# Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 12 Level $[12,6,-2w + 14]$ Label 2.2.157.1-12.2-f Dimension 3 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 $[12,6,-2w + 14]$ Label 2.2.157.1-12.2-f Dimension 3 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 7]$ $1$
4 $[4,2,2]$ $-1$