Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ |
Dimension: | $4$ |
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:
\(x^{4} + 2x^{3} - 24x^{2} - 70x - 25\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{2}{5}e^{2} - \frac{67}{10}e - 4$ |
19 | $[19, 19, w^{3} - 3w - 1]$ | $-\frac{1}{10}e^{3} - \frac{1}{5}e^{2} + \frac{19}{10}e + 2$ |
29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-\frac{2}{5}e^{3} + \frac{7}{10}e^{2} + \frac{33}{5}e - \frac{9}{2}$ |
29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{1}{2}e^{3} + \frac{21}{2}e + 12$ |
31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $\phantom{-}\frac{1}{10}e^{3} + \frac{1}{5}e^{2} - \frac{19}{10}e - 9$ |
41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $\phantom{-}\frac{3}{5}e^{3} - \frac{3}{10}e^{2} - \frac{67}{5}e - \frac{31}{2}$ |
49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{62}{5}e + 3$ |
59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{17}{2}e - 4$ |
59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{7}{10}e^{2} - \frac{28}{5}e + \frac{3}{2}$ |
59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $\phantom{-}\frac{3}{5}e^{3} - \frac{4}{5}e^{2} - \frac{62}{5}e - 9$ |
61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $\phantom{-}1$ |
64 | $[64, 2, -2]$ | $-\frac{3}{10}e^{3} - \frac{1}{10}e^{2} + \frac{67}{10}e + \frac{3}{2}$ |
71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $-\frac{1}{2}e^{2} + e + \frac{5}{2}$ |
79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $\phantom{-}\frac{7}{10}e^{3} + \frac{2}{5}e^{2} - \frac{153}{10}e - 22$ |
79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{1}{10}e^{2} - \frac{14}{5}e - \frac{25}{2}$ |
79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $\phantom{-}\frac{7}{10}e^{3} - \frac{3}{5}e^{2} - \frac{153}{10}e - 11$ |
81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $\phantom{-}\frac{7}{10}e^{3} - \frac{11}{10}e^{2} - \frac{153}{10}e - \frac{5}{2}$ |
89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{29}{2}e - 24$ |
101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{3}{5}e^{3} + \frac{9}{5}e^{2} + \frac{57}{5}e - 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$61$ | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $-1$ |