Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.e (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 22 | 0 |
Cusp forms | 14 | 14 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
20.4.e.a | $2$ | $1.180$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(4\) | \(0\) | \(-4\) | \(0\) | \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\) |
20.4.e.b | $12$ | $1.180$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-6\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) |