Defining parameters
Level: | \( N \) | \(=\) | \( 712 = 2^{3} \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 712.w (of order \(22\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 712 \) |
Character field: | \(\Q(\zeta_{22})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(712, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 30 | 0 |
Cusp forms | 10 | 10 | 0 |
Eisenstein series | 20 | 20 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(712, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
712.1.w.a | $10$ | $0.355$ | \(\Q(\zeta_{22})\) | $D_{22}$ | \(\Q(\sqrt{-2}) \) | None | \(-1\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{22}^{9}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{5})q^{3}-\zeta_{22}^{7}q^{4}+\cdots\) |