Properties

Base field \(\Q(\sqrt{65}) \)
Weight [2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 2.2.65.1-1.1-a
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 $[1, 1, 1]$
Label 2.2.65.1-1.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
2 $[2, 2, w + 1]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}2$
7 $[7, 7, w + 1]$ $\phantom{-}0$
7 $[7, 7, w + 5]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}2$
13 $[13, 13, w + 6]$ $-6$
29 $[29, 29, -2w + 7]$ $\phantom{-}6$
29 $[29, 29, 2w + 5]$ $\phantom{-}6$
37 $[37, 37, w + 9]$ $-6$
37 $[37, 37, w + 27]$ $-6$
47 $[47, 47, w + 10]$ $\phantom{-}8$
47 $[47, 47, w + 36]$ $\phantom{-}8$
61 $[61, 61, 2w - 3]$ $\phantom{-}6$
61 $[61, 61, -2w - 1]$ $\phantom{-}6$
67 $[67, 67, w + 23]$ $-12$
67 $[67, 67, w + 43]$ $-12$
73 $[73, 73, w + 24]$ $\phantom{-}6$
73 $[73, 73, w + 48]$ $\phantom{-}6$
79 $[79, 79, 2w - 13]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).