Defining parameters
| Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 384.r (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 64 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(512\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(384, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3616 | 0 | 3616 |
| Cusp forms | 3552 | 0 | 3552 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{8}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)