Defining parameters
| Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8400.fv (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 280 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| 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 | 7872 | 0 | 7872 |
| Cusp forms | 7488 | 0 | 7488 |
| Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4200, [\chi])\)\(^{\oplus 2}\)