Properties

Base field \(\Q(\sqrt{65}) \)
Weight [2, 2]
Level norm 180
Level $[180, 30, 6w + 12]$
Label 2.2.65.1-180.1-c
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{65}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 16\); narrow class number \(2\) and class number \(2\).

Form

Weight [2, 2]
Level $[180, 30, 6w + 12]$
Label 2.2.65.1-180.1-c
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 94

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
2 $[2, 2, w + 1]$ $-1$
5 $[5, 5, w + 2]$ $-1$
7 $[7, 7, w + 1]$ $-4$
7 $[7, 7, w + 5]$ $-4$
9 $[9, 3, 3]$ $\phantom{-}1$
13 $[13, 13, w + 6]$ $\phantom{-}2$
29 $[29, 29, -2w + 7]$ $-6$
29 $[29, 29, 2w + 5]$ $-6$
37 $[37, 37, w + 9]$ $\phantom{-}2$
37 $[37, 37, w + 27]$ $\phantom{-}2$
47 $[47, 47, w + 10]$ $\phantom{-}0$
47 $[47, 47, w + 36]$ $\phantom{-}0$
61 $[61, 61, 2w - 3]$ $-10$
61 $[61, 61, -2w - 1]$ $-10$
67 $[67, 67, w + 23]$ $-4$
67 $[67, 67, w + 43]$ $-4$
73 $[73, 73, w + 24]$ $\phantom{-}2$
73 $[73, 73, w + 48]$ $\phantom{-}2$
79 $[79, 79, 2w - 13]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $1$
2 $[2, 2, w + 1]$ $1$
5 $[5, 5, w + 2]$ $1$
9 $[9, 3, 3]$ $-1$