Defining parameters
| Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1400.dn (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 700 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(480\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3968 | 0 | 3968 |
| Cusp forms | 3712 | 0 | 3712 |
| Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)