Defining parameters
| Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 40.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(36\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(40, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 68 | 0 | 68 |
| Cusp forms | 52 | 0 | 52 |
| Eisenstein series | 16 | 0 | 16 |
Decomposition of \(S_{6}^{\mathrm{old}}(40, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)