Defining parameters
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(7, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 8 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(7, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
7.6.c.a | $4$ | $1.123$ | \(\Q(\sqrt{-3}, \sqrt{37})\) | None | \(-2\) | \(8\) | \(38\) | \(-168\) | \(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\) |