Properties

 Base field 3.3.316.1 Weight [2, 2, 2] Level norm 34 Level $[34, 34, -w^{2} - 1]$ Label 3.3.316.1-34.1-b Dimension 2 CM no Base change no

Related objects

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Base field 3.3.316.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 4x + 2$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2] Level $[34, 34, -w^{2} - 1]$ Label 3.3.316.1-34.1-b Dimension 2 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:
$$x^{2}$$ $$\mathstrut -\mathstrut 6$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{2} - w - 1]$ $-e$
17 $[17, 17, -w^{2} - w + 3]$ $-1$
19 $[19, 19, w^{2} - w + 1]$ $-2e + 2$
23 $[23, 23, 2w - 3]$ $-2e$
27 $[27, 3, 3]$ $-2e + 4$
29 $[29, 29, 2w + 1]$ $\phantom{-}e - 6$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}e - 4$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-4$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}2e + 6$
43 $[43, 43, w^{2} + w - 5]$ $-e - 4$
43 $[43, 43, -3w^{2} + w + 15]$ $-4$
43 $[43, 43, -2w^{2} + 2w + 11]$ $\phantom{-}2e + 8$
53 $[53, 53, w^{2} - w - 7]$ $\phantom{-}e + 6$
61 $[61, 61, 4w^{2} - 2w - 15]$ $\phantom{-}4e + 2$
67 $[67, 67, -5w^{2} + 3w + 23]$ $-3e - 4$
73 $[73, 73, 2w^{2} - 3]$ $-2e + 2$
73 $[73, 73, -3w^{2} - w + 7]$ $\phantom{-}e - 10$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-3e + 2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 1]$ $-1$
17 $[17, 17, -w^{2} - w + 3]$ $1$