Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(33, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6 | 6 | 0 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(33, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
33.2.d.a | $2$ | $0.264$ | \(\Q(\sqrt{-11}) \) | \(\Q(\sqrt{-11}) \) | \(0\) | \(1\) | \(0\) | \(0\) | \(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\) |