Properties

Label 5.5.170701.1-32.1-h
Base field 5.5.170701.1
Weight $[2, 2, 2, 2, 2]$
Level norm $32$
Level $[32, 2, 2]$
Dimension $2$
CM no
Base change no

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Base field 5.5.170701.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[32, 2, 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $35$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 3x - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ $\phantom{-}1$
7 $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ $\phantom{-}4$
8 $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ $-1$
11 $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ $\phantom{-}2$
23 $[23, 23, -w^{2} + 2]$ $-2$
23 $[23, 23, -w + 2]$ $-6$
31 $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ $\phantom{-}0$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $-e$
47 $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ $\phantom{-}2e - 4$
53 $[53, 53, w^{2} - w - 4]$ $-2e + 4$
53 $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ $\phantom{-}2e + 2$
53 $[53, 53, -w^{3} + w^{2} + 4w - 1]$ $-2e + 2$
71 $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ $-2e$
71 $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ $\phantom{-}0$
71 $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ $\phantom{-}8$
73 $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ $-2$
79 $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ $-4$
83 $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ $\phantom{-}2e - 2$
89 $[89, 89, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ $-1$
$8$ $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ $1$