Properties

Label 6.6.1528713.1-53.4-c
Base field 6.6.1528713.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$
Dimension $3$
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: $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$
Dimension: $3$
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:

\(x^{3} + x^{2} - 5x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ $\phantom{-}e$
8 $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ $-\frac{1}{2}e^{2} - e + \frac{1}{2}$
9 $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{5}{2}$
19 $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ $-2e^{2} - 2e + 6$
19 $[19, 19, -w + 2]$ $-\frac{3}{2}e^{2} - e + \frac{1}{2}$
37 $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ $-\frac{1}{2}e^{2} - 5e - \frac{1}{2}$
37 $[37, 37, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}e^{2} - e$
53 $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ $-2e^{2} + e + 13$
53 $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ $\phantom{-}3e - 3$
53 $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ $-6$
53 $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ $-1$
71 $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ $\phantom{-}3e + 3$
71 $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ $\phantom{-}\frac{5}{2}e^{2} - e - \frac{31}{2}$
73 $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ $-4e - 4$
73 $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ $\phantom{-}3e^{2} + 2e - 15$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ $\phantom{-}3e^{2} + e - 4$
73 $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ $\phantom{-}e^{2} + 5e - 2$
89 $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ $-\frac{5}{2}e^{2} - 8e + \frac{13}{2}$
89 $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ $\phantom{-}3e^{2} + 4e - 17$
107 $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ $\phantom{-}3e^{2} + 6e - 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$ $1$