Defining parameters
| Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1680.dh (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 840 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1536\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1680, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2336 | 0 | 2336 |
| Cusp forms | 2272 | 0 | 2272 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{4}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1680, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)