Defining parameters
| Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8712.dt (of order \(110\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 363 \) |
| Character field: | \(\Q(\zeta_{110})\) | ||
| Sturm bound: | \(3168\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8712, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 64000 | 5280 | 58720 |
| Cusp forms | 62720 | 5280 | 57440 |
| Eisenstein series | 1280 | 0 | 1280 |
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
\( S_{2}^{\mathrm{old}}(8712, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1452, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2178, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2904, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4356, [\chi])\)\(^{\oplus 2}\)