Defining parameters
| Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 384.q (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 192 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(576\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(384, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4128 | 0 | 4128 |
| Cusp forms | 4064 | 0 | 4064 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{9}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)