Properties

 Base field $$\Q(\sqrt{113})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.113.1-9.1-c Dimension 2 CM no Base change no

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 $[9, 3, 3]$ Label 2.2.113.1-9.1-c Dimension 2 Is CM no Is base change no Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $1$