Defining parameters
| Level: | \( N \) | = | \( 2 \) |
| Weight: | \( k \) | = | \( 32 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(8\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(2))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9 | 3 | 6 |
| Cusp forms | 7 | 3 | 4 |
| Eisenstein series | 2 | 0 | 2 |
Trace form
Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(2))\)
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 |
|---|---|---|---|---|
| 2.32.a | \(\chi_{2}(1, \cdot)\) | 2.32.a.a | 1 | 1 |
| 2.32.a.b | 2 |
Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces
\( S_{32}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)