Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.cl (of order \(40\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 800 \) |
Character field: | \(\Q(\zeta_{40})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11584 | 0 | 11584 |
Cusp forms | 11456 | 0 | 11456 |
Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{4}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)