Defining parameters
| Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 448.m (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 912 | 168 | 744 |
| Cusp forms | 880 | 168 | 712 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{8}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(448, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)