# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.157.1-9.1-d 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 $[9, 3, 3]$ Label 2.2.157.1-9.1-d Dimension 2 Is CM no Is base change no Parent newspace dimension 19

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

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