Defining parameters
| Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 448.p (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 664 | 164 | 500 |
| Cusp forms | 616 | 156 | 460 |
| Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)