Defining parameters
| Level: | \( N \) | \(=\) | \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8670.bb (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 85 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(3672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8670, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 7632 | 1088 | 6544 |
| Cusp forms | 7056 | 1088 | 5968 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(8670, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8670, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1445, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2890, [\chi])\)\(^{\oplus 2}\)