Defining parameters
| Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 414.m (of order \(33\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 207 \) |
| Character field: | \(\Q(\zeta_{33})\) | ||
| Sturm bound: | \(288\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(414, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4400 | 1440 | 2960 |
| Cusp forms | 4240 | 1440 | 2800 |
| Eisenstein series | 160 | 0 | 160 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(414, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(414, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)