# Properties

 Base field $$\Q(\sqrt{209})$$ Weight [2, 2] Level norm 4 Level $[4, 2, 2]$ Label 2.2.209.1-4.1-b Dimension 1 CM no 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 $[4, 2, 2]$ Label 2.2.209.1-4.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -11w - 74]$ $\phantom{-}1$
2 $[2, 2, -11w + 85]$ $-1$
5 $[5, 5, 4w - 31]$ $-2$
5 $[5, 5, -4w - 27]$ $-2$
9 $[9, 3, 3]$ $-3$
11 $[11, 11, -70w - 471]$ $\phantom{-}2$
13 $[13, 13, -2w - 13]$ $-3$
13 $[13, 13, -2w + 15]$ $\phantom{-}3$
19 $[19, 19, 92w - 711]$ $\phantom{-}0$
23 $[23, 23, -26w + 201]$ $\phantom{-}5$
23 $[23, 23, -26w - 175]$ $\phantom{-}5$
29 $[29, 29, 18w - 139]$ $-3$
29 $[29, 29, 18w + 121]$ $\phantom{-}3$
41 $[41, 41, -10w - 67]$ $\phantom{-}12$
41 $[41, 41, 10w - 77]$ $-12$
47 $[47, 47, 2w - 17]$ $-8$
47 $[47, 47, 2w + 15]$ $-8$
49 $[49, 7, -7]$ $-5$
79 $[79, 79, 40w - 309]$ $-12$
79 $[79, 79, 40w + 269]$ $\phantom{-}12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -11w - 74]$ $-1$
2 $[2, 2, -11w + 85]$ $1$