# Properties

 Base field $$\Q(\sqrt{209})$$ Weight [2, 2] Level norm 10 Level $[10,10,-7w + 54]$ Label 2.2.209.1-10.4-d Dimension 1 CM no Base change no

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## 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 $[10,10,-7w + 54]$ Label 2.2.209.1-10.4-d Dimension 1 Is CM no Is base change no Parent newspace dimension 32

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -11w - 74]$ $-1$
2 $[2, 2, -11w + 85]$ $-2$
5 $[5, 5, 4w - 31]$ $-1$
5 $[5, 5, -4w - 27]$ $\phantom{-}1$
9 $[9, 3, 3]$ $\phantom{-}1$
11 $[11, 11, -70w - 471]$ $\phantom{-}1$
13 $[13, 13, -2w - 13]$ $\phantom{-}0$
13 $[13, 13, -2w + 15]$ $-4$
19 $[19, 19, 92w - 711]$ $\phantom{-}0$
23 $[23, 23, -26w + 201]$ $\phantom{-}1$
23 $[23, 23, -26w - 175]$ $-3$
29 $[29, 29, 18w - 139]$ $-6$
29 $[29, 29, 18w + 121]$ $\phantom{-}8$
41 $[41, 41, -10w - 67]$ $-6$
41 $[41, 41, 10w - 77]$ $-12$
47 $[47, 47, 2w - 17]$ $\phantom{-}7$
47 $[47, 47, 2w + 15]$ $\phantom{-}9$
49 $[49, 7, -7]$ $\phantom{-}9$
79 $[79, 79, 40w - 309]$ $\phantom{-}4$
79 $[79, 79, 40w + 269]$ $\phantom{-}2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,11w + 74]$ $1$
5 $[5,5,-4w - 27]$ $-1$