Defining parameters
| Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8112.ft (of order \(156\) and degree \(48\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4056 \) |
| Character field: | \(\Q(\zeta_{156})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2912\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8112, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 70272 | 0 | 70272 |
| Cusp forms | 69504 | 0 | 69504 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(8112, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8112, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(4056, [\chi])\)\(^{\oplus 2}\)