Properties

Base field 4.4.13068.1
Weight [2, 2, 2, 2]
Level norm 8
Level $[8, 2, w^{3} - 2w^{2} - 4w + 3]$
Label 4.4.13068.1-8.1-b
Dimension 1
CM no
Base change yes

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Base field 4.4.13068.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[8, 2, w^{3} - 2w^{2} - 4w + 3]$
Label 4.4.13068.1-8.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $-1$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $-2$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}0$
17 $[17, 17, -w + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}6$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}6$
31 $[31, 31, -w^{2} + 2]$ $-4$
31 $[31, 31, -w^{3} + 7w + 5]$ $-4$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $-6$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $-6$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $-4$
67 $[67, 67, -w^{2} + 4w + 2]$ $-4$
83 $[83, 83, 2w^{2} - 5w - 2]$ $-12$
83 $[83, 83, -w^{3} + 8w + 6]$ $-12$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $-12$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $-12$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}8$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $\phantom{-}8$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $1$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $-1$