Defining parameters
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(1728\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1320 | 0 | 1320 |
Cusp forms | 1272 | 0 | 1272 |
Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)