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 | $[71, 71, 3w^{2} - 3w - 19]$ | $-\frac{1}{3}e^{7} + \frac{1}{3}e^{6} + 4e^{5} - \frac{14}{3}e^{4} - 14e^{3} + 15e^{2} + \frac{47}{3}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} + w + 3]$ | $-1$ |