Properties

 Base field $$\Q(\sqrt{61})$$ Weight [2, 2] Level norm 196 Level $[196, 14, -14]$ Label 2.2.61.1-196.1-a Dimension 1 CM no Base change yes

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Base field $$\Q(\sqrt{61})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 15$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2] Level $[196, 14, -14]$ Label 2.2.61.1-196.1-a Dimension 1 Is CM no Is base change yes Parent newspace dimension 131

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w - 3]$ $-2$
3 $[3, 3, -w + 4]$ $-2$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w - 5]$ $\phantom{-}0$
5 $[5, 5, -w - 4]$ $\phantom{-}0$
13 $[13, 13, -w - 1]$ $-4$
13 $[13, 13, w - 2]$ $-4$
19 $[19, 19, 3w - 14]$ $\phantom{-}2$
19 $[19, 19, -3w - 11]$ $\phantom{-}2$
41 $[41, 41, -w - 7]$ $\phantom{-}6$
41 $[41, 41, w - 8]$ $\phantom{-}6$
47 $[47, 47, 3w - 11]$ $-12$
47 $[47, 47, -3w - 8]$ $-12$
49 $[49, 7, -7]$ $\phantom{-}1$
61 $[61, 61, 2w - 1]$ $\phantom{-}8$
73 $[73, 73, -3w + 16]$ $\phantom{-}2$
73 $[73, 73, 3w + 13]$ $\phantom{-}2$
83 $[83, 83, 2w - 13]$ $-6$
83 $[83, 83, -2w - 11]$ $-6$
97 $[97, 97, 7w + 22]$ $-10$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-1$
49 $[49, 7, -7]$ $-1$