Defining parameters
| Level: | \( N \) | \(=\) | \( 5712 = 2^{4} \cdot 3 \cdot 7 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5712.fi (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 357 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(2304\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5712, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4704 | 1168 | 3536 |
| Cusp forms | 4512 | 1136 | 3376 |
| Eisenstein series | 192 | 32 | 160 |
Decomposition of \(S_{2}^{\mathrm{new}}(5712, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5712, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5712, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1428, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2856, [\chi])\)\(^{\oplus 2}\)