Defining parameters
| Level: | \( N \) | \(=\) | \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1870.v (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(1296\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1870, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3920 | 720 | 3200 |
| Cusp forms | 3856 | 720 | 3136 |
| Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1870, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)