Defining parameters
| Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 768.n (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(768, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1600 | 192 | 1408 |
| Cusp forms | 1472 | 192 | 1280 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(768, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(768, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)