Defining parameters
| Level: | \( N \) | = | \( 118 = 2 \cdot 59 \) |
| Weight: | \( k \) | = | \( 6 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Sturm bound: | \(5220\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(118))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2233 | 725 | 1508 |
| Cusp forms | 2117 | 725 | 1392 |
| Eisenstein series | 116 | 0 | 116 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(118))\)
We only show spaces with even 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 |
|---|---|---|---|---|
| 118.6.a | \(\chi_{118}(1, \cdot)\) | 118.6.a.a | 5 | 1 |
| 118.6.a.b | 6 | |||
| 118.6.a.c | 6 | |||
| 118.6.a.d | 8 | |||
| 118.6.c | \(\chi_{118}(3, \cdot)\) | n/a | 700 | 28 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(118))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(118)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)