# Properties

 Label 2.2.12.1-59.2-b Base field $$\Q(\sqrt{3})$$ Weight $[2, 2]$ Level norm $59$ Level $[59,59,-5w - 4]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{3})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2]$ Level: $[59,59,-5w - 4]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} + x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
3 $[3, 3, w]$ $-e - 2$
11 $[11, 11, -2w + 1]$ $\phantom{-}2e - 1$
11 $[11, 11, 2w + 1]$ $\phantom{-}e - 4$
13 $[13, 13, w + 4]$ $-4e - 3$
13 $[13, 13, -w + 4]$ $\phantom{-}3e - 2$
23 $[23, 23, -3w + 2]$ $-4e - 1$
23 $[23, 23, 3w + 2]$ $-3e - 3$
25 $[25, 5, 5]$ $-2e - 5$
37 $[37, 37, 2w - 7]$ $-3e - 6$
37 $[37, 37, -2w - 7]$ $\phantom{-}6e + 1$
47 $[47, 47, -4w - 1]$ $\phantom{-}7e + 3$
47 $[47, 47, 4w - 1]$ $\phantom{-}4e + 9$
49 $[49, 7, -7]$ $-e + 2$
59 $[59, 59, 5w - 4]$ $-4e + 3$
59 $[59, 59, -5w - 4]$ $\phantom{-}1$
61 $[61, 61, -w - 8]$ $\phantom{-}e$
61 $[61, 61, w - 8]$ $-6e - 6$
71 $[71, 71, 5w - 2]$ $\phantom{-}10e + 8$
71 $[71, 71, -5w - 2]$ $-5e - 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59,59,-5w - 4]$ $-1$