Defining parameters
| Level: | \( N \) | \(=\) | \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 30345.cu (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 357 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(9792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(30345, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 19872 | 11520 | 8352 |
| Cusp forms | 19296 | 11520 | 7776 |
| Eisenstein series | 576 | 0 | 576 |
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
\( S_{2}^{\mathrm{old}}(30345, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1785, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(6069, [\chi])\)\(^{\oplus 2}\)