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: | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 3x^{4} - 11x^{3} - 33x^{2} + 12x + 40\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}e^{2} + e - 6$ |
19 | $[19, 19, w^{3} - 3w - 1]$ | $\phantom{-}e^{2} - e - 6$ |
29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 12$ |
29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e + 3$ |
31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + 10e - 7$ |
41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e + 3$ |
49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $\phantom{-}5$ |
59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + e + 4$ |
59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{11}{2}e^{2} + 10e + 9$ |
59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} - 2e + 7$ |
61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $\phantom{-}e^{4} + e^{3} - 10e^{2} - 9e + 10$ |
64 | $[64, 2, -2]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 3e + 1$ |
71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $\phantom{-}e^{4} + e^{3} - 13e^{2} - 8e + 25$ |
79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $-1$ |
79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $-\frac{1}{2}e^{4} + \frac{15}{2}e^{2} - 22$ |
79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{9}{2}e^{2} + \frac{7}{2}e - 1$ |
81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{9}{2}e^{2} - 9e + 2$ |
89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 16$ |
101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{11}{2}e^{2} + 6e - 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$79$ | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $1$ |