Defining parameters
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(4, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5 | 5 | 0 |
Cusp forms | 3 | 3 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(4, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4.9.b.a | $1$ | $1.630$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(16\) | \(0\) | \(-1054\) | \(0\) | \(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\) |
4.9.b.b | $2$ | $1.630$ | \(\Q(\sqrt{-39}) \) | None | \(-20\) | \(0\) | \(1220\) | \(0\) | \(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\) |