Defining parameters
| Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 448.u (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1296 | 0 | 1296 |
| Cusp forms | 1264 | 0 | 1264 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{6}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)