Defining parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(9\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 2 | 8 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
18.3.b.a | $2$ | $0.490$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\) |