Properties

 Base field $$\Q(\sqrt{17})$$ Weight [2, 2] Level norm 196 Level $[196, 14, 14]$ Label 2.2.17.1-196.1-b Dimension 1 CM no Base change yes

Related objects

Base field $$\Q(\sqrt{17})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 4$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2] Level $[196, 14, 14]$ Label 2.2.17.1-196.1-b Dimension 1 Is CM no Is base change yes Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $-1$
2 $[2, 2, -w - 1]$ $-1$
9 $[9, 3, 3]$ $-2$
13 $[13, 13, -2w + 3]$ $-4$
13 $[13, 13, 2w + 1]$ $-4$
17 $[17, 17, -2w + 1]$ $\phantom{-}6$
19 $[19, 19, -2w + 7]$ $\phantom{-}2$
19 $[19, 19, 2w + 5]$ $\phantom{-}2$
25 $[25, 5, -5]$ $-10$
43 $[43, 43, 4w - 7]$ $\phantom{-}8$
43 $[43, 43, 4w + 3]$ $\phantom{-}8$
47 $[47, 47, -2w + 9]$ $-12$
47 $[47, 47, 2w + 7]$ $-12$
49 $[49, 7, -7]$ $\phantom{-}1$
53 $[53, 53, 4w - 13]$ $\phantom{-}6$
53 $[53, 53, 6w - 13]$ $\phantom{-}6$
59 $[59, 59, -4w - 1]$ $-6$
59 $[59, 59, 4w - 5]$ $-6$
67 $[67, 67, 4w - 3]$ $-4$
67 $[67, 67, 4w - 1]$ $-4$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $1$
2 $[2, 2, -w - 1]$ $1$
49 $[49, 7, -7]$ $-1$