Properties

Label 4.4.7168.1-9.1-b
Base field 4.4.7168.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{2} + w - 1]$
Dimension $2$
CM no
Base change no

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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: $[9, 3, w^{2} + w - 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
7 $[7, 7, w]$ $-e - 1$
9 $[9, 3, w^{2} + w - 1]$ $\phantom{-}1$
9 $[9, 3, w^{2} - w - 1]$ $\phantom{-}e - 2$
17 $[17, 17, -w^{3} + 3w - 1]$ $-3$
17 $[17, 17, w^{3} - 3w - 1]$ $-3$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-1$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $-1$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $-5e - 3$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}7e + 8$
49 $[49, 7, w^{2} - 6]$ $-4e - 7$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $\phantom{-}10e + 3$
71 $[71, 71, -2w^{2} - 2w + 1]$ $-2e - 8$
73 $[73, 73, w^{2} - 2w - 2]$ $-9$
73 $[73, 73, w^{2} + 2w - 2]$ $-13e - 8$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $-3e - 9$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-4e + 3$
89 $[89, 89, 2w - 1]$ $\phantom{-}10e$
89 $[89, 89, -2w - 1]$ $-3e + 1$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}9e - 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9,3,w^{2}+w-1]$ $-1$