Defining parameters
| Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8712.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 88 \) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(3168\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8712, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1632 | 548 | 1084 |
| Cusp forms | 1536 | 532 | 1004 |
| Eisenstein series | 96 | 16 | 80 |
Decomposition of \(S_{2}^{\mathrm{new}}(8712, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8712, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8712, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(968, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2904, [\chi])\)\(^{\oplus 2}\)