Defining parameters
| Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 200.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(180\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 324 | 0 | 324 |
| Cusp forms | 276 | 0 | 276 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{6}^{\mathrm{old}}(200, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)