Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 4 Level $[4, 2, 2]$ Label 2.2.113.1-4.1-f Dimension 2 CM no Base change yes

Related objects

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Base field $$\Q(\sqrt{113})$$

Generator $$w$$, with minimal polynomial $$x^{2} - x - 28$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2] Level $[4, 2, 2]$ Label 2.2.113.1-4.1-f Dimension 2 Is CM no Is base change yes Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 2x$$ $$\mathstrut -\mathstrut 12$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $\phantom{-}1$
2 $[2, 2, w + 5]$ $\phantom{-}1$
7 $[7, 7, 6w - 35]$ $\phantom{-}e$
7 $[7, 7, -6w - 29]$ $\phantom{-}e$
9 $[9, 3, 3]$ $-e$
11 $[11, 11, 4w + 19]$ $-e + 2$
11 $[11, 11, 4w - 23]$ $-e + 2$
13 $[13, 13, -2w + 11]$ $-4$
13 $[13, 13, 2w + 9]$ $-4$
25 $[25, 5, -5]$ $\phantom{-}8$
31 $[31, 31, 2w - 13]$ $-e + 4$
31 $[31, 31, -2w - 11]$ $-e + 4$
41 $[41, 41, -8w - 39]$ $\phantom{-}e - 2$
41 $[41, 41, 8w - 47]$ $\phantom{-}e - 2$
53 $[53, 53, -26w - 125]$ $\phantom{-}0$
53 $[53, 53, 26w - 151]$ $\phantom{-}0$
61 $[61, 61, -14w + 81]$ $-10$
61 $[61, 61, -14w - 67]$ $-10$
83 $[83, 83, 2w - 15]$ $\phantom{-}e - 14$
83 $[83, 83, -2w - 13]$ $\phantom{-}e - 14$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $-1$
2 $[2, 2, w + 5]$ $-1$