Properties

Base field 3.3.321.1
Weight [2, 2, 2]
Level norm 8
Level $[8, 2, 2]$
Label 3.3.321.1-8.1-a
Dimension 3
CM no
Base change no

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Base field 3.3.321.1

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

Form

Weight [2, 2, 2]
Level $[8, 2, 2]$
Label 3.3.321.1-8.1-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-e^{2} - e + 3$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}2e$
8 $[8, 2, 2]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e^{2} - 4$
23 $[23, 23, -w - 3]$ $\phantom{-}2e^{2} - 8$
29 $[29, 29, -w^{2} + 2w + 4]$ $\phantom{-}2e^{2} - 2$
31 $[31, 31, 2w - 3]$ $\phantom{-}2e^{2} + 2e - 8$
41 $[41, 41, -2w^{2} + 3w + 6]$ $-e^{2} - 3e + 7$
43 $[43, 43, w^{2} - 3w + 3]$ $\phantom{-}2e^{2} + 3e$
47 $[47, 47, w^{2} + w - 4]$ $-4e^{2} - 6e + 10$
49 $[49, 7, 2w^{2} - 3w - 3]$ $\phantom{-}3e^{2} + 2e - 6$
53 $[53, 53, w^{2} - 3w - 2]$ $\phantom{-}2e^{2} + 6e - 2$
59 $[59, 59, 2w^{2} - w - 5]$ $-4e^{2} - 3e + 10$
59 $[59, 59, w^{2} - w - 7]$ $-3e^{2} - 6e + 6$
59 $[59, 59, -w^{2} - w + 7]$ $-e^{2} + 3e + 1$
67 $[67, 67, 2w^{2} - 3w - 7]$ $\phantom{-}e^{2} - e - 7$
73 $[73, 73, -w^{2} + 4w - 5]$ $\phantom{-}4e^{2} + 5e - 10$
79 $[79, 79, w^{2} - 8]$ $-2e^{2} - 6e + 10$
79 $[79, 79, w^{2} - 5w + 5]$ $-2e^{2} - 4e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, 2]$ $-1$