Defining parameters
| Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2160.dz (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 540 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Sturm bound: | \(1728\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 15696 | 3888 | 11808 |
| Cusp forms | 15408 | 3888 | 11520 |
| Eisenstein series | 288 | 0 | 288 |
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
\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)