Defining parameters
| Level: | \( N \) | \(=\) | \( 8800 = 2^{5} \cdot 5^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8800.gk (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4400 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2880\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 11584 | 0 | 11584 |
| Cusp forms | 11456 | 0 | 11456 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{old}}(8800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(4400, [\chi])\)\(^{\oplus 2}\)