Defining parameters
| Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1152.x (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 96 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1600 | 128 | 1472 |
| Cusp forms | 1472 | 128 | 1344 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)