Defining parameters
| Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1680.bi (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1680, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1584 | 192 | 1392 |
| Cusp forms | 1488 | 192 | 1296 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1680, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)