Hilbert cusp form 6.6.371293.1-79.3-d

• Label: 6.6.371293.1-79.3-d
• Base field: $\Q(\zeta_{13})^+$
• Weight: $[2, 2, 2, 2, 2, 2]$
• Level norm: $79$
• Level: $[79,79,-w^{3} + w^{2} + 4w - 1]$
• Dimension: $1$
• CM: no
• Base change: no

Base field $\Q(\zeta_{13})^+$

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

Form

Weight:	$[2, 2, 2, 2, 2, 2]$
Level:	$[79,79,-w^{3} + w^{2} + 4w - 1]$
Dimension:	$1$
CM:	no
Base change:	no
Newspace dimension:	$9$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.

Norm	Prime	Eigenvalue
13	$[13, 13, w^{5} - 5w^{3} + 4w]$	$-2$
25	$[25, 5, w^{5} - 5w^{3} + 6w - 1]$	$-2$
25	$[25, 5, -w^{3} + w^{2} + 3w - 1]$	$-2$
25	$[25, 5, w^{5} - 4w^{3} - w^{2} + 3w + 2]$	$\phantom{-}10$
27	$[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 2]$	$\phantom{-}8$
27	$[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 3]$	$-4$
53	$[53, 53, -w^{4} + w^{3} + 3w^{2} - 2w + 1]$	$\phantom{-}6$
53	$[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$	$\phantom{-}6$
53	$[53, 53, -w^{5} + w^{4} + 4w^{3} - 4w^{2} - 3w + 1]$	$\phantom{-}6$
53	$[53, 53, w^{3} - 2w - 2]$	$\phantom{-}6$
53	$[53, 53, w^{5} - 5w^{3} - w^{2} + 5w]$	$-6$
53	$[53, 53, -w^{4} + 4w^{2} + w - 4]$	$\phantom{-}6$
64	$[64, 2, -2]$	$-11$
79	$[79, 79, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 9w + 2]$	$-8$
79	$[79, 79, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 6w - 1]$	$-8$
79	$[79, 79, w^{3} - w^{2} - 4w + 1]$	$-1$
79	$[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 9w + 3]$	$\phantom{-}4$
79	$[79, 79, -2w^{4} + w^{3} + 7w^{2} - 3w - 3]$	$-8$
79	$[79, 79, -w^{5} + 6w^{3} - w^{2} - 8w + 1]$	$-8$
103	$[103, 103, 2w^{4} - 7w^{2} - w + 3]$	$\phantom{-}8$

Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm	Prime	Eigenvalue
$79$	$[79,79,-w^{3} + w^{2} + 4w - 1]$	$1$