Properties

Label 6.6.1683101.1-43.2-e
Base field 6.6.1683101.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $43$
Level $[43,43,w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 2]$
Dimension $30$
CM no
Base change no

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Base field 6.6.1683101.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[43,43,w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 2]$
Dimension: $30$
CM: no
Base change: no
Newspace dimension: $50$

Hecke eigenvalues ($q$-expansion)

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

\(x^{30} - 8x^{29} - 95x^{28} + 884x^{27} + 3513x^{26} - 42380x^{25} - 53652x^{24} + 1151339x^{23} - 211922x^{22} - 19342997x^{21} + 23076545x^{20} + 203722179x^{19} - 429779809x^{18} - 1258759701x^{17} + 4233958883x^{16} + 3170461036x^{15} - 24030677248x^{14} + 11171311561x^{13} + 71632494964x^{12} - 106174231562x^{11} - 58824240389x^{10} + 268202993882x^{9} - 194480094432x^{8} - 124376074379x^{7} + 323122378435x^{6} - 260202149484x^{5} + 111232903414x^{4} - 26066872825x^{3} + 2982930327x^{2} - 114400080x - 547668\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w]$ $...$
7 $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ $\phantom{-}e$
13 $[13, 13, w^{2} - 3]$ $...$
13 $[13, 13, -w^{2} + 2w + 2]$ $...$
29 $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ $...$
29 $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ $...$
41 $[41, 41, -w^{2} + 4]$ $...$
41 $[41, 41, -w^{2} + 2w + 3]$ $...$
43 $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $...$
43 $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $-1$
64 $[64, 2, -2]$ $...$
71 $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ $...$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ $...$
71 $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $...$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ $...$
83 $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ $...$
83 $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ $...$
97 $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $...$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ $...$
113 $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43,43,w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 2]$ $1$