Properties

Label 2.2.5.1-139.2-a
Base field \(\Q(\sqrt{5}) \)
Weight $[2, 2]$
Level norm $139$
Level $[139,139,-2w - 11]$
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: $[139,139,-2w - 11]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$139$ $[139,139,-2w - 11]$ $1$