Defining parameters
| Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 5 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1440.y (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(1440, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2368 | 244 | 2124 |
| Cusp forms | 2240 | 236 | 2004 |
| Eisenstein series | 128 | 8 | 120 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{5}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)