Defining parameters
| Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 64.h (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(72\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(64, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 264 | 0 | 264 |
| Cusp forms | 248 | 0 | 248 |
| Eisenstein series | 16 | 0 | 16 |
Decomposition of \(S_{9}^{\mathrm{old}}(64, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)