Defining parameters
| Level: | \( N \) | = | \( 5 \) |
| Weight: | \( k \) | = | \( 34 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(68\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(5))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 35 | 29 | 6 |
| Cusp forms | 31 | 27 | 4 |
| Eisenstein series | 4 | 2 | 2 |
Trace form
Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(5))\)
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 |
|---|---|---|---|---|
| 5.34.a | \(\chi_{5}(1, \cdot)\) | 5.34.a.a | 5 | 1 |
| 5.34.a.b | 6 | |||
| 5.34.b | \(\chi_{5}(4, \cdot)\) | 5.34.b.a | 16 | 1 |
Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces
\( S_{34}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)