Hilbert cusp form 2.2.13.1-324.5-a

• Label: 2.2.13.1-324.5-a
• Base field: $\Q(\sqrt{13})$
• Weight: $[2, 2]$
• Level norm: $324$
• Level: $[324,162,10 w - 6]$
• Dimension: $1$
• CM: no
• Base change: no

Base field $\Q(\sqrt{13})$

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

Form

Weight:	$[2, 2]$
Level:	$[324,162,10 w - 6]$
Dimension:	$1$
CM:	no
Base change:	no
Newspace dimension:	$12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.

Norm	Prime	Eigenvalue
3	$[3, 3, -w]$	$\phantom{-}0$
3	$[3, 3, -w + 1]$	$\phantom{-}2$
4	$[4, 2, 2]$	$-1$
13	$[13, 13, -2 w + 1]$	$\phantom{-}1$
17	$[17, 17, w + 4]$	$\phantom{-}3$
17	$[17, 17, -w + 5]$	$\phantom{-}3$
23	$[23, 23, 3 w + 1]$	$-6$
23	$[23, 23, -3 w + 4]$	$\phantom{-}6$
25	$[25, 5, 5]$	$\phantom{-}7$
29	$[29, 29, 3 w - 2]$	$-3$
29	$[29, 29, -3 w + 1]$	$\phantom{-}6$
43	$[43, 43, -4 w - 1]$	$-4$
43	$[43, 43, 4 w - 5]$	$-10$
49	$[49, 7, -7]$	$\phantom{-}11$
53	$[53, 53, -w - 7]$	$\phantom{-}9$
53	$[53, 53, w - 8]$	$-3$
61	$[61, 61, -3 w - 8]$	$-2$
61	$[61, 61, 3 w - 11]$	$\phantom{-}1$
79	$[79, 79, 5 w - 4]$	$\phantom{-}10$
79	$[79, 79, 5 w - 1]$	$-14$

Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm	Prime	Eigenvalue
$3$	$[3,3,w]$	$1$
$4$	$[4,2,2]$	$1$