Properties

Label 4.4.16448.2-8.1-b
Base field 4.4.16448.2
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, -w^{3} + 3w^{2} + 4w - 12]$
Dimension $1$
CM no
Base change no

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Base field 4.4.16448.2

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 2, -w^{3} + 3w^{2} + 4w - 12]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ $\phantom{-}0$
2 $[2, 2, w^{3} - 6w - 5]$ $\phantom{-}1$
7 $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ $-2$
7 $[7, 7, -w^{3} + 5w + 3]$ $\phantom{-}4$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ $\phantom{-}6$
31 $[31, 31, -w^{2} - w + 1]$ $\phantom{-}0$
31 $[31, 31, -w^{2} + 3w - 1]$ $\phantom{-}0$
31 $[31, 31, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}0$
41 $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ $\phantom{-}2$
41 $[41, 41, w^{3} + w^{2} - 8w - 11]$ $-4$
47 $[47, 47, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2$
47 $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}2$
49 $[49, 7, 2w^{2} - 2w - 9]$ $-2$
71 $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ $\phantom{-}4$
71 $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ $-8$
73 $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ $-4$
73 $[73, 73, w^{3} - 5w - 1]$ $\phantom{-}2$
73 $[73, 73, w^{3} - 7w - 3]$ $-4$
73 $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ $\phantom{-}14$
81 $[81, 3, -3]$ $\phantom{-}2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ $-1$
$2$ $[2, 2, w^{3} - 6w - 5]$ $-1$