Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(20, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 70 | 70 | 0 |
Cusp forms | 62 | 62 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(20, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
20.12.e.a | $2$ | $15.367$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(64\) | \(0\) | \(-5284\) | \(0\) | \(q+(2^{5}+2^{5}i)q^{2}+2^{11}iq^{4}+(-2642+\cdots)q^{5}+\cdots\) |
20.12.e.b | $60$ | $15.367$ | None | \(-66\) | \(0\) | \(5280\) | \(0\) |