Properties

 Base field 3.3.1101.1 Weight [2, 2, 2] Level norm 2 Level $[2, 2, w - 2]$ Label 3.3.1101.1-2.1-c Dimension 3 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 $[2, 2, w - 2]$ Label 3.3.1101.1-2.1-c Dimension 3 Is CM no Is base change no Parent newspace dimension 5

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} + 2x^{2} - 8x - 12$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}1$
3 $[3, 3, -w + 3]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - 4$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}\frac{1}{2}e^{2} - 3$
19 $[19, 19, w + 1]$ $-\frac{1}{2}e^{2} - e + 6$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - e - 6$
31 $[31, 31, -2w^{2} + 19]$ $-\frac{1}{2}e^{2} + 2e + 6$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}e^{2} - e - 6$
31 $[31, 31, -3w + 5]$ $\phantom{-}2e - 2$
41 $[41, 41, w^{2} + 2w - 7]$ $-\frac{1}{2}e^{2} - 2e + 6$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}e^{2} + 2e - 6$
47 $[47, 47, 3w - 7]$ $\phantom{-}e^{2} - 2e - 12$
53 $[53, 53, -3w^{2} - 6w + 11]$ $-\frac{1}{2}e^{2} + e + 6$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{2} + e - 12$
67 $[67, 67, 2w^{2} + w - 19]$ $-3e^{2} - e + 16$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-e^{2} + 6$
67 $[67, 67, w - 5]$ $-2e^{2} - 4e + 12$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}\frac{3}{2}e^{2} + e - 6$
73 $[73, 73, 2w^{2} - w - 11]$ $-e^{2} + 12$
73 $[73, 73, w^{2} + 2w - 11]$ $\phantom{-}2e^{2} + e - 14$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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