Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[10, 10, 2w^{2} - 3w - 15]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 5x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 1]$ | $-1$ |
5 | $[5, 5, w]$ | $-1$ |
7 | $[7, 7, w^{2} - 2w - 8]$ | $\phantom{-}e$ |
7 | $[7, 7, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e$ |
7 | $[7, 7, -w^{2} + 2w + 6]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e$ |
11 | $[11, 11, w^{2} - 2w - 2]$ | $-e + 2$ |
19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$ |
23 | $[23, 23, -w^{2} + 3w + 1]$ | $\phantom{-}4$ |
25 | $[25, 5, w^{2} - w - 9]$ | $-\frac{1}{2}e^{2} + \frac{7}{2}e - 4$ |
27 | $[27, 3, 3]$ | $-3e + 6$ |
29 | $[29, 29, -w^{2} - w + 1]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}e - 2$ |
29 | $[29, 29, w^{2} - 2w - 4]$ | $-e^{2} + 4e - 2$ |
29 | $[29, 29, -w^{2} + w + 11]$ | $-e^{2} + 3e + 4$ |
43 | $[43, 43, 2w^{2} - 3w - 18]$ | $-e^{2} + 5e - 4$ |
47 | $[47, 47, -2w + 7]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 4$ |
53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{9}{2}e - 10$ |
61 | $[61, 61, w^{2} + 2w + 2]$ | $\phantom{-}e^{2} - 5e - 4$ |
67 | $[67, 67, -2w^{2} + 5w + 8]$ | $\phantom{-}e^{2} - 6e - 2$ |
79 | $[79, 79, w^{2} - 3w - 9]$ | $\phantom{-}3e^{2} - 10e - 6$ |
97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}3e^{2} - 14e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 1]$ | $1$ |
$5$ | $[5, 5, w]$ | $1$ |