Properties

Label 4.4.2000.1-76.4-b
Base field \(\Q(\zeta_{20})^+\)
Weight $[2, 2, 2, 2]$
Level norm $76$
Level $[76,38,-3w^{2} + w + 7]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\zeta_{20})^+\)

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[76,38,-3w^{2} + w + 7]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 3x^{2} - 5x + 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} - w^{2} + 3w + 4]$ $-1$
5 $[5, 5, w]$ $\phantom{-}e$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}e^{2} - e - 5$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $-e^{2} + 2e + 4$
19 $[19, 19, -w^{3} - w^{2} + 3w + 1]$ $\phantom{-}e^{2} - e - 5$
19 $[19, 19, -w^{2} - w + 4]$ $-1$
41 $[41, 41, w + 3]$ $-2e^{2} + 2e + 12$
41 $[41, 41, -w^{3} + 3w + 3]$ $\phantom{-}2e^{2} - 4e - 6$
41 $[41, 41, -w^{3} + 3w - 3]$ $-2e^{2} + 2e + 12$
41 $[41, 41, w - 3]$ $-e + 3$
59 $[59, 59, 2w^{2} + w - 7]$ $\phantom{-}e^{2} - 6$
59 $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ $-3e^{2} + 6e + 12$
59 $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ $-2e^{2} - e + 18$
59 $[59, 59, w^{3} - w^{2} - w + 3]$ $-2e^{2} - e + 18$
61 $[61, 61, 3w^{2} - w - 8]$ $\phantom{-}e^{2} - 3e - 1$
61 $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ $-3e^{2} + 3e + 17$
61 $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ $-e^{2} + 8$
61 $[61, 61, -3w^{2} - w + 8]$ $\phantom{-}2e^{2} + e - 16$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}2e - 2$
79 $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ $-e^{2} - 2e + 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w^{3} - w^{2} - 3w + 4]$ $1$
$19$ $[19,19,-w^{2} - w + 4]$ $1$