# Properties

 Base field $$\Q(\sqrt{34})$$ Weight [2, 2] Level norm 6 Level $[6, 6, w + 2]$ Label 2.2.136.1-6.1-e Dimension 4 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## 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 2.2.136.1-6.1-e Dimension 4 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:
$$x^{4}$$ $$\mathstrut +\mathstrut 12x^{2}$$ $$\mathstrut +\mathstrut 16$$
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $-1$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $-\frac{1}{8}e^{3} - e$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $\phantom{-}0$
11 $[11, 11, w + 1]$ $\phantom{-}2e$
11 $[11, 11, w + 10]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
17 $[17, 17, -3w + 17]$ $\phantom{-}2$
29 $[29, 29, w + 11]$ $-\frac{1}{2}e^{3} - 3e$
29 $[29, 29, w + 18]$ $-\frac{1}{2}e^{3} - 4e$
37 $[37, 37, w + 16]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
37 $[37, 37, w + 21]$ $-\frac{1}{2}e^{3} - 6e$
47 $[47, 47, -w - 9]$ $-e^{2}$
47 $[47, 47, w - 9]$ $\phantom{-}e^{2} + 8$
49 $[49, 7, -7]$ $-e^{2} - 10$
61 $[61, 61, w + 20]$ $-\frac{1}{2}e^{3} - 3e$
61 $[61, 61, w + 41]$ $\phantom{-}\frac{3}{2}e^{3} + 12e$
89 $[89, 89, 2w - 15]$ $-2$
89 $[89, 89, -2w - 15]$ $\phantom{-}2e^{2} + 14$
103 $[103, 103, -14w + 81]$ $-e^{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $1$
3 $[3, 3, w + 2]$ $\frac{1}{8}e^{3} + e$