# Properties

 Base field $$\Q(\sqrt{34})$$ Weight [2, 2] Level norm 3 Level $[3,3,-w + 1]$ Label 2.2.136.1-3.2-b Dimension 2 CM no Base change no

# 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 $[3,3,-w + 1]$ Label 2.2.136.1-3.2-b Dimension 2 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}e - 2$
3 $[3, 3, w + 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $-2e - 1$
5 $[5, 5, w + 3]$ $\phantom{-}3e - 2$
11 $[11, 11, w + 1]$ $-e - 2$
11 $[11, 11, w + 10]$ $-e - 2$
17 $[17, 17, -3w + 17]$ $-2e + 3$
29 $[29, 29, w + 11]$ $-4e + 1$
29 $[29, 29, w + 18]$ $-3e - 5$
37 $[37, 37, w + 16]$ $\phantom{-}e + 4$
37 $[37, 37, w + 21]$ $-4e + 5$
47 $[47, 47, -w - 9]$ $\phantom{-}e - 5$
47 $[47, 47, w - 9]$ $\phantom{-}4e + 6$
49 $[49, 7, -7]$ $\phantom{-}3e - 9$
61 $[61, 61, w + 20]$ $\phantom{-}4e + 3$
61 $[61, 61, w + 41]$ $-7e + 11$
89 $[89, 89, 2w - 15]$ $\phantom{-}4e - 12$
89 $[89, 89, -2w - 15]$ $-4e + 7$
103 $[103, 103, -14w + 81]$ $-8e - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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