Defining parameters
| Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 336.bf (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(576\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(336, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1040 | 0 | 1040 |
| Cusp forms | 1008 | 0 | 1008 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{9}^{\mathrm{old}}(336, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(336, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)