Base field 6.6.1312625.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 7x^{3} + 12x^{2} - 12x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[16, 4, -w^{5} - w^{4} + 7w^{3} + 5w^{2} - 11w - 3]$ |
Dimension: | $8$ |
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:
\(x^{8} - 57x^{6} + 807x^{4} - 1807x^{2} + 768\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}e$ |
16 | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $-\frac{101}{7248}e^{7} + \frac{5665}{7248}e^{5} - \frac{75683}{7248}e^{3} + \frac{31517}{2416}e$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{5}{604}e^{6} - \frac{66}{151}e^{4} + \frac{3047}{604}e^{2} - \frac{56}{151}$ |
29 | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $-\frac{5}{604}e^{6} + \frac{66}{151}e^{4} - \frac{3047}{604}e^{2} + \frac{660}{151}$ |
31 | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $-e$ |
41 | $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ | $\phantom{-}\frac{1}{1812}e^{7} - \frac{83}{1812}e^{5} + \frac{2059}{1812}e^{3} - \frac{4555}{604}e$ |
41 | $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ | $-\frac{17}{1812}e^{7} + \frac{479}{906}e^{5} - \frac{13259}{1812}e^{3} + \frac{4365}{302}e$ |
59 | $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ | $-\frac{1}{1812}e^{7} + \frac{83}{1812}e^{5} - \frac{2059}{1812}e^{3} + \frac{3347}{604}e$ |
61 | $[61, 61, w^{5} - 7w^{3} + 10w]$ | $\phantom{-}\frac{1}{453}e^{6} - \frac{83}{453}e^{4} + \frac{1606}{453}e^{2} - \frac{780}{151}$ |
61 | $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ | $-\frac{1}{1812}e^{7} + \frac{83}{1812}e^{5} - \frac{2059}{1812}e^{3} + \frac{4555}{604}e$ |
71 | $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ | $\phantom{-}\frac{17}{1812}e^{7} - \frac{479}{906}e^{5} + \frac{13259}{1812}e^{3} - \frac{4667}{302}e$ |
71 | $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ | $\phantom{-}\frac{49}{1812}e^{6} - \frac{677}{453}e^{4} + \frac{35659}{1812}e^{2} - \frac{3364}{151}$ |
71 | $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ | $-\frac{11}{604}e^{7} + \frac{611}{604}e^{5} - \frac{8153}{604}e^{3} + \frac{13509}{604}e$ |
79 | $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ | $-\frac{1}{1812}e^{7} + \frac{83}{1812}e^{5} - \frac{2059}{1812}e^{3} + \frac{5763}{604}e$ |
79 | $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ | $-\frac{4}{453}e^{7} + \frac{875}{1812}e^{5} - \frac{2800}{453}e^{3} + \frac{5383}{604}e$ |
79 | $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ | $-\frac{5}{604}e^{6} + \frac{66}{151}e^{4} - \frac{3047}{604}e^{2} + \frac{1264}{151}$ |
89 | $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ | $\phantom{-}\frac{1}{1812}e^{7} - \frac{83}{1812}e^{5} + \frac{2059}{1812}e^{3} - \frac{5159}{604}e$ |
89 | $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ | $-\frac{67}{3624}e^{7} + \frac{3749}{3624}e^{5} - \frac{49165}{3624}e^{3} + \frac{14057}{1208}e$ |
89 | $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ | $-\frac{15}{604}e^{6} + \frac{198}{151}e^{4} - \frac{9745}{604}e^{2} + \frac{3792}{151}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $1$ |