Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 4 Level $[4, 2, -w^{2} + w + 3]$ Label 4.4.8768.1-4.1-a Dimension 3 CM no Base change yes

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Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight [2, 2, 2, 2] Level $[4, 2, -w^{2} + w + 3]$ Label 4.4.8768.1-4.1-a Dimension 3 Is CM no Is base change yes Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut +\mathstrut 3x^{2}$$ $$\mathstrut -\mathstrut 4x$$ $$\mathstrut -\mathstrut 7$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-e^{2} - e + 5$
7 $[7, 7, w^{2} - 2]$ $-e^{2} - e + 5$
7 $[7, 7, w - 1]$ $\phantom{-}e$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e^{2} + 4e - 2$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}e^{2} + 4e - 2$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}2e + 6$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}2e + 6$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}2e - 4$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}2e - 4$
47 $[47, 47, w^{2} - 2w - 5]$ $-2e^{2} - 6e + 4$
47 $[47, 47, w^{2} - 6]$ $-2e^{2} - 6e + 4$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-e^{2} - 2e + 2$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-e^{2} - 2e + 2$
79 $[79, 79, -w - 3]$ $-2e^{2} - 4e + 10$
79 $[79, 79, w - 4]$ $-2e^{2} - 4e + 10$
81 $[81, 3, -3]$ $\phantom{-}3e^{2} + 5e - 5$
89 $[89, 89, w^{2} - 3w - 2]$ $-2e^{2} - 4e$
89 $[89, 89, w^{2} + w - 4]$ $-2e^{2} - 4e$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $1$