Defining parameters
| Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 768.bb (of order \(64\) and degree \(32\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 256 \) |
| Character field: | \(\Q(\zeta_{64})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8256 | 4096 | 4160 |
| Cusp forms | 8128 | 4096 | 4032 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(768, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)