Defining parameters
| Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1400.cb (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(240\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 48 | 0 | 48 |
| Cusp forms | 16 | 0 | 16 |
| Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)