Properties

Label 6.6.810448.1-27.1-b
Base field 6.6.810448.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$
Dimension $2$
CM no
Base change yes

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Base field 6.6.810448.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - 5x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$
Dimension: $2$
CM: no
Base change: yes
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ $\phantom{-}e$
25 $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ $\phantom{-}3$
25 $[25, 5, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - 2w + 2]$ $\phantom{-}3$
25 $[25, 5, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $\phantom{-}3$
27 $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ $-1$
27 $[27, 3, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 6w - 4]$ $-3e - 1$
37 $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 3w + 2]$ $-5$
37 $[37, 37, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 5w + 5]$ $-5$
37 $[37, 37, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} - 2]$ $-5$
67 $[67, 67, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 2]$ $\phantom{-}e + 15$
67 $[67, 67, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 7w - 5]$ $-3e - 9$
67 $[67, 67, -2w^{5} + 6w^{4} + 4w^{3} - 16w^{2} - 3w + 5]$ $\phantom{-}e + 15$
67 $[67, 67, -2w^{5} + 4w^{4} + 8w^{3} - 12w^{2} - 9w + 6]$ $-3e - 9$
67 $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 6w + 4]$ $\phantom{-}e + 15$
67 $[67, 67, w^{5} - 4w^{4} + 10w^{2} - 2w - 3]$ $-3e - 9$
107 $[107, 107, w^{5} - 3w^{4} - w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}2e + 15$
107 $[107, 107, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 5]$ $\phantom{-}2e + 15$
107 $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 13w^{2} + 6w - 4]$ $\phantom{-}2e + 15$
107 $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 15w^{2} + 4w - 6]$ $\phantom{-}3e + 6$
107 $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $\phantom{-}3e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$27$ $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ $1$