# Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 8 Level $[8, 4, -2w + 12]$ Label 2.2.113.1-8.1-a Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{113})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 28$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[8, 4, -2w + 12]$ Label 2.2.113.1-8.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 6x$$ $$\mathstrut +\mathstrut 6$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}0$
2 $[2, 2, w + 5]$ $\phantom{-}1$
7 $[7, 7, 6w - 35]$ $\phantom{-}e$
7 $[7, 7, -6w - 29]$ $-2e + 6$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, 4w + 19]$ $-2e + 8$
11 $[11, 11, 4w - 23]$ $\phantom{-}e - 4$
13 $[13, 13, -2w + 11]$ $\phantom{-}e - 4$
13 $[13, 13, 2w + 9]$ $-2e + 8$
25 $[25, 5, -5]$ $\phantom{-}2e - 10$
31 $[31, 31, 2w - 13]$ $\phantom{-}4$
31 $[31, 31, -2w - 11]$ $\phantom{-}3e - 8$
41 $[41, 41, -8w - 39]$ $\phantom{-}e - 8$
41 $[41, 41, 8w - 47]$ $\phantom{-}e + 4$
53 $[53, 53, -26w - 125]$ $\phantom{-}5e - 12$
53 $[53, 53, 26w - 151]$ $\phantom{-}2e - 12$
61 $[61, 61, -14w + 81]$ $\phantom{-}4e - 10$
61 $[61, 61, -14w - 67]$ $\phantom{-}4e - 10$
83 $[83, 83, 2w - 15]$ $\phantom{-}e - 8$
83 $[83, 83, -2w - 13]$ $-2e + 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $-1$
2 $[2, 2, w + 5]$ $-1$