Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.bf (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 192 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Sturm bound: | \(1152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 6960 | 3072 | 3888 |
| Cusp forms | 6864 | 3072 | 3792 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)