Defining parameters
| Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8470.cv (of order \(110\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 605 \) |
| Character field: | \(\Q(\zeta_{110})\) | ||
| Sturm bound: | \(3168\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8470, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 63680 | 15840 | 47840 |
| Cusp forms | 63040 | 15840 | 47200 |
| Eisenstein series | 640 | 0 | 640 |
Decomposition of \(S_{2}^{\mathrm{new}}(8470, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8470, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4235, [\chi])\)\(^{\oplus 2}\)