Defining parameters
| Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1680.g (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| 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 | 1168 | 0 | 1168 |
| Cusp forms | 1136 | 0 | 1136 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1680, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)