Defining parameters
Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5400.dz (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 900 \) |
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 \(M_{2}(5400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8832 | 0 | 8832 |
Cusp forms | 8448 | 0 | 8448 |
Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{old}}(5400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)