Properties

Base field \(\Q(\sqrt{5}) \)
Weight [2, 2]
Level norm 131
Level $[131,131,12w - 13]$
Label 2.2.5.1-131.2-a
Dimension 2
CM no
Base change no

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Base field \(\Q(\sqrt{5}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[131,131,12w - 13]$
Label 2.2.5.1-131.2-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, -2w + 1]$ $-e$
9 $[9, 3, 3]$ $-2e - 2$
11 $[11, 11, -3w + 2]$ $\phantom{-}2e + 2$
11 $[11, 11, -3w + 1]$ $\phantom{-}1$
19 $[19, 19, -4w + 3]$ $-2$
19 $[19, 19, -4w + 1]$ $-2$
29 $[29, 29, w + 5]$ $-2e - 4$
29 $[29, 29, -w + 6]$ $\phantom{-}4e - 1$
31 $[31, 31, -5w + 2]$ $-4e - 3$
31 $[31, 31, -5w + 3]$ $-e + 4$
41 $[41, 41, -6w + 5]$ $\phantom{-}e + 4$
41 $[41, 41, w - 7]$ $\phantom{-}4e$
49 $[49, 7, -7]$ $\phantom{-}6e - 2$
59 $[59, 59, 2w - 9]$ $\phantom{-}e$
59 $[59, 59, 7w - 5]$ $\phantom{-}2e + 6$
61 $[61, 61, 3w - 10]$ $-2e + 6$
61 $[61, 61, -3w - 7]$ $-4$
71 $[71, 71, -8w + 7]$ $-4e + 4$
71 $[71, 71, w - 9]$ $-4e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
131 $[131,131,12w - 13]$ $1$