Properties

Base field \(\Q(\sqrt{5}) \)
Weight [2, 2]
Level norm 61
Level $[61, 61, 3w - 10]$
Label 2.2.5.1-61.1-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 $[61, 61, 3w - 10]$
Label 2.2.5.1-61.1-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:
\(x^{2} \) \(\mathstrut +\mathstrut 2x \) \(\mathstrut -\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61, 61, 3w - 10]$ $1$