Defining parameters
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(7, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 12 | 0 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(7, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
7.9.d.a | $8$ | $2.852$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(-4\) | \(-84\) | \(-840\) | \(-140\) | \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots\) |