Properties

Label 6.6.1541581.1-47.1-c
Base field 6.6.1541581.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $47$
Level $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$
Dimension $1$
CM no
Base change no

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Base field 6.6.1541581.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $47$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}0$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $-2$
11 $[11, 11, w^{2} - w - 2]$ $\phantom{-}0$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $\phantom{-}6$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $-8$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}2$
37 $[37, 37, -w^{2} + 2w + 2]$ $\phantom{-}10$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $-1$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $-2$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $\phantom{-}8$
64 $[64, 2, -2]$ $\phantom{-}13$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $\phantom{-}10$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $\phantom{-}2$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $-2$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $\phantom{-}8$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $\phantom{-}8$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $-16$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $-4$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}18$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $1$