Defining parameters
| Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2160.cr (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 720 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(1728\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5232 | 1744 | 3488 |
| Cusp forms | 5136 | 1712 | 3424 |
| Eisenstein series | 96 | 32 | 64 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)