Defining parameters
Level: | \( N \) | \(=\) | \( 1412 = 2^{2} \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1412.r (of order \(44\) and degree \(20\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1412 \) |
Character field: | \(\Q(\zeta_{44})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(177\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1412, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 60 | 0 |
Cusp forms | 20 | 20 | 0 |
Eisenstein series | 40 | 40 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 20 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1412, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1412.1.r.a | $20$ | $0.705$ | \(\Q(\zeta_{44})\) | $D_{44}$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{44}^{14}q^{2}-\zeta_{44}^{6}q^{4}+(-\zeta_{44}+\zeta_{44}^{4}+\cdots)q^{5}+\cdots\) |