Defining parameters
| Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 768.u (of order \(32\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 128 \) |
| Character field: | \(\Q(\zeta_{32})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4160 | 0 | 4160 |
| Cusp forms | 4032 | 0 | 4032 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)