Properties

Base field \(\Q(\sqrt{5}) \)
Weight [2, 2]
Level norm 500
Level $[500, 50, -20w + 10]$
Label 2.2.5.1-500.1-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 $[500, 50, -20w + 10]$
Label 2.2.5.1-500.1-a
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut -\mathstrut 5x \) \(\mathstrut -\mathstrut 25\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -2w + 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, -3w + 2]$ $\phantom{-}2$
11 $[11, 11, -3w + 1]$ $\phantom{-}2$
19 $[19, 19, -4w + 3]$ $\phantom{-}e$
19 $[19, 19, -4w + 1]$ $-e + 5$
29 $[29, 29, w + 5]$ $\phantom{-}e$
29 $[29, 29, -w + 6]$ $-e + 5$
31 $[31, 31, -5w + 2]$ $-e + 2$
31 $[31, 31, -5w + 3]$ $\phantom{-}e - 3$
41 $[41, 41, -6w + 5]$ $-e + 2$
41 $[41, 41, w - 7]$ $\phantom{-}e - 3$
49 $[49, 7, -7]$ $-10$
59 $[59, 59, 2w - 9]$ $-e - 5$
59 $[59, 59, 7w - 5]$ $\phantom{-}e - 10$
61 $[61, 61, 3w - 10]$ $-2e + 2$
61 $[61, 61, -3w - 7]$ $\phantom{-}2e - 8$
71 $[71, 71, -8w + 7]$ $\phantom{-}e - 8$
71 $[71, 71, w - 9]$ $-e - 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $1$
5 $[5, 5, -2w + 1]$ $1$