 | 2 |
| 1328.1.o | \(\chi_{1328}(97, \cdot)\) | None | 0 | 40 |
| 1328.1.p | \(\chi_{1328}(7, \cdot)\) | None | 0 | 40 |
| 1328.1.q | \(\chi_{1328}(57, \cdot)\) | None | 0 | 40 |
| 1328.1.r | \(\chi_{1328}(31, \cdot)\) | None | 0 | 40 |
| 1328.1.v | \(\chi_{1328}(3, \cdot)\) | None | 0 | 80 |
| 1328.1.x | \(\chi_{1328}(5, \cdot)\) | None | 0 | 80 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1328))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1328)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(664))\)\(^{\oplus 2}\)