# Properties

 Base field $$\Q(\sqrt{209})$$ Weight [2, 2] Level norm 16 Level $[16, 16, -15w + 116]$ Label 2.2.209.1-16.4-a Dimension 1 CM yes Base change no

# Related objects

## Base field $$\Q(\sqrt{209})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 52$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2] Level $[16, 16, -15w + 116]$ Label 2.2.209.1-16.4-a Dimension 1 Is CM yes Is base change no Parent newspace dimension 53

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -11w - 74]$ $\phantom{-}0$
2 $[2, 2, -11w + 85]$ $\phantom{-}0$
5 $[5, 5, 4w - 31]$ $-3$
5 $[5, 5, -4w - 27]$ $-3$
9 $[9, 3, 3]$ $\phantom{-}5$
11 $[11, 11, -70w - 471]$ $\phantom{-}0$
13 $[13, 13, -2w - 13]$ $\phantom{-}0$
13 $[13, 13, -2w + 15]$ $\phantom{-}0$
19 $[19, 19, 92w - 711]$ $\phantom{-}0$
23 $[23, 23, -26w + 201]$ $-9$
23 $[23, 23, -26w - 175]$ $\phantom{-}9$
29 $[29, 29, 18w - 139]$ $\phantom{-}0$
29 $[29, 29, 18w + 121]$ $\phantom{-}0$
41 $[41, 41, -10w - 67]$ $\phantom{-}0$
41 $[41, 41, 10w - 77]$ $\phantom{-}0$
47 $[47, 47, 2w - 17]$ $-12$
47 $[47, 47, 2w + 15]$ $\phantom{-}12$
49 $[49, 7, -7]$ $-14$
79 $[79, 79, 40w - 309]$ $\phantom{-}0$
79 $[79, 79, 40w + 269]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -11w - 74]$ $-1$