# Properties

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

# Related objects

## 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 $[52, 26, 2w + 12]$ Label 2.2.65.1-52.1-i Dimension 1 Is CM no Is base change yes Parent newspace dimension 34

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