Properties

Label 6.6.966125.1-55.1-a
Base field 6.6.966125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $55$
Level $[55, 55, -w^{3} + 5w + 1]$
Dimension $2$
CM no
Base change no

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Base field 6.6.966125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[55, 55, -w^{3} + 5w + 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 40\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}1$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ $\phantom{-}e$
25 $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ $-4$
29 $[29, 29, -w^{4} + 4w^{2} + 1]$ $-e + 4$
31 $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ $\phantom{-}e$
31 $[31, 31, -w^{2} + 2]$ $\phantom{-}6$
59 $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ $-e$
59 $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ $\phantom{-}8$
59 $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ $\phantom{-}e - 2$
61 $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ $\phantom{-}0$
64 $[64, 2, 2]$ $\phantom{-}e + 9$
71 $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ $\phantom{-}0$
71 $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ $-e - 8$
71 $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ $\phantom{-}10$
71 $[71, 71, w^{3} - 5w]$ $-e + 6$
79 $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ $-12$
89 $[89, 89, w^{3} - w^{2} - 4w + 1]$ $-2$
101 $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ $\phantom{-}0$
101 $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ $-2e - 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w - 1]$ $-1$
$11$ $[11, 11, w^{3} - 3w]$ $-1$