Defining parameters
| Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8400.da (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3840\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3936 | 0 | 3936 |
| Cusp forms | 3744 | 0 | 3744 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)