Defining parameters
| Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1728.v (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1152\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3504 | 0 | 3504 |
| Cusp forms | 3408 | 0 | 3408 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)