Defining parameters
| Level: | \( N \) | = | \( 356 = 2^{2} \cdot 89 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(7920\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(356))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 245 | 111 | 134 |
| Cusp forms | 25 | 25 | 0 |
| Eisenstein series | 220 | 86 | 134 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 25 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(356))\)
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 |
|---|---|---|---|---|
| 356.1.b | \(\chi_{356}(179, \cdot)\) | None | 0 | 1 |
| 356.1.d | \(\chi_{356}(355, \cdot)\) | 356.1.d.a | 1 | 1 |
| 356.1.d.b | 1 | |||
| 356.1.d.c | 1 | |||
| 356.1.d.d | 2 | |||
| 356.1.e | \(\chi_{356}(55, \cdot)\) | None | 0 | 2 |
| 356.1.g | \(\chi_{356}(37, \cdot)\) | None | 0 | 4 |
| 356.1.j | \(\chi_{356}(11, \cdot)\) | 356.1.j.a | 10 | 10 |
| 356.1.l | \(\chi_{356}(39, \cdot)\) | 356.1.l.a | 10 | 10 |
| 356.1.n | \(\chi_{356}(47, \cdot)\) | None | 0 | 20 |
| 356.1.p | \(\chi_{356}(13, \cdot)\) | None | 0 | 40 |