Properties

Label 6.6.453789.1-43.4-e
Base field \(\Q(\zeta_{21})^+\)
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $43$
Level $[43,43,w^{3} - w^{2} - 4w + 2]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\zeta_{21})^+\)

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 8x^{2} - 8x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[43,43,w^{3} - w^{2} - 4w + 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 10x + 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, -w^{5} + 5w^{3} - 5w - 1]$ $\phantom{-}4$
27 $[27, 3, -2w^{5} + 10w^{3} - w^{2} - 10w + 2]$ $\phantom{-}e$
41 $[41, 41, -w^{5} + 6w^{3} - w^{2} - 7w + 2]$ $-2e - 12$
41 $[41, 41, w^{4} - w^{3} - 4w^{2} + 3w + 1]$ $-e$
41 $[41, 41, -2w^{5} + 12w^{3} - 2w^{2} - 17w + 5]$ $-e$
41 $[41, 41, w^{5} - 5w^{3} + 2w^{2} + 5w - 5]$ $-12$
41 $[41, 41, -w^{4} - 2w^{3} + 4w^{2} + 6w - 3]$ $-2e - 12$
41 $[41, 41, -2w^{5} + 10w^{3} - w^{2} - 10w + 3]$ $\phantom{-}2e + 12$
43 $[43, 43, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 9w + 4]$ $\phantom{-}4$
43 $[43, 43, -w^{4} - w^{3} + 4w^{2} + 4w - 3]$ $-4e - 20$
43 $[43, 43, -w^{4} + 3w^{2} + 1]$ $\phantom{-}2e + 10$
43 $[43, 43, -w^{3} + w^{2} + 4w - 2]$ $-1$
43 $[43, 43, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 3]$ $-4e - 20$
43 $[43, 43, -w^{2} - w + 3]$ $\phantom{-}2e + 10$
64 $[64, 2, -2]$ $-2e - 11$
83 $[83, 83, -w^{5} + 6w^{3} - w^{2} - 10w + 4]$ $-2e$
83 $[83, 83, -2w^{5} + w^{4} + 12w^{3} - 6w^{2} - 17w + 6]$ $\phantom{-}5e + 24$
83 $[83, 83, w^{5} - 6w^{3} + 2w^{2} + 8w - 3]$ $\phantom{-}e + 12$
83 $[83, 83, w^{5} - 4w^{3} + w - 1]$ $\phantom{-}4e + 24$
83 $[83, 83, -2w^{5} + 11w^{3} - w^{2} - 13w + 1]$ $\phantom{-}5e + 24$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43,43,w^{3} - w^{2} - 4w + 2]$ $1$