Properties

Label 4.4.7168.1-1.1-a
Base field 4.4.7168.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM no
Base change yes

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Base field 4.4.7168.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 8x^{2} + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
7 $[7, 7, w]$ $-e^{3} + 6e$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
9 $[9, 3, w^{2} - w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 4e$
17 $[17, 17, -w^{3} + 3w - 1]$ $-\frac{1}{2}e^{3} + 2e$
17 $[17, 17, w^{3} - 3w - 1]$ $-\frac{1}{2}e^{3} + 2e$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-2e^{2} + 8$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $-2e^{2} + 8$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $\phantom{-}2e^{2} - 10$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}2e^{2} - 10$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}2e^{2} - 2$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $\phantom{-}e^{3} - 2e$
71 $[71, 71, -2w^{2} - 2w + 1]$ $\phantom{-}e^{3} - 2e$
73 $[73, 73, w^{2} - 2w - 2]$ $\phantom{-}\frac{5}{2}e^{3} - 12e$
73 $[73, 73, w^{2} + 2w - 2]$ $\phantom{-}\frac{5}{2}e^{3} - 12e$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}4e$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $\phantom{-}4e$
89 $[89, 89, 2w - 1]$ $\phantom{-}\frac{1}{2}e^{3}$
89 $[89, 89, -2w - 1]$ $\phantom{-}\frac{1}{2}e^{3}$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $-\frac{1}{2}e^{3} + 6e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).