# Properties

 Base field $$\Q(\sqrt{34})$$ Weight [2, 2] Level norm 1 Level $[1, 1, 1]$ Label 2.2.136.1-1.1-a Dimension 8 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 $[1, 1, 1]$ Label 2.2.136.1-1.1-a Dimension 8 Is CM no Is base change yes Parent newspace dimension 16

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8}$$ $$\mathstrut -\mathstrut 14x^{6}$$ $$\mathstrut +\mathstrut 56x^{4}$$ $$\mathstrut -\mathstrut 76x^{2}$$ $$\mathstrut +\mathstrut 32$$
Norm Prime Eigenvalue
2 $[2, 2, w - 6]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + 13e^{2} - 11$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{1}{4}e^{7} - 3e^{5} + 8e^{3} - 3e$
5 $[5, 5, w + 3]$ $\phantom{-}\frac{1}{4}e^{7} - 3e^{5} + 8e^{3} - 3e$
11 $[11, 11, w + 1]$ $-e^{7} + 13e^{5} - 43e^{3} + 33e$
11 $[11, 11, w + 10]$ $-e^{7} + 13e^{5} - 43e^{3} + 33e$
17 $[17, 17, -3w + 17]$ $-e^{6} + 12e^{4} - 34e^{2} + 22$
29 $[29, 29, w + 11]$ $\phantom{-}\frac{3}{4}e^{7} - 10e^{5} + 34e^{3} - 25e$
29 $[29, 29, w + 18]$ $\phantom{-}\frac{3}{4}e^{7} - 10e^{5} + 34e^{3} - 25e$
37 $[37, 37, w + 16]$ $\phantom{-}\frac{5}{4}e^{7} - 16e^{5} + 52e^{3} - 41e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{5}{4}e^{7} - 16e^{5} + 52e^{3} - 41e$
47 $[47, 47, -w - 9]$ $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + 18e^{2} - 16$
47 $[47, 47, w - 9]$ $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + 18e^{2} - 16$
49 $[49, 7, -7]$ $\phantom{-}e^{6} - 13e^{4} + 43e^{2} - 26$
61 $[61, 61, w + 20]$ $-\frac{5}{4}e^{7} + 16e^{5} - 52e^{3} + 43e$
61 $[61, 61, w + 41]$ $-\frac{5}{4}e^{7} + 16e^{5} - 52e^{3} + 43e$
89 $[89, 89, 2w - 15]$ $-2e^{6} + 25e^{4} - 75e^{2} + 46$
89 $[89, 89, -2w - 15]$ $-2e^{6} + 25e^{4} - 75e^{2} + 46$
103 $[103, 103, -14w + 81]$ $\phantom{-}3e^{6} - 40e^{4} + 138e^{2} - 104$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.