Defining parameters
| Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6840.nl (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1140 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2880\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6840, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 17664 | 0 | 17664 |
| Cusp forms | 16896 | 0 | 16896 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{old}}(6840, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3420, [\chi])\)\(^{\oplus 2}\)