Defining parameters
| Level: | \( N \) | \(=\) | \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 30345.jp (of order \(272\) and degree \(128\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4335 \) |
| Character field: | \(\Q(\zeta_{272})\) | ||
| Sturm bound: | \(9792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(30345, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 627712 | 470016 | 157696 |
| Cusp forms | 625664 | 470016 | 155648 |
| Eisenstein series | 2048 | 0 | 2048 |
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
\( S_{2}^{\mathrm{old}}(30345, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(4335, [\chi])\)\(^{\oplus 2}\)