Properties

Label 4.4.15317.1-8.1-a
Base field 4.4.15317.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, w^{3} - w^{2} - 5w]$
Dimension $1$
CM no
Base change no

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Base field 4.4.15317.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 2, w^{3} - w^{2} - 5w]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, -w + 1]$ $\phantom{-}1$
4 $[4, 2, -w^{2} + w + 1]$ $-1$
19 $[19, 19, -w^{3} + 5w + 3]$ $-8$
19 $[19, 19, w^{3} - 3w^{2} - 2w + 7]$ $\phantom{-}8$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}4$
43 $[43, 43, -w^{3} + w^{2} + 2w - 1]$ $\phantom{-}0$
43 $[43, 43, w^{3} - 2w^{2} - w + 1]$ $-8$
43 $[43, 43, -w^{3} + 5w + 1]$ $-4$
47 $[47, 47, -w^{3} + w^{2} + 2w + 1]$ $\phantom{-}0$
47 $[47, 47, w^{3} - 5w - 5]$ $\phantom{-}4$
47 $[47, 47, -w^{3} + 3w^{2} + 2w - 9]$ $\phantom{-}4$
47 $[47, 47, w^{3} - 2w^{2} - w + 3]$ $\phantom{-}8$
49 $[49, 7, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}2$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 7]$ $-6$
53 $[53, 53, 2w - 1]$ $\phantom{-}10$
67 $[67, 67, -w^{3} + w^{2} + 4w - 3]$ $-12$
67 $[67, 67, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}4$
81 $[81, 3, -3]$ $-10$
83 $[83, 83, 2w^{3} - 4w^{2} - 6w + 9]$ $\phantom{-}4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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