Defining parameters
| Level: | \( N \) | \(=\) | \( 8064 = 2^{7} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8064.hn (of order \(48\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 448 \) |
| Character field: | \(\Q(\zeta_{48})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3072\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8064, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 24832 | 0 | 24832 |
| Cusp forms | 24320 | 0 | 24320 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(8064, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8064, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2688, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4032, [\chi])\)\(^{\oplus 2}\)