Defining parameters
| Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1380.s (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 592 | 264 | 328 |
| Cusp forms | 560 | 264 | 296 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1380, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)