Base field 6.6.1528713.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 5x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
8 | $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ | $-\frac{1}{2}e^{2} - e + \frac{1}{2}$ |
9 | $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} + 2e - \frac{5}{2}$ |
19 | $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ | $-2e^{2} - 2e + 6$ |
19 | $[19, 19, -w + 2]$ | $-\frac{3}{2}e^{2} - e + \frac{1}{2}$ |
37 | $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{2} - 5e - \frac{1}{2}$ |
37 | $[37, 37, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}e^{2} - e$ |
53 | $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ | $-2e^{2} + e + 13$ |
53 | $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ | $\phantom{-}3e - 3$ |
53 | $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ | $-6$ |
53 | $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ | $-1$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ | $\phantom{-}3e + 3$ |
71 | $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ | $\phantom{-}\frac{5}{2}e^{2} - e - \frac{31}{2}$ |
73 | $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ | $-4e - 4$ |
73 | $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ | $\phantom{-}3e^{2} + 2e - 15$ |
73 | $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}3e^{2} + e - 4$ |
73 | $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ | $\phantom{-}e^{2} + 5e - 2$ |
89 | $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ | $-\frac{5}{2}e^{2} - 8e + \frac{13}{2}$ |
89 | $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ | $\phantom{-}3e^{2} + 4e - 17$ |
107 | $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ | $\phantom{-}3e^{2} + 6e - 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53,53,4w^{5} - 14w^{4} - 4w^{3} + 27w^{2} - 4w - 6]$ | $1$ |