Properties

Label 3.3.81.1-71.3-a
Base field \(\Q(\zeta_{9})^+\)
Weight $[2, 2, 2]$
Level norm $71$
Level $[71,71,-2w^{2} + w - 1]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\zeta_{9})^+\)

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

Form

Weight: $[2, 2, 2]$
Level: $[71,71,-2w^{2} + w - 1]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - x^{2} - 4x + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-2e^{2} + 6$
17 $[17, 17, -2w^{2} + w + 3]$ $-e^{2} - e + 3$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}2e^{2} - 2e - 6$
17 $[17, 17, -w^{2} + 2w + 3]$ $\phantom{-}e^{2} + 2e - 6$
19 $[19, 19, -2w^{2} + 2w + 5]$ $-e^{2} - e + 5$
19 $[19, 19, -2w^{2} + 3]$ $\phantom{-}2e^{2} - 2e - 4$
19 $[19, 19, -2w + 1]$ $\phantom{-}2e^{2} - 2e - 4$
37 $[37, 37, -w^{2} + 3w + 3]$ $\phantom{-}2e^{2} + 4e - 10$
37 $[37, 37, 2w^{2} + w - 5]$ $-2e^{2} - 2e + 8$
37 $[37, 37, 3w^{2} - 2w - 5]$ $-3e^{2} + 2e + 8$
53 $[53, 53, -w - 4]$ $\phantom{-}4e^{2} - e - 6$
53 $[53, 53, -w^{2} + w - 2]$ $\phantom{-}e^{2} + 3e - 9$
53 $[53, 53, w^{2} - 6]$ $-4e$
71 $[71, 71, w^{2} + w - 7]$ $\phantom{-}e^{2} - 2e - 6$
71 $[71, 71, w^{2} - 2w - 7]$ $\phantom{-}2e^{2} - 6e - 6$
71 $[71, 71, -2w^{2} + w - 1]$ $\phantom{-}1$
73 $[73, 73, 3w^{2} - 3w - 8]$ $-2e^{2} + 7e + 8$
73 $[73, 73, 2w^{2} - 3w - 7]$ $\phantom{-}2e - 4$
73 $[73, 73, w^{2} + 2w - 5]$ $-4e^{2} - 4e + 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$71$ $[71,71,-2w^{2} + w - 1]$ $-1$