Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(20, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 46 | 0 |
Cusp forms | 38 | 38 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(20, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
20.8.e.a | $2$ | $6.248$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(-16\) | \(0\) | \(556\) | \(0\) | \(q+(-8-8i)q^{2}+2^{7}iq^{4}+(278+29i)q^{5}+\cdots\) |
20.8.e.b | $36$ | $6.248$ | None | \(14\) | \(0\) | \(-560\) | \(0\) |