Defining parameters
| Level: | \( N \) | \(=\) | \( 40320 = 2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 40320.he (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 840 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(18432\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(40320, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 18688 | 1536 | 17152 |
| Cusp forms | 18176 | 1536 | 16640 |
| Eisenstein series | 512 | 0 | 512 |
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
\( S_{2}^{\mathrm{old}}(40320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2520, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3360, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(6720, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(10080, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(13440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(20160, [\chi])\)\(^{\oplus 2}\)