Defining parameters
| Level: | \( N \) | \(=\) | \( 8640 = 2^{6} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8640.hw (of order \(144\) and degree \(48\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1728 \) |
| Character field: | \(\Q(\zeta_{144})\) | ||
| Sturm bound: | \(3456\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8640, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 83136 | 55296 | 27840 |
| Cusp forms | 82752 | 55296 | 27456 |
| Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{new}}(8640, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8640, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)