Defining parameters
| Level: | \( N \) | = | \( 355 = 5 \cdot 71 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(10080\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(355))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 293 | 213 | 80 |
| Cusp forms | 13 | 7 | 6 |
| Eisenstein series | 280 | 206 | 74 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(355))\)
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 |
|---|---|---|---|---|
| 355.1.c | \(\chi_{355}(354, \cdot)\) | 355.1.c.a | 1 | 1 |
| 355.1.c.b | 6 | |||
| 355.1.d | \(\chi_{355}(141, \cdot)\) | None | 0 | 1 |
| 355.1.f | \(\chi_{355}(72, \cdot)\) | None | 0 | 2 |
| 355.1.i | \(\chi_{355}(46, \cdot)\) | None | 0 | 4 |
| 355.1.j | \(\chi_{355}(14, \cdot)\) | None | 0 | 4 |
| 355.1.l | \(\chi_{355}(26, \cdot)\) | None | 0 | 6 |
| 355.1.m | \(\chi_{355}(34, \cdot)\) | None | 0 | 6 |
| 355.1.o | \(\chi_{355}(57, \cdot)\) | None | 0 | 8 |
| 355.1.q | \(\chi_{355}(32, \cdot)\) | None | 0 | 12 |
| 355.1.u | \(\chi_{355}(44, \cdot)\) | None | 0 | 24 |
| 355.1.v | \(\chi_{355}(11, \cdot)\) | None | 0 | 24 |
| 355.1.x | \(\chi_{355}(2, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(355))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(355)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 2}\)