Properties

 Base field 3.3.940.1 Weight [2, 2, 2] Level norm 2 Level $[2, 2, -w - 1]$ Label 3.3.940.1-2.2-a Dimension 2 CM no Base change no

Related objects

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Base field 3.3.940.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 4$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2] Level $[2, 2, -w - 1]$ Label 3.3.940.1-2.2-a Dimension 2 Is CM no Is base change no Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} + x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}1$
5 $[5, 5, -w^{2} + w + 7]$ $-2e + 1$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}2e$
17 $[17, 17, -w^{2} + 3w + 1]$ $-2e + 2$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}4e + 1$
27 $[27, 3, 3]$ $-2e + 1$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}4e + 7$
37 $[37, 37, w^{2} + w + 1]$ $\phantom{-}4e + 4$
41 $[41, 41, w^{2} - w - 9]$ $-2$
43 $[43, 43, -3w^{2} + 3w + 17]$ $\phantom{-}6e + 4$
47 $[47, 47, 2w^{2} - 2w - 13]$ $\phantom{-}2e - 2$
47 $[47, 47, -2w + 5]$ $\phantom{-}2e - 2$
53 $[53, 53, 3w^{2} - w - 19]$ $-2e + 5$
59 $[59, 59, 2w - 1]$ $\phantom{-}5$
67 $[67, 67, w^{2} + w - 5]$ $-8e - 7$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}2e - 11$
79 $[79, 79, 3w^{2} - w - 23]$ $-4e - 7$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-6e - 13$
89 $[89, 89, -2w^{2} - 2w + 5]$ $\phantom{-}2e - 4$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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