Properties

 Base field $$\Q(\sqrt{34})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.136.1-9.1-e Dimension 1 CM no Base change no

Related objects

Base field $$\Q(\sqrt{34})$$

Generator $$w$$, with minimal polynomial $$x^{2} - 34$$; narrow class number $$4$$ and class number $$2$$.

Form

 Weight [2, 2] Level $[9, 3, 3]$ Label 2.2.136.1-9.1-e Dimension 1 Is CM no Is base change no Parent newspace dimension 48

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-2$
3 $[3, 3, w + 1]$ $-1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $-2$
5 $[5, 5, w + 3]$ $\phantom{-}2$
11 $[11, 11, w + 1]$ $\phantom{-}0$
11 $[11, 11, w + 10]$ $\phantom{-}0$
17 $[17, 17, -3w + 17]$ $\phantom{-}2$
29 $[29, 29, w + 11]$ $-6$
29 $[29, 29, w + 18]$ $\phantom{-}6$
37 $[37, 37, w + 16]$ $-8$
37 $[37, 37, w + 21]$ $\phantom{-}8$
47 $[47, 47, -w - 9]$ $-12$
47 $[47, 47, w - 9]$ $-12$
49 $[49, 7, -7]$ $-10$
61 $[61, 61, w + 20]$ $\phantom{-}0$
61 $[61, 61, w + 41]$ $\phantom{-}0$
89 $[89, 89, 2w - 15]$ $-10$
89 $[89, 89, -2w - 15]$ $-10$
103 $[103, 103, -14w + 81]$ $\phantom{-}6$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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