Properties

Label 6.6.820125.1-71.1-e
Base field 6.6.820125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $71$
Level $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$
Dimension $4$
CM no
Base change no

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Base field 6.6.820125.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$
Dimension: $4$
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:

\(x^{4} - 8x^{2} + 3x + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -\frac{6}{19}w^{5} + \frac{4}{19}w^{4} + \frac{45}{19}w^{3} - \frac{6}{19}w^{2} - \frac{12}{19}w + \frac{28}{19}]$ $\phantom{-}e$
19 $[19, 19, -\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{18}{19}w^{2} - \frac{116}{19}w + \frac{11}{19}]$ $\phantom{-}\frac{1}{3}e^{3} - e^{2} - \frac{11}{3}e + 4$
19 $[19, 19, -\frac{10}{19}w^{5} - \frac{6}{19}w^{4} + \frac{94}{19}w^{3} + \frac{85}{19}w^{2} - \frac{77}{19}w - \frac{42}{19}]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e - 2$
19 $[19, 19, -\frac{16}{19}w^{5} - \frac{2}{19}w^{4} + \frac{139}{19}w^{3} + \frac{79}{19}w^{2} - \frac{108}{19}w - \frac{33}{19}]$ $\phantom{-}\frac{4}{3}e^{3} + 2e^{2} - \frac{17}{3}e - 8$
19 $[19, 19, -\frac{4}{19}w^{5} + \frac{9}{19}w^{4} + \frac{30}{19}w^{3} - \frac{61}{19}w^{2} - \frac{8}{19}w + \frac{44}{19}]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e + 1$
19 $[19, 19, -\frac{8}{19}w^{5} - \frac{1}{19}w^{4} + \frac{79}{19}w^{3} + \frac{30}{19}w^{2} - \frac{111}{19}w - \frac{7}{19}]$ $-\frac{5}{3}e^{3} - 2e^{2} + \frac{22}{3}e + 4$
19 $[19, 19, \frac{2}{19}w^{5} + \frac{5}{19}w^{4} - \frac{15}{19}w^{3} - \frac{55}{19}w^{2} - \frac{34}{19}w + \frac{35}{19}]$ $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{2}{3}e - 5$
64 $[64, 2, 2]$ $\phantom{-}e^{3} + 4e^{2} - 6e - 16$
71 $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ $\phantom{-}1$
71 $[71, 71, -\frac{11}{19}w^{5} + \frac{20}{19}w^{4} + \frac{92}{19}w^{3} - \frac{125}{19}w^{2} - \frac{117}{19}w + \frac{64}{19}]$ $-2e^{3} + 13e - 6$
71 $[71, 71, \frac{12}{19}w^{5} - \frac{8}{19}w^{4} - \frac{109}{19}w^{3} + \frac{12}{19}w^{2} + \frac{138}{19}w + \frac{1}{19}]$ $-e - 3$
71 $[71, 71, \frac{22}{19}w^{5} - \frac{21}{19}w^{4} - \frac{184}{19}w^{3} + \frac{79}{19}w^{2} + \frac{177}{19}w - \frac{52}{19}]$ $\phantom{-}e^{3} - 7e - 3$
71 $[71, 71, w^{5} - w^{4} - 8w^{3} + 4w^{2} + 6w - 3]$ $-e^{3} - e^{2} + 11e$
71 $[71, 71, -\frac{24}{19}w^{5} + \frac{16}{19}w^{4} + \frac{199}{19}w^{3} - \frac{24}{19}w^{2} - \frac{162}{19}w - \frac{21}{19}]$ $-e^{3} + 7e - 9$
89 $[89, 89, \frac{13}{19}w^{5} + \frac{4}{19}w^{4} - \frac{126}{19}w^{3} - \frac{82}{19}w^{2} + \frac{159}{19}w + \frac{66}{19}]$ $-2e^{3} - 3e^{2} + 11e + 3$
89 $[89, 89, -\frac{17}{19}w^{5} + \frac{5}{19}w^{4} + \frac{137}{19}w^{3} + \frac{40}{19}w^{2} - \frac{53}{19}w - \frac{41}{19}]$ $\phantom{-}3e^{3} + 2e^{2} - 14e + 3$
89 $[89, 89, -\frac{29}{19}w^{5} + \frac{13}{19}w^{4} + \frac{246}{19}w^{3} + \frac{9}{19}w^{2} - \frac{210}{19}w + \frac{15}{19}]$ $\phantom{-}e^{3} - 9e$
89 $[89, 89, \frac{3}{19}w^{5} + \frac{17}{19}w^{4} - \frac{32}{19}w^{3} - \frac{149}{19}w^{2} - \frac{13}{19}w + \frac{62}{19}]$ $-e^{3} - 3e^{2} + 6$
89 $[89, 89, \frac{7}{19}w^{5} - \frac{11}{19}w^{4} - \frac{62}{19}w^{3} + \frac{64}{19}w^{2} + \frac{71}{19}w - \frac{39}{19}]$ $-3e^{3} - 3e^{2} + 20e + 3$
89 $[89, 89, -\frac{9}{19}w^{5} + \frac{6}{19}w^{4} + \frac{77}{19}w^{3} - \frac{28}{19}w^{2} - \frac{56}{19}w + \frac{42}{19}]$ $\phantom{-}e^{2} - 3e - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$71$ $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ $-1$