# Properties

 Label 2.2.65.1-1.1-b Base field $$\Q(\sqrt{65})$$ Weight $[2, 2]$ Level norm $1$ Level $[1, 1, 1]$ 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: $[1, 1, 1]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $4$

## 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 $[5, 5, w + 2]$ $-2$
7 $[7, 7, w + 1]$ $\phantom{-}0$
7 $[7, 7, w + 5]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}2$
13 $[13, 13, w + 6]$ $\phantom{-}6$
29 $[29, 29, -2w + 7]$ $\phantom{-}6$
29 $[29, 29, 2w + 5]$ $\phantom{-}6$
37 $[37, 37, w + 9]$ $\phantom{-}6$
37 $[37, 37, w + 27]$ $\phantom{-}6$
47 $[47, 47, w + 10]$ $-8$
47 $[47, 47, w + 36]$ $-8$
61 $[61, 61, 2w - 3]$ $\phantom{-}6$
61 $[61, 61, -2w - 1]$ $\phantom{-}6$
67 $[67, 67, w + 23]$ $\phantom{-}12$
67 $[67, 67, w + 43]$ $\phantom{-}12$
73 $[73, 73, w + 24]$ $-6$
73 $[73, 73, w + 48]$ $-6$
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 $$(1)$$.