Properties

Label 4.4.13625.1-20.1-e
Base field 4.4.13625.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, \frac{1}{2}w^{2} - \frac{3}{2}w - \frac{5}{2}]$
Dimension $2$
CM no
Base change no

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Base field 4.4.13625.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20, 10, \frac{1}{2}w^{2} - \frac{3}{2}w - \frac{5}{2}]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 9x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ $\phantom{-}1$
4 $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ $\phantom{-}1$
5 $[5, 5, w - 3]$ $-1$
11 $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ $\phantom{-}e + 4$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 5]$ $\phantom{-}e + 4$
31 $[31, 31, w]$ $-4e - 20$
31 $[31, 31, w + 3]$ $-4$
31 $[31, 31, -w + 4]$ $-e$
31 $[31, 31, w - 1]$ $\phantom{-}2e + 8$
41 $[41, 41, -w^{2} + 2]$ $-4e - 18$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ $\phantom{-}2$
59 $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ $-4e - 16$
59 $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ $\phantom{-}e - 4$
79 $[79, 79, -w^{2} + 8]$ $-2e - 4$
79 $[79, 79, w^{2} - 2w - 7]$ $-6e - 24$
81 $[81, 3, -3]$ $\phantom{-}2e + 2$
101 $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ $-5e - 18$
101 $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ $-2e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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