Defining parameters
| Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8450.y (of order \(13\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 169 \) |
| Character field: | \(\Q(\zeta_{13})\) | ||
| Sturm bound: | \(2730\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8450, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 16512 | 3468 | 13044 |
| Cusp forms | 16224 | 3468 | 12756 |
| Eisenstein series | 288 | 0 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(8450, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8450, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4225, [\chi])\)\(^{\oplus 2}\)