# Properties

 Base field $$\Q(\sqrt{34})$$ Weight [2, 2] Level norm 6 Level $[6,6,-w + 2]$ Label 2.2.136.1-6.2-c Dimension 3 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 $[6,6,-w + 2]$ Label 2.2.136.1-6.2-c Dimension 3 Is CM no Is base change no Parent newspace dimension 20

## Hecke eigenvalues ($q$-expansion)

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

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,-w - 6]$ $-1$
3 $[3,3,-w + 2]$ $-1$