Defining parameters
| Level: | \( N \) | = | \( 135 = 3^{3} \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(1296\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(135))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 122 | 50 | 72 |
| Cusp forms | 2 | 2 | 0 |
| Eisenstein series | 120 | 48 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)
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 |
|---|---|---|---|---|
| 135.1.c | \(\chi_{135}(26, \cdot)\) | None | 0 | 1 |
| 135.1.d | \(\chi_{135}(134, \cdot)\) | 135.1.d.a | 1 | 1 |
| 135.1.d.b | 1 | |||
| 135.1.g | \(\chi_{135}(28, \cdot)\) | None | 0 | 2 |
| 135.1.h | \(\chi_{135}(44, \cdot)\) | None | 0 | 2 |
| 135.1.i | \(\chi_{135}(71, \cdot)\) | None | 0 | 2 |
| 135.1.l | \(\chi_{135}(37, \cdot)\) | None | 0 | 4 |
| 135.1.n | \(\chi_{135}(14, \cdot)\) | None | 0 | 6 |
| 135.1.o | \(\chi_{135}(11, \cdot)\) | None | 0 | 6 |
| 135.1.r | \(\chi_{135}(7, \cdot)\) | None | 0 | 12 |