Defining parameters
| Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8112.ds (of order \(39\) and degree \(24\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 169 \) |
| Character field: | \(\Q(\zeta_{39})\) | ||
| Sturm bound: | \(2912\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8112, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 35232 | 4368 | 30864 |
| Cusp forms | 34656 | 4368 | 30288 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(8112, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8112, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8112, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2028, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2704, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4056, [\chi])\)\(^{\oplus 2}\)