# Properties

 Label 2.2.65.1-52.1-h Base field $$\Q(\sqrt{65})$$ Weight $[2, 2]$ Level norm $52$ Level $[52, 26, 2w + 12]$ 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: $[52, 26, 2w + 12]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $34$

## 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 $[5, 5, w + 2]$ $\phantom{-}1$
7 $[7, 7, w + 1]$ $-1$
7 $[7, 7, w + 5]$ $-1$
9 $[9, 3, 3]$ $\phantom{-}3$
13 $[13, 13, w + 6]$ $\phantom{-}1$
29 $[29, 29, -2w + 7]$ $\phantom{-}2$
29 $[29, 29, 2w + 5]$ $\phantom{-}2$
37 $[37, 37, w + 9]$ $-3$
37 $[37, 37, w + 27]$ $-3$
47 $[47, 47, w + 10]$ $-13$
47 $[47, 47, w + 36]$ $-13$
61 $[61, 61, 2w - 3]$ $-8$
61 $[61, 61, -2w - 1]$ $-8$
67 $[67, 67, w + 23]$ $\phantom{-}2$
67 $[67, 67, w + 43]$ $\phantom{-}2$
73 $[73, 73, w + 24]$ $\phantom{-}10$
73 $[73, 73, w + 48]$ $\phantom{-}10$
79 $[79, 79, 2w - 13]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$2$ $[2, 2, w + 1]$ $1$
$13$ $[13, 13, w + 6]$ $-1$