Defining parameters
Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8712.cq (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 396 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(3168\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8712, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13056 | 0 | 13056 |
Cusp forms | 12288 | 0 | 12288 |
Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(8712, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8712, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4356, [\chi])\)\(^{\oplus 2}\)