Properties

Label 6.6.1922000.1-44.1-b
Base field 6.6.1922000.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, 3w^{5} - 5w^{4} - 20w^{3} + 8w^{2} + 28w + 7]$
Dimension $1$
CM no
Base change no

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Base field 6.6.1922000.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 8x^{4} - x^{3} + 12x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[44, 22, 3w^{5} - 5w^{4} - 20w^{3} + 8w^{2} + 28w + 7]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ $-1$
11 $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $\phantom{-}1$
11 $[11, 11, -w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ $-4$
11 $[11, 11, w - 1]$ $\phantom{-}3$
31 $[31, 31, -4w^{5} + 6w^{4} + 28w^{3} - 8w^{2} - 39w - 11]$ $-3$
41 $[41, 41, -4w^{5} + 5w^{4} + 31w^{3} - 4w^{2} - 49w - 16]$ $\phantom{-}3$
41 $[41, 41, w^{4} - 3w^{3} - 3w^{2} + 8w + 1]$ $\phantom{-}0$
41 $[41, 41, -w^{2} + w + 2]$ $\phantom{-}2$
59 $[59, 59, w^{2} - w - 4]$ $\phantom{-}11$
59 $[59, 59, 4w^{5} - 5w^{4} - 31w^{3} + 4w^{2} + 49w + 14]$ $-3$
59 $[59, 59, -w^{4} + 3w^{3} + 3w^{2} - 8w - 3]$ $-4$
71 $[71, 71, 5w^{5} - 7w^{4} - 37w^{3} + 9w^{2} + 55w + 16]$ $-2$
71 $[71, 71, -w^{5} + 11w^{3} + 4w^{2} - 19w - 7]$ $-6$
71 $[71, 71, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ $-10$
79 $[79, 79, 3w^{5} - 6w^{4} - 17w^{3} + 11w^{2} + 21w + 7]$ $\phantom{-}1$
79 $[79, 79, -5w^{5} + 8w^{4} + 35w^{3} - 14w^{2} - 52w - 11]$ $\phantom{-}10$
79 $[79, 79, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 2]$ $\phantom{-}8$
101 $[101, 101, -2w^{5} + 3w^{4} + 14w^{3} - 3w^{2} - 21w - 9]$ $-12$
101 $[101, 101, -2w^{5} + 2w^{4} + 17w^{3} - 29w - 9]$ $\phantom{-}10$
101 $[101, 101, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 9w + 1]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ $1$
$11$ $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $-1$