Properties

Label 4.4.17609.1-8.1-b
Base field 4.4.17609.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 2, w^{3} - 7w + 3]$
Dimension $1$
CM no
Base change no

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Base field 4.4.17609.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 2, w^{3} - 7w + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $-2$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $\phantom{-}3$
7 $[7, 7, -w^{3} + 6w - 2]$ $-5$
8 $[8, 2, w^{3} - 7w + 3]$ $\phantom{-}1$
11 $[11, 11, -w^{3} + 6w - 4]$ $-1$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $-4$
17 $[17, 17, -w^{2} - w + 3]$ $-4$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $\phantom{-}10$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $-7$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}8$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $\phantom{-}0$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}6$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}3$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $\phantom{-}0$
59 $[59, 59, w^{2} + w - 1]$ $-11$
59 $[59, 59, w^{2} + 2w - 6]$ $-3$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $-7$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}0$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-10$
81 $[81, 3, -3]$ $-7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, w^{3} - 7w + 3]$ $-1$