Defining parameters
| Level: | \( N \) | \(=\) | \( 40320 = 2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 40320.nb (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5040 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(18432\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(40320, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 37120 | 9280 | 27840 |
| Cusp forms | 36608 | 9152 | 27456 |
| Eisenstein series | 512 | 128 | 384 |
Decomposition of \(S_{2}^{\mathrm{new}}(40320, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(40320, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(40320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(5040, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(20160, [\chi])\)\(^{\oplus 2}\)