# Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 11 Level $[11, 11, 4w + 19]$ Label 2.2.113.1-11.1-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 $[11, 11, 4w + 19]$ Label 2.2.113.1-11.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 27

## 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 $[2, 2, -w + 6]$ $\phantom{-}e$
2 $[2, 2, w + 5]$ $\phantom{-}e$
7 $[7, 7, 6w - 35]$ $-2e + 1$
7 $[7, 7, -6w - 29]$ $\phantom{-}2e$
9 $[9, 3, 3]$ $-2e - 1$
11 $[11, 11, 4w + 19]$ $\phantom{-}1$
11 $[11, 11, 4w - 23]$ $-e - 2$
13 $[13, 13, -2w + 11]$ $-e + 5$
13 $[13, 13, 2w + 9]$ $\phantom{-}e - 5$
25 $[25, 5, -5]$ $\phantom{-}e$
31 $[31, 31, 2w - 13]$ $\phantom{-}5e - 4$
31 $[31, 31, -2w - 11]$ $\phantom{-}e - 3$
41 $[41, 41, -8w - 39]$ $-7e + 2$
41 $[41, 41, 8w - 47]$ $-2e - 4$
53 $[53, 53, -26w - 125]$ $-e - 8$
53 $[53, 53, 26w - 151]$ $-4e + 7$
61 $[61, 61, -14w + 81]$ $\phantom{-}e + 3$
61 $[61, 61, -14w - 67]$ $\phantom{-}4e - 12$
83 $[83, 83, 2w - 15]$ $-6e + 13$
83 $[83, 83, -2w - 13]$ $-9e + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, 4w + 19]$ $-1$