Defining parameters
| Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8400.cg (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(3840\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3888 | 912 | 2976 |
| Cusp forms | 3792 | 912 | 2880 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{2}^{\mathrm{new}}(8400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2800, [\chi])\)\(^{\oplus 2}\)