Defining parameters
| Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 416.bf (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(224\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(416, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 680 | 576 | 104 |
| Cusp forms | 664 | 576 | 88 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(416, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(416, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(416, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)