Properties

Base field \(\Q(\sqrt{5}) \)
Weight [2, 2]
Level norm 31
Level $[31, 31, -5w + 2]$
Label 2.2.5.1-31.1-a
Dimension 1
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 $[31, 31, -5w + 2]$
Label 2.2.5.1-31.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 1

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-3$
5 $[5, 5, -2w + 1]$ $-2$
9 $[9, 3, 3]$ $2$
11 $[11, 11, -3w + 2]$ $4$
11 $[11, 11, -3w + 1]$ $-4$
19 $[19, 19, -4w + 3]$ $-4$
19 $[19, 19, -4w + 1]$ $4$
29 $[29, 29, w + 5]$ $-2$
29 $[29, 29, -w + 6]$ $-2$
31 $[31, 31, -5w + 2]$ $-1$
31 $[31, 31, -5w + 3]$ $8$
41 $[41, 41, -6w + 5]$ $-6$
41 $[41, 41, w - 7]$ $-6$
49 $[49, 7, -7]$ $2$
59 $[59, 59, 2w - 9]$ $12$
59 $[59, 59, 7w - 5]$ $-4$
61 $[61, 61, 3w - 10]$ $6$
61 $[61, 61, -3w - 7]$ $-2$
71 $[71, 71, -8w + 7]$ $0$
71 $[71, 71, w - 9]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, -5w + 2]$ $1$