# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 3 Level $[3,3,-w + 7]$ Label 2.2.157.1-3.2-a Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{157})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 39$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[3,3,-w + 7]$ Label 2.2.157.1-3.2-a Dimension 2 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 3x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}e$
3 $[3, 3, -w + 7]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}0$
11 $[11, 11, -3w - 17]$ $\phantom{-}4$
11 $[11, 11, 3w - 20]$ $-e$
13 $[13, 13, 2w - 13]$ $-3e + 4$
13 $[13, 13, 2w + 11]$ $\phantom{-}3e - 1$
17 $[17, 17, w + 7]$ $\phantom{-}0$
17 $[17, 17, -w + 8]$ $-5e + 9$
19 $[19, 19, -w - 4]$ $\phantom{-}2e$
19 $[19, 19, -w + 5]$ $\phantom{-}2e$
25 $[25, 5, 5]$ $\phantom{-}2e - 6$
31 $[31, 31, -6w - 35]$ $\phantom{-}4e - 6$
31 $[31, 31, -6w + 41]$ $-6e + 12$
37 $[37, 37, -w - 1]$ $-4e + 12$
37 $[37, 37, w - 2]$ $\phantom{-}6e - 6$
47 $[47, 47, 3w + 16]$ $-e - 3$
47 $[47, 47, -3w + 19]$ $-6e + 6$
49 $[49, 7, -7]$ $\phantom{-}3e - 9$
67 $[67, 67, 3w - 22]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 7]$ $1$