Defining parameters
| Level: | \( N \) | \(=\) | \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5400.fk (of order \(180\) and degree \(48\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2700 \) |
| Character field: | \(\Q(\zeta_{180})\) | ||
| 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 | 52224 | 0 | 52224 |
| Cusp forms | 51456 | 0 | 51456 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(5400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)