Base field 6.6.1767625.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[44, 22, w^{2} - w - 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 4x^{3} - 10x^{2} + 28x + 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w + 1]$ | $-1$ |
9 | $[9, 3, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{3}{2}w^{2} - 5w + \frac{1}{2}]$ | $\phantom{-}0$ |
11 | $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ | $\phantom{-}1$ |
16 | $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ | $\phantom{-}e$ |
29 | $[29, 29, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 4w^{3} + \frac{5}{2}w^{2} - 6w + \frac{1}{2}]$ | $-\frac{1}{4}e^{3} + \frac{5}{4}e^{2} + \frac{3}{4}e - \frac{23}{4}$ |
41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{3}{2}w^{2} + 3w + \frac{3}{2}]$ | $\phantom{-}\frac{1}{2}e^{2} - 2e - \frac{7}{2}$ |
41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 2w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}]$ | $-e^{2} + 2e + 7$ |
59 | $[59, 59, -\frac{3}{2}w^{5} + \frac{1}{2}w^{4} + 9w^{3} + \frac{1}{2}w^{2} - 11w - \frac{5}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{11}{2}e + 10$ |
59 | $[59, 59, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 3w^{3} + \frac{5}{2}w^{2} - 4w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{7}{2}e + 6$ |
59 | $[59, 59, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 2w^{3} - \frac{1}{2}w^{2} - \frac{3}{2}]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 1$ |
59 | $[59, 59, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 11w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{7}{2}e + 6$ |
61 | $[61, 61, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{1}{2}w^{2} + 4w + \frac{5}{2}]$ | $-\frac{1}{2}e^{2} + 2e - \frac{5}{2}$ |
71 | $[71, 71, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 5w^{3} + \frac{5}{2}w^{2} - 11w - \frac{3}{2}]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{11}{4}e + \frac{45}{4}$ |
71 | $[71, 71, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 4w^{3} - \frac{5}{2}w^{2} - 7w + \frac{3}{2}]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{15}{2}e - \frac{25}{2}$ |
79 | $[79, 79, -w^{5} + 6w^{3} + 2w^{2} - 8w - 2]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{15}{2}e - \frac{29}{2}$ |
79 | $[79, 79, -\frac{3}{2}w^{5} + \frac{3}{2}w^{4} + 9w^{3} - \frac{11}{2}w^{2} - 12w + \frac{3}{2}]$ | $\phantom{-}e^{3} - 3e^{2} - 11e + 11$ |
81 | $[81, 3, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 8w + \frac{3}{2}]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{19}{4}e + \frac{25}{4}$ |
89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 14w + \frac{7}{2}]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{3}{4}e - \frac{25}{4}$ |
89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 10w - \frac{1}{2}]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{19}{4}e - \frac{19}{4}$ |
89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 15w + \frac{9}{2}]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w + 1]$ | $1$ |
$11$ | $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ | $-1$ |