Defining parameters
| Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 432.l (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(432, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1020 | 448 | 572 |
| Cusp forms | 996 | 448 | 548 |
| Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(432, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{8}^{\mathrm{old}}(432, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)