Defining parameters
| Level: | \( N \) | = | \( 155 = 5 \cdot 31 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(1920\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(155))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 125 | 89 | 36 |
| Cusp forms | 5 | 3 | 2 |
| Eisenstein series | 120 | 86 | 34 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)
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 |
|---|---|---|---|---|
| 155.1.c | \(\chi_{155}(154, \cdot)\) | 155.1.c.a | 1 | 1 |
| 155.1.c.b | 2 | |||
| 155.1.d | \(\chi_{155}(61, \cdot)\) | None | 0 | 1 |
| 155.1.g | \(\chi_{155}(32, \cdot)\) | None | 0 | 2 |
| 155.1.i | \(\chi_{155}(99, \cdot)\) | None | 0 | 2 |
| 155.1.k | \(\chi_{155}(6, \cdot)\) | None | 0 | 2 |
| 155.1.l | \(\chi_{155}(46, \cdot)\) | None | 0 | 4 |
| 155.1.m | \(\chi_{155}(29, \cdot)\) | None | 0 | 4 |
| 155.1.o | \(\chi_{155}(67, \cdot)\) | None | 0 | 4 |
| 155.1.s | \(\chi_{155}(2, \cdot)\) | None | 0 | 8 |
| 155.1.t | \(\chi_{155}(11, \cdot)\) | None | 0 | 8 |
| 155.1.v | \(\chi_{155}(24, \cdot)\) | None | 0 | 8 |
| 155.1.w | \(\chi_{155}(7, \cdot)\) | None | 0 | 16 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)