Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[55, 55, w^{5} - 8w^{3} - 2w^{2} + 15w + 5]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - 27x^{3} - 6x^{2} + 40x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $-1$ |
9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $\phantom{-}e$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}1$ |
25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $-e$ |
29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $\phantom{-}\frac{5}{2}e^{4} + \frac{3}{2}e^{3} - \frac{133}{2}e^{2} - \frac{109}{2}e + 59$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}\frac{3}{4}e^{4} + \frac{1}{2}e^{3} - \frac{81}{4}e^{2} - 17e + 21$ |
49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $-\frac{1}{2}e^{4} + \frac{27}{2}e^{2} + 2e - 16$ |
59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $-\frac{5}{2}e^{4} - 2e^{3} + \frac{133}{2}e^{2} + 66e - 66$ |
59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-\frac{9}{4}e^{4} - \frac{3}{2}e^{3} + \frac{239}{4}e^{2} + 53e - 57$ |
61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $\phantom{-}e^{4} + e^{3} - 27e^{2} - 31e + 24$ |
61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $-\frac{3}{2}e^{4} - e^{3} + \frac{81}{2}e^{2} + 36e - 48$ |
64 | $[64, 2, 2]$ | $\phantom{-}\frac{9}{4}e^{4} + e^{3} - \frac{239}{4}e^{2} - \frac{87}{2}e + 59$ |
71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}e^{4} + \frac{1}{2}e^{3} - 27e^{2} - \frac{39}{2}e + 25$ |
71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $-\frac{7}{2}e^{4} - 2e^{3} + \frac{185}{2}e^{2} + 74e - 86$ |
79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $-\frac{5}{4}e^{4} - \frac{1}{2}e^{3} + \frac{135}{4}e^{2} + 21e - 41$ |
81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{79}{2}e^{2} - \frac{47}{2}e + 41$ |
89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $\phantom{-}\frac{7}{2}e^{4} + \frac{5}{2}e^{3} - \frac{187}{2}e^{2} - \frac{175}{2}e + 89$ |
89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $\phantom{-}\frac{9}{4}e^{4} + \frac{3}{2}e^{3} - \frac{239}{4}e^{2} - 54e + 53$ |
89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $-4e^{4} - \frac{5}{2}e^{3} + 106e^{2} + \frac{181}{2}e - 101$ |
89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $-e^{4} - e^{3} + 27e^{2} + 31e - 32$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $1$ |
$11$ | $[11, 11, w - 1]$ | $-1$ |