Defining parameters
| Level: | \( N \) | \(=\) | \( 3400 = 2^{3} \cdot 5^{2} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3400.cc (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 85 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(1080\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2256 | 328 | 1928 |
| Cusp forms | 2064 | 328 | 1736 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1700, [\chi])\)\(^{\oplus 2}\)