Defining parameters
| Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 400.bb (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(240\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 736 | 0 | 736 |
| Cusp forms | 704 | 0 | 704 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)