# Properties

 Label 2.2.5.1-1764.1-d Base field $$\Q(\sqrt{5})$$ Weight $[2, 2]$ Level norm $1764$ Level $[1764, 42, -42]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{5})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[1764, 42, -42]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $17$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
5 $[5, 5, -2w + 1]$ $-2$
9 $[9, 3, 3]$ $-1$
11 $[11, 11, -3w + 2]$ $-2$
11 $[11, 11, -3w + 1]$ $-2$
19 $[19, 19, -4w + 3]$ $\phantom{-}2$
19 $[19, 19, -4w + 1]$ $\phantom{-}2$
29 $[29, 29, w + 5]$ $\phantom{-}6$
29 $[29, 29, -w + 6]$ $\phantom{-}6$
31 $[31, 31, -5w + 2]$ $\phantom{-}6$
31 $[31, 31, -5w + 3]$ $\phantom{-}6$
41 $[41, 41, -6w + 5]$ $\phantom{-}6$
41 $[41, 41, w - 7]$ $\phantom{-}6$
49 $[49, 7, -7]$ $-1$
59 $[59, 59, 2w - 9]$ $\phantom{-}8$
59 $[59, 59, 7w - 5]$ $\phantom{-}8$
61 $[61, 61, 3w - 10]$ $\phantom{-}10$
61 $[61, 61, -3w - 7]$ $\phantom{-}10$
71 $[71, 71, -8w + 7]$ $-14$
71 $[71, 71, w - 9]$ $-14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, 2]$ $1$
$9$ $[9, 3, 3]$ $1$
$49$ $[49, 7, -7]$ $1$