Defining parameters
| Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1380.bi (of order \(22\) and degree \(10\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 460 \) |
| Character field: | \(\Q(\zeta_{22})\) | ||
| Sturm bound: | \(1152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1380, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8720 | 4320 | 4400 |
| Cusp forms | 8560 | 4320 | 4240 |
| Eisenstein series | 160 | 0 | 160 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1380, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)