# Properties

 Base field $$\Q(\sqrt{13})$$ Weight [2, 2] Level norm 1089 Level $[1089, 33, 33]$ Label 2.2.13.1-1089.1-d Dimension 1 CM no Base change yes

# Related objects

## Base field $$\Q(\sqrt{13})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 3$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[1089, 33, 33]$ Label 2.2.13.1-1089.1-d Dimension 1 Is CM no Is base change yes Parent newspace dimension 41

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w]$ $-1$
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, 2]$ $-3$
13 $[13, 13, -2w + 1]$ $-2$
17 $[17, 17, w + 4]$ $-2$
17 $[17, 17, -w + 5]$ $-2$
23 $[23, 23, 3w + 1]$ $\phantom{-}8$
23 $[23, 23, -3w + 4]$ $\phantom{-}8$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, 3w - 2]$ $-6$
29 $[29, 29, -3w + 1]$ $-6$
43 $[43, 43, -4w - 1]$ $\phantom{-}0$
43 $[43, 43, 4w - 5]$ $\phantom{-}0$
49 $[49, 7, -7]$ $\phantom{-}2$
53 $[53, 53, -w - 7]$ $\phantom{-}6$
53 $[53, 53, w - 8]$ $\phantom{-}6$
61 $[61, 61, -3w - 8]$ $\phantom{-}6$
61 $[61, 61, 3w - 11]$ $\phantom{-}6$
79 $[79, 79, 5w - 4]$ $-4$
79 $[79, 79, 5w - 1]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w]$ $1$
3 $[3, 3, -w + 1]$ $1$
121 $[121, 11, -11]$ $-1$