Defining parameters
Level: | \( N \) | \(=\) | \( 119 = 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 119.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 119 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(119, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 6 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 2 | 2 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(119, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
119.1.d.a | $2$ | $0.059$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-119}) \) | None | \(-1\) | \(-1\) | \(-1\) | \(2\) | \(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\) |
119.1.d.b | $2$ | $0.059$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-119}) \) | None | \(-1\) | \(1\) | \(1\) | \(-2\) | \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\) |