Properties

Label 6.6.1081856.1-47.1-f
Base field 6.6.1081856.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $47$
Level $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$
Dimension $14$
CM no
Base change no

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Base field 6.6.1081856.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 6x^{13} - 23x^{12} + 168x^{11} + 135x^{10} - 1470x^{9} - 377x^{8} + 5386x^{7} + 1046x^{6} - 7870x^{5} - 1832x^{4} + 3170x^{3} + 798x^{2} - 378x - 100\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ $\phantom{-}e$
8 $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ $...$
17 $[17, 17, -w^{2} + w + 2]$ $...$
23 $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ $...$
25 $[25, 5, -w^{3} + w^{2} + 4w]$ $...$
31 $[31, 31, -w^{3} + 4w + 1]$ $...$
31 $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ $...$
41 $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ $...$
47 $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ $-1$
49 $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ $...$
71 $[71, 71, -w^{4} + 5w^{2} + w - 3]$ $...$
71 $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ $...$
73 $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ $...$
73 $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ $...$
79 $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ $...$
89 $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ $...$
97 $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ $...$
103 $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ $...$
103 $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ $...$
103 $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$47$ $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ $1$