Properties

Label 4.4.4352.1-34.1-b
Base field 4.4.4352.1
Weight $[2, 2, 2, 2]$
Level norm $34$
Level $[34, 34, w^{2} - w - 6]$
Dimension $1$
CM no
Base change yes

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Base field 4.4.4352.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[34, 34, w^{2} - w - 6]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $-1$
7 $[7, 7, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}2$
7 $[7, 7, -w + 1]$ $\phantom{-}2$
17 $[17, 17, -w^{3} + 2w^{2} + 4w - 3]$ $-1$
23 $[23, 23, -2w^{3} + 2w^{2} + 9w + 1]$ $-6$
23 $[23, 23, -w^{3} + w^{2} + 3w + 1]$ $-6$
31 $[31, 31, w^{2} - w - 1]$ $-4$
31 $[31, 31, w^{3} - 2w^{2} - 3w + 5]$ $-4$
41 $[41, 41, w^{3} - 3w^{2} - 2w + 7]$ $\phantom{-}6$
41 $[41, 41, w^{3} - 3w^{2} - 2w + 5]$ $\phantom{-}6$
49 $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ $\phantom{-}2$
71 $[71, 71, -2w^{3} + 3w^{2} + 8w - 1]$ $\phantom{-}6$
71 $[71, 71, w^{2} - 5]$ $\phantom{-}6$
73 $[73, 73, -3w^{3} + 4w^{2} + 11w - 3]$ $\phantom{-}14$
73 $[73, 73, 2w^{3} - w^{2} - 9w - 3]$ $\phantom{-}14$
79 $[79, 79, 3w^{3} - 4w^{2} - 13w + 3]$ $\phantom{-}8$
79 $[79, 79, w^{2} + w - 3]$ $\phantom{-}8$
81 $[81, 3, -3]$ $-2$
89 $[89, 89, -w^{3} + 3w^{2} + 3w - 11]$ $-6$
89 $[89, 89, 3w^{3} - 2w^{2} - 14w - 3]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $1$
$17$ $[17, 17, -w^{3} + 2w^{2} + 4w - 3]$ $1$