Defining parameters
| Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9800.hb (of order \(210\) and degree \(48\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4900 \) |
| Character field: | \(\Q(\zeta_{210})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3360\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 81024 | 0 | 81024 |
| Cusp forms | 80256 | 0 | 80256 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(9800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4900, [\chi])\)\(^{\oplus 2}\)