Defining parameters
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.bh (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
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 | 1472 | 0 | 1472 |
Cusp forms | 1408 | 0 | 1408 |
Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{4}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)