Properties

Label 6.6.1868969.1-32.1-a
Base field 6.6.1868969.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $32$
Level $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$
Dimension $27$
CM no
Base change no

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Base field 6.6.1868969.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$
Dimension: $27$
CM: no
Base change: no
Newspace dimension: $54$

Hecke eigenvalues ($q$-expansion)

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

\(x^{27} - 10x^{26} + 11x^{25} + 202x^{24} - 652x^{23} - 1333x^{22} + 8228x^{21} + 257x^{20} - 51239x^{19} + 43477x^{18} + 181482x^{17} - 269936x^{16} - 368674x^{15} + 834160x^{14} + 367020x^{13} - 1526598x^{12} + 24186x^{11} + 1707808x^{10} - 482971x^{9} - 1137004x^{8} + 521306x^{7} + 410095x^{6} - 244327x^{5} - 61138x^{4} + 47747x^{3} - 22x^{2} - 2151x + 81\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $...$
17 $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ $...$
23 $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $...$
31 $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ $...$
32 $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ $-1$
43 $[43, 43, w^{4} - 5w^{2} + 3]$ $...$
47 $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ $...$
49 $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ $...$
53 $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ $...$
59 $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ $...$
71 $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ $...$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $...$
83 $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ $...$
83 $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ $...$
89 $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ $...$
89 $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ $...$
89 $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ $...$
89 $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ $...$
101 $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$32$ $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ $1$