Defining parameters
| Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7800.cz (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 780 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3360\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3456 | 0 | 3456 |
| Cusp forms | 3264 | 0 | 3264 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{old}}(7800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(3900, [\chi])\)\(^{\oplus 2}\)