Properties

Label 6.6.1416125.1-41.1-a
Base field 6.6.1416125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$
Dimension $16$
CM no
Base change no

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Base field 6.6.1416125.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $37$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} + 5x^{15} - 34x^{14} - 194x^{13} + 346x^{12} + 2633x^{11} - 1004x^{10} - 16838x^{9} - 3708x^{8} + 54656x^{7} + 29001x^{6} - 87412x^{5} - 61533x^{4} + 60755x^{3} + 48257x^{2} - 14845x - 12565\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ $\phantom{-}e$
11 $[11, 11, w^{3} - w^{2} - 4w + 2]$ $...$
19 $[19, 19, -w^{3} + 4w]$ $...$
19 $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ $...$
19 $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ $...$
25 $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ $...$
29 $[29, 29, -w^{3} + 4w + 1]$ $...$
41 $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $\phantom{-}1$
49 $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ $...$
59 $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ $...$
59 $[59, 59, -w^{3} + w^{2} + 2w - 3]$ $...$
61 $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ $...$
64 $[64, 2, -2]$ $...$
71 $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ $...$
71 $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ $...$
79 $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ $...$
79 $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ $...$
89 $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ $...$
109 $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ $...$
109 $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $-1$