Defining parameters
| Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3420.ha (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 285 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Sturm bound: | \(1440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8928 | 480 | 8448 |
| Cusp forms | 8352 | 480 | 7872 |
| Eisenstein series | 576 | 0 | 576 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1710, [\chi])\)\(^{\oplus 2}\)