# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.157.1-9.1-b Dimension 1 CM no Base change no

# Related objects

## 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 $[9, 3, 3]$ Label 2.2.157.1-9.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 19

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $\phantom{-}1$
3 $[3, 3, -w + 7]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}1$
11 $[11, 11, -3w - 17]$ $-6$
11 $[11, 11, 3w - 20]$ $\phantom{-}2$
13 $[13, 13, 2w - 13]$ $\phantom{-}5$
13 $[13, 13, 2w + 11]$ $-3$
17 $[17, 17, w + 7]$ $\phantom{-}1$
17 $[17, 17, -w + 8]$ $-3$
19 $[19, 19, -w - 4]$ $\phantom{-}2$
19 $[19, 19, -w + 5]$ $-6$
25 $[25, 5, 5]$ $-2$
31 $[31, 31, -6w - 35]$ $\phantom{-}4$
31 $[31, 31, -6w + 41]$ $\phantom{-}4$
37 $[37, 37, -w - 1]$ $-7$
37 $[37, 37, w - 2]$ $-7$
47 $[47, 47, 3w + 16]$ $\phantom{-}0$
47 $[47, 47, -3w + 19]$ $-8$
49 $[49, 7, -7]$ $-1$
67 $[67, 67, 3w - 22]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $-1$
3 $[3, 3, -w + 7]$ $1$