# Properties

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

# Related objects

• L-function not available

## 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-i Dimension 2 Is CM no Is base change yes Parent newspace dimension 48

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 9$$
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-2$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{3}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{3}e$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $-\frac{5}{3}e$
11 $[11, 11, w + 10]$ $-\frac{5}{3}e$
17 $[17, 17, -3w + 17]$ $\phantom{-}8$
29 $[29, 29, w + 11]$ $\phantom{-}2e$
29 $[29, 29, w + 18]$ $\phantom{-}2e$
37 $[37, 37, w + 16]$ $\phantom{-}\frac{2}{3}e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{2}{3}e$
47 $[47, 47, -w - 9]$ $-2$
47 $[47, 47, w - 9]$ $-2$
49 $[49, 7, -7]$ $\phantom{-}10$
61 $[61, 61, w + 20]$ $\phantom{-}\frac{10}{3}e$
61 $[61, 61, w + 41]$ $\phantom{-}\frac{10}{3}e$
89 $[89, 89, 2w - 15]$ $-10$
89 $[89, 89, -2w - 15]$ $-10$
103 $[103, 103, -14w + 81]$ $\phantom{-}9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-\frac{1}{3}e$
3 $[3, 3, w + 2]$ $-\frac{1}{3}e$