Properties

Label 6.6.1528713.1-53.3-b
Base field 6.6.1528713.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53,53,-2w^{5} + 6w^{4} + 5w^{3} - 12w^{2} - 2w + 3]$
Dimension $2$
CM no
Base change no

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Base field 6.6.1528713.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[53,53,-2w^{5} + 6w^{4} + 5w^{3} - 12w^{2} - 2w + 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 19\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ $\phantom{-}\frac{1}{2}e - \frac{5}{2}$
9 $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ $\phantom{-}2$
19 $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ $\phantom{-}4$
19 $[19, 19, -w + 2]$ $\phantom{-}e + 1$
37 $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ $\phantom{-}2e$
37 $[37, 37, -w^{3} + 3w^{2} + w - 3]$ $-6$
53 $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ $-10$
53 $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ $-e + 9$
53 $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ $\phantom{-}1$
53 $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ $-2$
71 $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ $-e + 7$
71 $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ $\phantom{-}2e - 6$
73 $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ $-e + 9$
73 $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ $\phantom{-}6$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ $-e - 11$
73 $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ $\phantom{-}2e + 4$
89 $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ $-e - 7$
89 $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ $-2e$
107 $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ $-2e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-2w^{5} + 6w^{4} + 5w^{3} - 12w^{2} - 2w + 3]$ $-1$