Defining parameters
| Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8040.ha (of order \(132\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1340 \) |
| Character field: | \(\Q(\zeta_{132})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3264\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8040, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 65920 | 0 | 65920 |
| Cusp forms | 64640 | 0 | 64640 |
| Eisenstein series | 1280 | 0 | 1280 |
Decomposition of \(S_{2}^{\mathrm{old}}(8040, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1340, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4020, [\chi])\)\(^{\oplus 2}\)