Properties

Label 6.6.905177.1-43.3-g
Base field 6.6.905177.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $43$
Level $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$
Dimension $7$
CM no
Base change no

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Base field 6.6.905177.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 9x^{3} + 7x^{2} - 9x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$
Dimension: $7$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{7} - 6x^{6} - 18x^{5} + 172x^{4} - 135x^{3} - 1105x^{2} + 2670x - 1759\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, -2w^{5} - w^{4} + 13w^{3} + w^{2} - 16w - 1]$ $\phantom{-}e$
8 $[8, 2, -3w^{5} - w^{4} + 19w^{3} - 2w^{2} - 20w + 1]$ $\phantom{-}\frac{3}{2}e^{6} - \frac{11}{2}e^{5} - \frac{79}{2}e^{4} + \frac{331}{2}e^{3} + 177e^{2} - \frac{2475}{2}e + \frac{2289}{2}$
13 $[13, 13, -w^{2} + 3]$ $-\frac{7}{6}e^{6} + \frac{23}{6}e^{5} + \frac{185}{6}e^{4} - \frac{701}{6}e^{3} - \frac{439}{3}e^{2} + \frac{5303}{6}e - \frac{4699}{6}$
29 $[29, 29, -w^{5} - w^{4} + 5w^{3} + 2w^{2} - 3w - 1]$ $\phantom{-}\frac{7}{3}e^{6} - \frac{26}{3}e^{5} - \frac{185}{3}e^{4} + \frac{785}{3}e^{3} + \frac{824}{3}e^{2} - \frac{5891}{3}e + \frac{5512}{3}$
41 $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$ $\phantom{-}4e^{6} - 16e^{5} - 105e^{4} + 478e^{3} + 442e^{2} - 3549e + 3414$
41 $[41, 41, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 5]$ $\phantom{-}e^{5} - 26e^{3} + 15e^{2} + 164e - 218$
43 $[43, 43, -w^{2} - w + 2]$ $\phantom{-}\frac{3}{2}e^{6} - \frac{11}{2}e^{5} - \frac{79}{2}e^{4} + \frac{333}{2}e^{3} + 174e^{2} - \frac{2507}{2}e + \frac{2379}{2}$
43 $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 5]$ $-\frac{20}{3}e^{6} + \frac{73}{3}e^{5} + \frac{526}{3}e^{4} - \frac{2206}{3}e^{3} - \frac{2329}{3}e^{2} + \frac{16567}{3}e - \frac{15539}{3}$
43 $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$ $\phantom{-}1$
43 $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 15w + 3]$ $-\frac{9}{2}e^{6} + \frac{35}{2}e^{5} + \frac{237}{2}e^{4} - \frac{1049}{2}e^{3} - 512e^{2} + \frac{7813}{2}e - \frac{7409}{2}$
49 $[49, 7, -w^{5} - w^{4} + 6w^{3} + 3w^{2} - 7w]$ $-\frac{4}{3}e^{6} + \frac{17}{3}e^{5} + \frac{107}{3}e^{4} - \frac{503}{3}e^{3} - \frac{467}{3}e^{2} + \frac{3704}{3}e - \frac{3496}{3}$
71 $[71, 71, -5w^{5} - 2w^{4} + 32w^{3} - w^{2} - 35w - 2]$ $-\frac{61}{6}e^{6} + \frac{227}{6}e^{5} + \frac{1601}{6}e^{4} - \frac{6839}{6}e^{3} - \frac{3493}{3}e^{2} + \frac{51203}{6}e - \frac{48367}{6}$
71 $[71, 71, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 6]$ $\phantom{-}\frac{4}{3}e^{6} - \frac{8}{3}e^{5} - \frac{104}{3}e^{4} + \frac{269}{3}e^{3} + \frac{536}{3}e^{2} - \frac{2219}{3}e + \frac{1822}{3}$
71 $[71, 71, -3w^{5} - 2w^{4} + 19w^{3} + 5w^{2} - 22w - 7]$ $-\frac{8}{3}e^{6} + \frac{31}{3}e^{5} + \frac{211}{3}e^{4} - \frac{934}{3}e^{3} - \frac{913}{3}e^{2} + \frac{6994}{3}e - \frac{6635}{3}$
71 $[71, 71, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 6]$ $-\frac{5}{2}e^{6} + \frac{23}{2}e^{5} + \frac{131}{2}e^{4} - \frac{679}{2}e^{3} - 250e^{2} + \frac{4983}{2}e - \frac{4999}{2}$
83 $[83, 83, -2w^{5} - w^{4} + 12w^{3} - 12w + 1]$ $-\frac{1}{6}e^{6} + \frac{5}{6}e^{5} + \frac{23}{6}e^{4} - \frac{137}{6}e^{3} - \frac{25}{3}e^{2} + \frac{923}{6}e - \frac{1033}{6}$
83 $[83, 83, -2w^{5} - w^{4} + 13w^{3} - 16w + 1]$ $\phantom{-}\frac{25}{6}e^{6} - \frac{107}{6}e^{5} - \frac{659}{6}e^{4} + \frac{3167}{6}e^{3} + \frac{1360}{3}e^{2} - \frac{23297}{6}e + \frac{22561}{6}$
83 $[83, 83, -4w^{5} - 2w^{4} + 26w^{3} + 3w^{2} - 29w - 6]$ $\phantom{-}\frac{22}{3}e^{6} - \frac{80}{3}e^{5} - \frac{578}{3}e^{4} + \frac{2417}{3}e^{3} + \frac{2558}{3}e^{2} - \frac{18149}{3}e + \frac{17014}{3}$
83 $[83, 83, 2w^{5} - 13w^{3} + 5w^{2} + 13w - 1]$ $\phantom{-}\frac{4}{3}e^{6} - \frac{14}{3}e^{5} - \frac{107}{3}e^{4} + \frac{425}{3}e^{3} + \frac{506}{3}e^{2} - \frac{3206}{3}e + \frac{2890}{3}$
97 $[97, 97, -3w^{5} + 20w^{3} - 8w^{2} - 22w + 5]$ $\phantom{-}\frac{17}{3}e^{6} - \frac{67}{3}e^{5} - \frac{448}{3}e^{4} + \frac{1999}{3}e^{3} + \frac{1942}{3}e^{2} - \frac{14824}{3}e + \frac{13991}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$43$ $[43,43,-w^{5}+7w^{3}-w^{2}-8w-3]$ $-1$