Properties

Label 4.4.12400.1-20.2-f
Base field 4.4.12400.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20,10,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{7}{2}]$
Dimension $2$
CM no
Base change no

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Base field 4.4.12400.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[20,10,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{7}{2}]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 6x + 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ $-1$
5 $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ $\phantom{-}1$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ $-e - 4$
9 $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ $\phantom{-}2e + 3$
19 $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ $-e - 5$
19 $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ $-4e - 11$
29 $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ $\phantom{-}e + 8$
29 $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ $\phantom{-}3e + 13$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $\phantom{-}2e + 5$
59 $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ $\phantom{-}9e + 28$
59 $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ $-3e - 16$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ $-6e - 14$
61 $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ $\phantom{-}3e + 3$
71 $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ $-4e - 21$
71 $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ $\phantom{-}4e + 14$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ $\phantom{-}e + 3$
79 $[79, 79, -2w^{2} + w + 10]$ $-5$
79 $[79, 79, 2w^{2} + w - 10]$ $-4e - 8$
79 $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{11}{2}]$ $1$
$5$ $[5,5,\frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 4]$ $-1$