Defining parameters
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(11\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(19, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 22 | 0 |
Cusp forms | 18 | 18 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(19, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
19.7.d.a | $18$ | $4.371$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(-3\) | \(27\) | \(-57\) | \(-260\) | \(q+(\beta _{1}-\beta _{3})q^{2}+(2+\beta _{2}-\beta _{7})q^{3}+(21+\cdots)q^{4}+\cdots\) |