Defining parameters
| Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 840.w (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 280 \) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(768\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(840, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 584 | 288 | 296 |
| Cusp forms | 568 | 288 | 280 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(840, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(840, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)