Defining parameters
| Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 32.e (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(16\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(32, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 28 | 0 | 28 |
| Cusp forms | 20 | 0 | 20 |
| Eisenstein series | 8 | 0 | 8 |
Decomposition of \(S_{4}^{\mathrm{old}}(32, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)