Properties

Label 3.3.568.1-17.1-b
Base field 3.3.568.1
Weight $[2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{2} + w + 3]$
Dimension $8$
CM no
Base change no

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Base field 3.3.568.1

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

Form

Weight: $[2, 2, 2]$
Level: $[17, 17, -w^{2} + w + 3]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - x^{7} - 11x^{6} + 10x^{5} + 33x^{4} - 22x^{3} - 26x^{2} + 3x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{3}e^{6} - \frac{31}{6}e^{5} + \frac{7}{2}e^{4} + \frac{40}{3}e^{3} - 8e^{2} - 6e + \frac{7}{6}$
5 $[5, 5, w^{2} - w - 7]$ $-\frac{1}{3}e^{7} + \frac{2}{3}e^{6} + \frac{11}{3}e^{5} - \frac{20}{3}e^{4} - \frac{31}{3}e^{3} + 15e^{2} + \frac{17}{3}e - \frac{5}{3}$
11 $[11, 11, -w^{2} + w + 1]$ $-\frac{2}{3}e^{7} + \frac{2}{3}e^{6} + 7e^{5} - \frac{19}{3}e^{4} - 19e^{3} + 12e^{2} + \frac{40}{3}e + 1$
17 $[17, 17, -w^{2} + w + 3]$ $\phantom{-}1$
25 $[25, 5, -w^{2} - w - 1]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{4}{3}e^{6} - \frac{31}{6}e^{5} + \frac{25}{2}e^{4} + \frac{37}{3}e^{3} - 26e^{2} - 4e + \frac{43}{6}$
27 $[27, 3, 3]$ $-\frac{1}{6}e^{7} + \frac{1}{3}e^{6} + \frac{11}{6}e^{5} - \frac{23}{6}e^{4} - \frac{14}{3}e^{3} + 10e^{2} - \frac{2}{3}e - \frac{5}{6}$
29 $[29, 29, -w^{2} + 3w - 1]$ $-\frac{1}{6}e^{7} - \frac{1}{3}e^{6} + \frac{3}{2}e^{5} + \frac{19}{6}e^{4} - 3e^{3} - 7e^{2} - \frac{2}{3}e + \frac{5}{2}$
37 $[37, 37, 3w^{2} - 5w - 13]$ $\phantom{-}\frac{7}{6}e^{7} - \frac{7}{3}e^{6} - \frac{77}{6}e^{5} + \frac{137}{6}e^{4} + \frac{116}{3}e^{3} - 50e^{2} - \frac{91}{3}e + \frac{41}{6}$
41 $[41, 41, 2w - 1]$ $\phantom{-}\frac{1}{2}e^{7} + \frac{1}{3}e^{6} - \frac{29}{6}e^{5} - \frac{5}{2}e^{4} + \frac{29}{3}e^{3} + 2e^{2} + 4e + \frac{29}{6}$
53 $[53, 53, 5w^{2} - 9w - 21]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{3}e^{6} - \frac{37}{6}e^{5} + \frac{7}{2}e^{4} + \frac{64}{3}e^{3} - 9e^{2} - 18e + \frac{25}{6}$
53 $[53, 53, 3w^{2} - 5w - 15]$ $-2e^{7} + \frac{7}{3}e^{6} + \frac{62}{3}e^{5} - 23e^{4} - \frac{163}{3}e^{3} + 49e^{2} + 31e - \frac{17}{3}$
53 $[53, 53, w^{2} - 3w - 7]$ $\phantom{-}\frac{3}{2}e^{7} - \frac{5}{3}e^{6} - \frac{101}{6}e^{5} + \frac{33}{2}e^{4} + \frac{155}{3}e^{3} - 37e^{2} - 37e + \frac{29}{6}$
59 $[59, 59, w^{2} - 3w - 5]$ $-\frac{13}{6}e^{7} + \frac{7}{3}e^{6} + \frac{137}{6}e^{5} - \frac{137}{6}e^{4} - \frac{185}{3}e^{3} + 48e^{2} + \frac{103}{3}e - \frac{29}{6}$
61 $[61, 61, 2w^{2} - 4w - 9]$ $-2e^{7} + \frac{7}{3}e^{6} + \frac{68}{3}e^{5} - 24e^{4} - \frac{214}{3}e^{3} + 56e^{2} + 58e - \frac{23}{3}$
61 $[61, 61, 2w - 7]$ $-\frac{4}{3}e^{7} + \frac{4}{3}e^{6} + 14e^{5} - \frac{35}{3}e^{4} - 37e^{3} + 18e^{2} + \frac{59}{3}e + 7$
61 $[61, 61, 2w - 5]$ $\phantom{-}\frac{2}{3}e^{7} - \frac{23}{3}e^{5} - \frac{2}{3}e^{4} + \frac{70}{3}e^{3} + 5e^{2} - \frac{43}{3}e - \frac{13}{3}$
67 $[67, 67, -w^{2} + w - 1]$ $\phantom{-}\frac{1}{6}e^{7} - \frac{13}{6}e^{5} - \frac{1}{6}e^{4} + \frac{22}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{5}{6}$
71 $[71, 71, -2w - 5]$ $\phantom{-}\frac{1}{3}e^{7} - \frac{5}{3}e^{6} - \frac{8}{3}e^{5} + \frac{50}{3}e^{4} + \frac{7}{3}e^{3} - 40e^{2} + \frac{10}{3}e + \frac{29}{3}$
71 $[71, 71, 3w^{2} - 3w - 19]$ $-\frac{1}{3}e^{7} + \frac{1}{3}e^{6} + 4e^{5} - \frac{14}{3}e^{4} - 14e^{3} + 15e^{2} + \frac{47}{3}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{2} + w + 3]$ $-1$