Defining parameters
| Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 448.z (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 112 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(256\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 800 | 200 | 600 |
| Cusp forms | 736 | 184 | 552 |
| Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(448, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)