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: | $[71,71,-\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{37}{19}w^{2} - \frac{135}{19}w - \frac{27}{19}]$ |
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:
\(x^{4} + x^{3} - 29x^{2} + 16x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -\frac{6}{19}w^{5} + \frac{4}{19}w^{4} + \frac{45}{19}w^{3} - \frac{6}{19}w^{2} - \frac{12}{19}w + \frac{28}{19}]$ | $\phantom{-}4$ |
19 | $[19, 19, -\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{18}{19}w^{2} - \frac{116}{19}w + \frac{11}{19}]$ | $\phantom{-}\frac{23}{68}e^{3} + \frac{27}{68}e^{2} - \frac{683}{68}e + \frac{32}{17}$ |
19 | $[19, 19, -\frac{10}{19}w^{5} - \frac{6}{19}w^{4} + \frac{94}{19}w^{3} + \frac{85}{19}w^{2} - \frac{77}{19}w - \frac{42}{19}]$ | $\phantom{-}e$ |
19 | $[19, 19, -\frac{16}{19}w^{5} - \frac{2}{19}w^{4} + \frac{139}{19}w^{3} + \frac{79}{19}w^{2} - \frac{108}{19}w - \frac{33}{19}]$ | $-\frac{1}{34}e^{3} - \frac{13}{34}e^{2} - \frac{25}{34}e + \frac{114}{17}$ |
19 | $[19, 19, -\frac{4}{19}w^{5} + \frac{9}{19}w^{4} + \frac{30}{19}w^{3} - \frac{61}{19}w^{2} - \frac{8}{19}w + \frac{44}{19}]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{29}{4}e - 2$ |
19 | $[19, 19, -\frac{8}{19}w^{5} - \frac{1}{19}w^{4} + \frac{79}{19}w^{3} + \frac{30}{19}w^{2} - \frac{111}{19}w - \frac{7}{19}]$ | $-\frac{3}{17}e^{3} - \frac{5}{17}e^{2} + \frac{78}{17}e - \frac{47}{17}$ |
19 | $[19, 19, \frac{2}{19}w^{5} + \frac{5}{19}w^{4} - \frac{15}{19}w^{3} - \frac{55}{19}w^{2} - \frac{34}{19}w + \frac{35}{19}]$ | $\phantom{-}\frac{1}{34}e^{3} + \frac{13}{34}e^{2} - \frac{9}{34}e - \frac{46}{17}$ |
64 | $[64, 2, 2]$ | $-2e - 3$ |
71 | $[71, 71, \frac{16}{19}w^{5} - \frac{17}{19}w^{4} - \frac{139}{19}w^{3} + \frac{73}{19}w^{2} + \frac{165}{19}w - \frac{5}{19}]$ | $-\frac{5}{68}e^{3} + \frac{3}{68}e^{2} + \frac{249}{68}e - \frac{174}{17}$ |
71 | $[71, 71, -\frac{11}{19}w^{5} + \frac{20}{19}w^{4} + \frac{92}{19}w^{3} - \frac{125}{19}w^{2} - \frac{117}{19}w + \frac{64}{19}]$ | $-1$ |
71 | $[71, 71, \frac{12}{19}w^{5} - \frac{8}{19}w^{4} - \frac{109}{19}w^{3} + \frac{12}{19}w^{2} + \frac{138}{19}w + \frac{1}{19}]$ | $-\frac{1}{34}e^{3} - \frac{13}{34}e^{2} - \frac{25}{34}e + \frac{114}{17}$ |
71 | $[71, 71, \frac{22}{19}w^{5} - \frac{21}{19}w^{4} - \frac{184}{19}w^{3} + \frac{79}{19}w^{2} + \frac{177}{19}w - \frac{52}{19}]$ | $\phantom{-}\frac{21}{68}e^{3} + \frac{69}{68}e^{2} - \frac{529}{68}e - \frac{58}{17}$ |
71 | $[71, 71, w^{5} - w^{4} - 8w^{3} + 4w^{2} + 6w - 3]$ | $\phantom{-}\frac{5}{34}e^{3} - \frac{3}{34}e^{2} - \frac{79}{34}e + \frac{178}{17}$ |
71 | $[71, 71, -\frac{24}{19}w^{5} + \frac{16}{19}w^{4} + \frac{199}{19}w^{3} - \frac{24}{19}w^{2} - \frac{162}{19}w - \frac{21}{19}]$ | $\phantom{-}\frac{11}{34}e^{3} + \frac{7}{34}e^{2} - \frac{269}{34}e + \frac{208}{17}$ |
89 | $[89, 89, \frac{13}{19}w^{5} + \frac{4}{19}w^{4} - \frac{126}{19}w^{3} - \frac{82}{19}w^{2} + \frac{159}{19}w + \frac{66}{19}]$ | $-\frac{15}{68}e^{3} + \frac{9}{68}e^{2} + \frac{339}{68}e - \frac{182}{17}$ |
89 | $[89, 89, -\frac{17}{19}w^{5} + \frac{5}{19}w^{4} + \frac{137}{19}w^{3} + \frac{40}{19}w^{2} - \frac{53}{19}w - \frac{41}{19}]$ | $-\frac{3}{34}e^{3} - \frac{5}{34}e^{2} - \frac{7}{34}e - \frac{49}{17}$ |
89 | $[89, 89, -\frac{29}{19}w^{5} + \frac{13}{19}w^{4} + \frac{246}{19}w^{3} + \frac{9}{19}w^{2} - \frac{210}{19}w + \frac{15}{19}]$ | $\phantom{-}\frac{2}{17}e^{3} + \frac{9}{17}e^{2} - \frac{18}{17}e - \frac{14}{17}$ |
89 | $[89, 89, \frac{3}{19}w^{5} + \frac{17}{19}w^{4} - \frac{32}{19}w^{3} - \frac{149}{19}w^{2} - \frac{13}{19}w + \frac{62}{19}]$ | $\phantom{-}\frac{9}{34}e^{3} + \frac{15}{34}e^{2} - \frac{217}{34}e - \frac{40}{17}$ |
89 | $[89, 89, \frac{7}{19}w^{5} - \frac{11}{19}w^{4} - \frac{62}{19}w^{3} + \frac{64}{19}w^{2} + \frac{71}{19}w - \frac{39}{19}]$ | $-\frac{7}{68}e^{3} - \frac{23}{68}e^{2} + \frac{199}{68}e + \frac{42}{17}$ |
89 | $[89, 89, -\frac{9}{19}w^{5} + \frac{6}{19}w^{4} + \frac{77}{19}w^{3} - \frac{28}{19}w^{2} - \frac{56}{19}w + \frac{42}{19}]$ | $-\frac{2}{17}e^{3} - \frac{9}{17}e^{2} + \frac{18}{17}e + \frac{184}{17}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$71$ | $[71,71,-\frac{20}{19}w^{5} + \frac{7}{19}w^{4} + \frac{169}{19}w^{3} + \frac{37}{19}w^{2} - \frac{135}{19}w - \frac{27}{19}]$ | $1$ |