Base field 5.5.161121.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[27, 3, w^{4} - 2w^{3} - 5w^{2} + 7w + 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 5x^{7} - 4x^{6} + 43x^{5} - 7x^{4} - 119x^{3} + 38x^{2} + 104x - 30\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ | $\phantom{-}1$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
9 | $[9, 3, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 5]$ | $-1$ |
17 | $[17, 17, 2w^{4} - 2w^{3} - 11w^{2} + 7w + 6]$ | $\phantom{-}\frac{2}{5}e^{7} - \frac{7}{5}e^{6} - \frac{11}{5}e^{5} + \frac{42}{5}e^{4} + \frac{19}{5}e^{3} - \frac{57}{5}e^{2} - \frac{17}{5}e$ |
31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 7w - 4]$ | $-\frac{1}{5}e^{7} + \frac{1}{5}e^{6} + \frac{13}{5}e^{5} - \frac{11}{5}e^{4} - \frac{42}{5}e^{3} + \frac{31}{5}e^{2} + \frac{41}{5}e - 2$ |
31 | $[31, 31, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 7]$ | $\phantom{-}e^{6} - 3e^{5} - 6e^{4} + 18e^{3} + 5e^{2} - 22e + 10$ |
32 | $[32, 2, 2]$ | $-\frac{1}{5}e^{7} + \frac{6}{5}e^{6} - \frac{2}{5}e^{5} - \frac{36}{5}e^{4} + \frac{28}{5}e^{3} + \frac{71}{5}e^{2} - \frac{34}{5}e - 9$ |
37 | $[37, 37, w^{4} - 2w^{3} - 4w^{2} + 7w]$ | $\phantom{-}\frac{3}{5}e^{7} - \frac{13}{5}e^{6} - \frac{4}{5}e^{5} + \frac{68}{5}e^{4} - \frac{49}{5}e^{3} - \frac{73}{5}e^{2} + \frac{102}{5}e - 2$ |
41 | $[41, 41, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 6]$ | $-\frac{2}{5}e^{7} + \frac{2}{5}e^{6} + \frac{36}{5}e^{5} - \frac{42}{5}e^{4} - \frac{154}{5}e^{3} + \frac{142}{5}e^{2} + \frac{192}{5}e - 18$ |
43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}\frac{1}{5}e^{7} - \frac{6}{5}e^{6} - \frac{3}{5}e^{5} + \frac{41}{5}e^{4} + \frac{22}{5}e^{3} - \frac{81}{5}e^{2} - \frac{81}{5}e + 8$ |
43 | $[43, 43, 3w^{4} - 4w^{3} - 16w^{2} + 15w + 7]$ | $-\frac{1}{5}e^{7} + \frac{6}{5}e^{6} - \frac{12}{5}e^{5} - \frac{11}{5}e^{4} + \frac{93}{5}e^{3} - \frac{54}{5}e^{2} - \frac{144}{5}e + 16$ |
47 | $[47, 47, w^{2} - 3]$ | $-\frac{3}{5}e^{7} + \frac{13}{5}e^{6} + \frac{4}{5}e^{5} - \frac{73}{5}e^{4} + \frac{59}{5}e^{3} + \frac{93}{5}e^{2} - \frac{112}{5}e$ |
67 | $[67, 67, -2w^{4} + 3w^{3} + 10w^{2} - 11w - 5]$ | $-\frac{4}{5}e^{7} + \frac{19}{5}e^{6} + \frac{7}{5}e^{5} - \frac{114}{5}e^{4} + \frac{52}{5}e^{3} + \frac{139}{5}e^{2} - \frac{86}{5}e + 10$ |
71 | $[71, 71, 4w^{4} - 5w^{3} - 22w^{2} + 18w + 12]$ | $-\frac{3}{5}e^{7} + \frac{13}{5}e^{6} + \frac{14}{5}e^{5} - \frac{93}{5}e^{4} - \frac{1}{5}e^{3} + \frac{153}{5}e^{2} - \frac{42}{5}e$ |
79 | $[79, 79, -2w^{4} + 3w^{3} + 12w^{2} - 12w - 9]$ | $\phantom{-}\frac{4}{5}e^{7} - \frac{14}{5}e^{6} - \frac{22}{5}e^{5} + \frac{84}{5}e^{4} + \frac{48}{5}e^{3} - \frac{139}{5}e^{2} - \frac{64}{5}e + 10$ |
79 | $[79, 79, 3w^{4} - 3w^{3} - 16w^{2} + 8w + 4]$ | $\phantom{-}\frac{1}{5}e^{7} - \frac{1}{5}e^{6} - \frac{23}{5}e^{5} + \frac{31}{5}e^{4} + \frac{102}{5}e^{3} - \frac{91}{5}e^{2} - \frac{111}{5}e + 8$ |
83 | $[83, 83, w^{4} - 2w^{3} - 6w^{2} + 8w + 7]$ | $\phantom{-}\frac{1}{5}e^{7} - \frac{1}{5}e^{6} - \frac{18}{5}e^{5} + \frac{11}{5}e^{4} + \frac{97}{5}e^{3} - \frac{21}{5}e^{2} - \frac{146}{5}e$ |
97 | $[97, 97, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 4]$ | $\phantom{-}\frac{3}{5}e^{7} - \frac{8}{5}e^{6} - \frac{19}{5}e^{5} + \frac{38}{5}e^{4} + \frac{46}{5}e^{3} - \frac{48}{5}e^{2} - \frac{53}{5}e + 8$ |
107 | $[107, 107, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 9]$ | $-\frac{1}{5}e^{7} + \frac{1}{5}e^{6} + \frac{18}{5}e^{5} - \frac{11}{5}e^{4} - \frac{97}{5}e^{3} + \frac{11}{5}e^{2} + \frac{156}{5}e + 6$ |
107 | $[107, 107, w^{4} - w^{3} - 5w^{2} + 4w]$ | $-e^{7} + 4e^{6} + e^{5} - 17e^{4} + 16e^{3} + 8e^{2} - 27e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ | $-1$ |
$9$ | $[9, 3, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 5]$ | $1$ |