Defining parameters
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.dk (of order \(60\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 900 \) |
Character field: | \(\Q(\zeta_{60})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 17408 | 0 | 17408 |
Cusp forms | 17152 | 0 | 17152 |
Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)