Defining parameters
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(19, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 14 | 0 |
Cusp forms | 10 | 10 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(19, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
19.5.d.a | $10$ | $1.964$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(-3\) | \(9\) | \(8\) | \(-24\) | \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{3}+(6\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\) |