Defining parameters
| Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1440.co (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 160 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(1152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1440, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3488 | 1448 | 2040 |
| Cusp forms | 3424 | 1432 | 1992 |
| Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)