Base field 3.3.404.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[9, 3, w^{2} - 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $3$ |
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 |
---|---|---|
2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$ |
7 | $[7, 7, -w + 2]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}$ |
9 | $[9, 3, w^{2} - 2]$ | $\phantom{-}1$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}e - 1$ |
29 | $[29, 29, -2w + 1]$ | $\phantom{-}\frac{3}{2}e^{2} + 4e - \frac{11}{2}$ |
37 | $[37, 37, 2w^{2} - 4w - 3]$ | $-3e^{2} - 5e + 10$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $-\frac{3}{2}e^{2} - 2e + \frac{15}{2}$ |
37 | $[37, 37, 2w^{2} - w - 8]$ | $-\frac{3}{2}e^{2} - 4e + \frac{7}{2}$ |
41 | $[41, 41, w^{2} - 4w + 2]$ | $-\frac{1}{2}e^{2} + \frac{13}{2}$ |
43 | $[43, 43, -2w^{2} + 2w + 7]$ | $\phantom{-}e^{2} - 5$ |
43 | $[43, 43, -2w^{2} + 3w + 6]$ | $-\frac{1}{2}e^{2} - 4e + \frac{1}{2}$ |
43 | $[43, 43, -w^{2} + 6]$ | $-e^{2} - 4e + 5$ |
49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}3e^{2} + 2e - 3$ |
53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-2e^{2} + 12$ |
59 | $[59, 59, 2w - 3]$ | $\phantom{-}e + 7$ |
61 | $[61, 61, -w - 4]$ | $-2e^{2} - 2e + 6$ |
67 | $[67, 67, -2w^{2} - w + 2]$ | $-4e^{2} - 2e + 10$ |
73 | $[73, 73, 2w^{2} - 3w - 12]$ | $\phantom{-}4e + 2$ |
83 | $[83, 83, -2w - 5]$ | $\phantom{-}4e^{2} + 6e - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{2} - 2]$ | $-1$ |