Defining parameters
| Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 10 \) |
| Character orbit: | \([\chi]\) | \(=\) | 80.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(120\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(80, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 112 | 0 | 112 |
| Cusp forms | 104 | 0 | 104 |
| Eisenstein series | 8 | 0 | 8 |
Decomposition of \(S_{10}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)