Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 8
Level $[8, 2, 2]$
Label 3.3.1101.1-8.1-b
Dimension 4
CM no
Base change no

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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 $[8, 2, 2]$
Label 3.3.1101.1-8.1-b
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut x^{3} \) \(\mathstrut -\mathstrut 12x^{2} \) \(\mathstrut -\mathstrut 7x \) \(\mathstrut +\mathstrut 32\)

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Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $-1$
3 $[3, 3, -w + 3]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}e^{2} - 6$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $\phantom{-}e^{3} - 7e + 2$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}2e^{2} - 14$
31 $[31, 31, -2w^{2} + 19]$ $\phantom{-}2$
31 $[31, 31, -w^{2} + 5]$ $-2e^{2} + 16$
31 $[31, 31, -3w + 5]$ $\phantom{-}2e^{2} - 12$
41 $[41, 41, w^{2} + 2w - 7]$ $-e^{3} - 2e^{2} + 7e + 8$
43 $[43, 43, w^{2} - 11]$ $-2e^{2} - 3e + 16$
47 $[47, 47, 3w - 7]$ $\phantom{-}0$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}2e^{2} - 8$
59 $[59, 59, 2w - 1]$ $-e^{2} + 4$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{3} + 2e^{2} + 7e - 12$
67 $[67, 67, 3w^{2} + 2w - 25]$ $-2e^{3} + 2e^{2} + 17e - 12$
67 $[67, 67, w - 5]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 16$
73 $[73, 73, -4w^{2} - 3w + 29]$ $-e^{2} + 12$
73 $[73, 73, 2w^{2} - w - 11]$ $-e^{3} - 2e^{2} + 7e + 10$
73 $[73, 73, w^{2} + 2w - 11]$ $\phantom{-}2e^{2} + 3e - 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $1$
4 $[4, 2, w^{2} + w - 7]$ $-1$