# Properties

 Label 2.2.57.1-57.1-a Base field $$\Q(\sqrt{57})$$ Weight $[2, 2]$ Level norm $57$ Level $[57, 57, -2w + 1]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{57})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 14$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[57, 57, -2w + 1]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $42$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 4]$ $\phantom{-}2$
2 $[2, 2, -w - 3]$ $\phantom{-}2$
3 $[3, 3, -4w - 13]$ $-1$
7 $[7, 7, -2w - 7]$ $\phantom{-}3$
7 $[7, 7, -2w + 9]$ $\phantom{-}3$
19 $[19, 19, 10w + 33]$ $-1$
25 $[25, 5, 5]$ $-9$
29 $[29, 29, -6w - 19]$ $\phantom{-}10$
29 $[29, 29, -6w + 25]$ $\phantom{-}10$
41 $[41, 41, 2w - 5]$ $\phantom{-}8$
41 $[41, 41, -2w - 3]$ $\phantom{-}8$
43 $[43, 43, 2w - 11]$ $-1$
43 $[43, 43, 2w + 9]$ $-1$
53 $[53, 53, 2w - 3]$ $\phantom{-}6$
53 $[53, 53, -2w - 1]$ $\phantom{-}6$
59 $[59, 59, 4w - 15]$ $\phantom{-}0$
59 $[59, 59, 4w + 11]$ $\phantom{-}0$
61 $[61, 61, -4w - 15]$ $\phantom{-}7$
61 $[61, 61, -4w + 19]$ $\phantom{-}7$
71 $[71, 71, 8w + 25]$ $-12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -4w - 13]$ $1$
$19$ $[19, 19, 10w + 33]$ $1$