Properties

Label 6.6.1134389.1-64.1-a
Base field 6.6.1134389.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $64$
Level $[64, 2, -2]$
Dimension $2$
CM no
Base change no

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Base field 6.6.1134389.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[64, 2, -2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{2} - w - 2]$ $\phantom{-}e$
13 $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}e$
17 $[17, 17, -w^{3} + w^{2} + 3w]$ $-2e$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}0$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ $-2$
23 $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ $-e$
31 $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ $\phantom{-}2e$
37 $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $\phantom{-}10$
37 $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ $\phantom{-}e$
47 $[47, 47, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}12$
64 $[64, 2, -2]$ $-1$
67 $[67, 67, 2w - 1]$ $\phantom{-}4$
79 $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ $\phantom{-}2e$
79 $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ $-e$
97 $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ $-2$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ $\phantom{-}6e$
101 $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ $\phantom{-}3e$
101 $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ $\phantom{-}4e$
103 $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ $\phantom{-}5e$
107 $[107, 107, w^{2} - 2w - 3]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$64$ $[64,2,-2]$ $1$