Defining parameters
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(19, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 15 | 0 |
Cusp forms | 13 | 13 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(19, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
19.9.b.a | $1$ | $7.740$ | \(\Q\) | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(-289\) | \(527\) | \(q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots\) |
19.9.b.b | $12$ | $7.740$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(8\) | \(3686\) | \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-131+\beta _{2})q^{4}+\cdots\) |