Properties

Label 4.4.19796.1-8.4-a
Base field 4.4.19796.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 8, w]$
Dimension $3$
CM no
Base change no

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Base field 4.4.19796.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 8, w]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} + 2x^{2} - 2x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2]$ $\phantom{-}0$
2 $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ $-e^{2} + 4$
13 $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ $\phantom{-}e^{2} + 2e - 6$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{2} - 4e - 2$
19 $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ $-2e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $-e^{2} - 2e - 2$
31 $[31, 31, -w^{2} + w + 1]$ $\phantom{-}4e^{2} + 6e - 4$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}4$
49 $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ $-3e^{2} - 8e + 4$
53 $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ $\phantom{-}3e^{2} + 4e - 8$
53 $[53, 53, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}4e - 2$
61 $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ $-3e^{2} + 6$
61 $[61, 61, 2w^{2} - 7]$ $\phantom{-}5e^{2} + 10e - 8$
71 $[71, 71, w^{2} - 3w - 5]$ $\phantom{-}5e^{2} + 6e - 10$
73 $[73, 73, 2w - 3]$ $\phantom{-}3e^{2} + 2e$
73 $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ $\phantom{-}3e^{2} + 8e - 2$
79 $[79, 79, 2w^{2} - 5]$ $-5e^{2} - 6e + 6$
81 $[81, 3, -3]$ $\phantom{-}4e^{2} - 18$
101 $[101, 101, 2w^{2} - 4w - 9]$ $-3e^{2} - 4e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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