Defining parameters
| Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 5 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1440.r (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1440\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(1440, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2336 | 0 | 2336 |
| Cusp forms | 2272 | 0 | 2272 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{5}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)