Properties

 Base field $$\Q(\sqrt{157})$$ Weight [2, 2] Level norm 12 Level $[12,6,-2w + 14]$ Label 2.2.157.1-12.2-a 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 $[12,6,-2w + 14]$ Label 2.2.157.1-12.2-a Dimension 1 Is CM no Is base change no Parent newspace dimension 22

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 6]$ $-1$
3 $[3, 3, -w + 7]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}1$
11 $[11, 11, -3w - 17]$ $-6$
11 $[11, 11, 3w - 20]$ $\phantom{-}1$
13 $[13, 13, 2w - 13]$ $\phantom{-}2$
13 $[13, 13, 2w + 11]$ $\phantom{-}1$
17 $[17, 17, w + 7]$ $\phantom{-}5$
17 $[17, 17, -w + 8]$ $-6$
19 $[19, 19, -w - 4]$ $-2$
19 $[19, 19, -w + 5]$ $\phantom{-}3$
25 $[25, 5, 5]$ $\phantom{-}7$
31 $[31, 31, -6w - 35]$ $-5$
31 $[31, 31, -6w + 41]$ $-2$
37 $[37, 37, -w - 1]$ $-4$
37 $[37, 37, w - 2]$ $-2$
47 $[47, 47, 3w + 16]$ $\phantom{-}8$
47 $[47, 47, -3w + 19]$ $\phantom{-}7$
49 $[49, 7, -7]$ $-12$
67 $[67, 67, 3w - 22]$ $-7$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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