Defining parameters
| Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5040.ft (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 168 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2304\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5040, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2368 | 0 | 2368 |
| Cusp forms | 2240 | 0 | 2240 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{old}}(5040, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2520, [\chi])\)\(^{\oplus 2}\)