Properties

Label 4.4.8468.1-8.4-a
Base field 4.4.8468.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 8, w^{2} - 2w]$
Dimension $2$
CM no
Base change no

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Base field 4.4.8468.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 8, w^{2} - 2w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w - 2]$ $\phantom{-}0$
2 $[2, 2, w - 1]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 5w + 1]$ $-2e - 2$
17 $[17, 17, -w^{3} + 3w + 1]$ $\phantom{-}0$
23 $[23, 23, w^{3} + w^{2} - 4w - 5]$ $\phantom{-}2e - 2$
29 $[29, 29, -w^{3} + w^{2} + 2w - 1]$ $\phantom{-}2e - 4$
29 $[29, 29, w^{3} + w^{2} - 6w - 5]$ $-8$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-2e - 8$
47 $[47, 47, w^{3} - 3w - 3]$ $-4e - 4$
53 $[53, 53, 2w^{2} - 2w - 5]$ $\phantom{-}6e + 8$
53 $[53, 53, -w^{3} + 2w^{2} + 5w - 7]$ $\phantom{-}6e + 4$
59 $[59, 59, 2w^{3} - 8w - 3]$ $\phantom{-}4e + 8$
59 $[59, 59, w^{3} - w^{2} - 2w + 3]$ $-4e - 4$
67 $[67, 67, 2w - 1]$ $-4e$
71 $[71, 71, 2w^{2} - 5]$ $\phantom{-}4e$
73 $[73, 73, -w^{3} + w^{2} + 4w + 1]$ $-2e$
73 $[73, 73, -2w^{3} + 8w + 1]$ $\phantom{-}2e$
73 $[73, 73, -w^{3} + 5w - 1]$ $-6e - 8$
79 $[79, 79, w^{2} - w + 1]$ $\phantom{-}2e - 10$
79 $[79, 79, w^{3} + w^{2} - 4w - 7]$ $\phantom{-}4e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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