Defining parameters
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.fc (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1800 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(2160\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11584 | 0 | 11584 |
Cusp forms | 11456 | 0 | 11456 |
Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)