Properties

Label 4.4.19025.1-20.1-g
Base field 4.4.19025.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, w + 1]$
Dimension $12$
CM no
Base change no

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Base field 4.4.19025.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20, 10, w + 1]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $35$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{12} - 40x^{10} - 2x^{9} + 557x^{8} + 44x^{7} - 3076x^{6} - 288x^{5} + 5367x^{4} + 964x^{3} - 2092x^{2} + 50x + 115\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}1$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $...$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $...$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $...$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $...$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $...$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $...$
81 $[81, 3, -3]$ $...$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $...$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $...$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + 7]$ $-1$
$5$ $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $-1$