Base field 5.5.81589.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[17, 17, w^{4} - 4w^{2} + 2]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 22x^{10} + 178x^{8} - 644x^{6} + 1006x^{4} - 543x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2} - 3]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{1}{3}e^{6} + \frac{11}{3}e^{4} - 10e^{2} + \frac{16}{3}$ |
13 | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{1}{3}e^{7} + \frac{14}{3}e^{5} - 19e^{3} + \frac{58}{3}e$ |
16 | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{160}{3}e^{5} + \frac{487}{6}e^{3} - \frac{165}{4}e$ |
17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}1$ |
31 | $[31, 31, w^{4} - 4w^{2} - w + 3]$ | $\phantom{-}\frac{1}{6}e^{11} - \frac{10}{3}e^{9} + \frac{71}{3}e^{7} - 70e^{5} + 75e^{3} - \frac{97}{6}e$ |
43 | $[43, 43, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{14}{3}e^{5} + 19e^{3} - \frac{64}{3}e$ |
53 | $[53, 53, w^{4} - 3w^{2} - 1]$ | $-\frac{1}{6}e^{11} + \frac{11}{3}e^{9} - \frac{89}{3}e^{7} + \frac{320}{3}e^{5} - \frac{481}{3}e^{3} + \frac{145}{2}e$ |
53 | $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{11}{3}e^{4} + 10e^{2} - \frac{10}{3}$ |
53 | $[53, 53, -w^{3} - w^{2} + 3w + 4]$ | $-2e^{2} + 8$ |
61 | $[61, 61, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{1}{3}e^{9} - 6e^{7} + \frac{110}{3}e^{5} - \frac{262}{3}e^{3} + \frac{199}{3}e$ |
61 | $[61, 61, w^{4} - 4w^{2} + w + 1]$ | $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{163}{3}e^{5} + \frac{535}{6}e^{3} - \frac{197}{4}e$ |
61 | $[61, 61, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}\frac{1}{3}e^{8} - \frac{14}{3}e^{6} + 18e^{4} - \frac{37}{3}e^{2} - 6$ |
67 | $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{3}e^{8} - \frac{16}{3}e^{6} + \frac{82}{3}e^{4} - \frac{139}{3}e^{2} + \frac{44}{3}$ |
71 | $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ | $-\frac{1}{3}e^{10} + \frac{19}{3}e^{8} - 42e^{6} + \frac{338}{3}e^{4} - \frac{305}{3}e^{2} + \frac{35}{3}$ |
71 | $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ | $-\frac{1}{12}e^{11} + \frac{11}{6}e^{9} - \frac{89}{6}e^{7} + \frac{163}{3}e^{5} - \frac{535}{6}e^{3} + \frac{205}{4}e$ |
73 | $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ | $-\frac{1}{4}e^{11} + \frac{11}{2}e^{9} - \frac{263}{6}e^{7} + \frac{455}{3}e^{5} - \frac{427}{2}e^{3} + \frac{1141}{12}e$ |
73 | $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ | $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{163}{3}e^{5} + \frac{547}{6}e^{3} - \frac{253}{4}e$ |
79 | $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ | $-\frac{1}{4}e^{11} + \frac{31}{6}e^{9} - \frac{77}{2}e^{7} + \frac{373}{3}e^{5} - \frac{997}{6}e^{3} + \frac{929}{12}e$ |
83 | $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ | $-2e^{4} + 14e^{2} - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, w^{4} - 4w^{2} + 2]$ | $-1$ |