Defining parameters
| Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1792.w (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(768\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1792, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2112 | 384 | 1728 |
| Cusp forms | 1984 | 384 | 1600 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)