Defining parameters
| Level: | \( N \) | \(=\) | \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 30345.bj (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(9792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(30345, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9936 | 4336 | 5600 |
| Cusp forms | 9648 | 4336 | 5312 |
| Eisenstein series | 288 | 0 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(30345, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(30345, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(30345, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(595, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1785, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(10115, [\chi])\)\(^{\oplus 2}\)