Properties

 Base field 3.3.1101.1 Weight [2, 2, 2] Level norm 12 Level $[12, 12, w]$ Label 3.3.1101.1-12.3-a Dimension 2 CM no Base change no

Related objects

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Base field 3.3.1101.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 9x + 12$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2] Level $[12, 12, w]$ Label 3.3.1101.1-12.3-a Dimension 2 Is CM no Is base change no Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - x - 3$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}0$
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}e$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}2$
19 $[19, 19, w + 1]$ $\phantom{-}2$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}e - 1$
31 $[31, 31, -2w^{2} + 19]$ $\phantom{-}4e - 2$
31 $[31, 31, -w^{2} + 5]$ $-2e - 2$
31 $[31, 31, -3w + 5]$ $-e + 3$
41 $[41, 41, w^{2} + 2w - 7]$ $-2e + 2$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}8$
47 $[47, 47, 3w - 7]$ $\phantom{-}0$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}6e$
59 $[59, 59, 2w - 1]$ $-5e + 5$
67 $[67, 67, 2w^{2} + w - 19]$ $\phantom{-}e + 10$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-4e + 6$
67 $[67, 67, w - 5]$ $\phantom{-}6e + 2$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-2e + 4$
73 $[73, 73, 2w^{2} - w - 11]$ $-4e + 6$
73 $[73, 73, w^{2} + 2w - 11]$ $-3e + 5$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $-1$
3 $[3, 3, -w + 3]$ $1$