Properties

Label 4.4.19664.1-4.3-a
Base field 4.4.19664.1
Weight $[2, 2, 2, 2]$
Level norm $4$
Level $[4, 2, w^{3} - 3w^{2} - w + 1]$
Dimension $2$
CM yes
Base change no

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Base field 4.4.19664.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[4, 2, w^{3} - 3w^{2} - w + 1]$
Dimension: $2$
CM: yes
Base change: no
Newspace dimension: $2$

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 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ $-e - 3$
7 $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + w + 3]$ $\phantom{-}5e + 3$
29 $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ $-2e - 7$
31 $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ $\phantom{-}0$
41 $[41, 41, -w^{3} + 4w^{2} - w - 3]$ $-4e + 1$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}0$
47 $[47, 47, w^{2} - 3w - 3]$ $\phantom{-}0$
53 $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}2e + 9$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}0$
61 $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ $-6e - 1$
67 $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ $\phantom{-}0$
67 $[67, 67, w^{3} - 4w^{2} + w + 5]$ $\phantom{-}0$
67 $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ $\phantom{-}0$
67 $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ $\phantom{-}0$
71 $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ $\phantom{-}0$
71 $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ $\phantom{-}0$
79 $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 1]$ $-1$