Defining parameters
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.bt (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 360 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
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 | 2640 | 0 | 2640 |
Cusp forms | 2544 | 0 | 2544 |
Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)