Base field 3.3.316.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[31, 31, 2w^{2} - 2w - 9]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 2x^{3} - 6x^{2} + 12x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
2 | $[2, 2, w - 1]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{7}{2}e - \frac{5}{2}$ |
11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{19}{2}e + \frac{9}{2}$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $-e^{3} - e^{2} + 5e + 7$ |
19 | $[19, 19, w^{2} - w + 1]$ | $-e^{2} + 5$ |
23 | $[23, 23, 2w - 3]$ | $\phantom{-}e^{2} - 9$ |
27 | $[27, 3, 3]$ | $-e^{3} - e^{2} + 7e + 3$ |
29 | $[29, 29, 2w + 1]$ | $\phantom{-}2e^{3} - e^{2} - 12e + 5$ |
31 | $[31, 31, 2w^{2} - 2w - 9]$ | $\phantom{-}1$ |
37 | $[37, 37, 2w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{3}{2}$ |
41 | $[41, 41, 2w^{2} - 9]$ | $-e^{3} + 5e - 2$ |
43 | $[43, 43, w^{2} + w - 5]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{3}{2}e^{2} - \frac{19}{2}e + \frac{11}{2}$ |
43 | $[43, 43, -3w^{2} + w + 15]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{11}{2}e - \frac{17}{2}$ |
43 | $[43, 43, -2w^{2} + 2w + 11]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 8$ |
53 | $[53, 53, w^{2} - w - 7]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{7}{2}$ |
61 | $[61, 61, 4w^{2} - 2w - 15]$ | $\phantom{-}e^{3} - 9e + 6$ |
67 | $[67, 67, -5w^{2} + 3w + 23]$ | $-e^{3} + 2e^{2} + 3e - 12$ |
73 | $[73, 73, 2w^{2} - 3]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e + \frac{13}{2}$ |
73 | $[73, 73, -3w^{2} - w + 7]$ | $\phantom{-}e^{3} + e^{2} - 5e + 5$ |
73 | $[73, 73, -6w^{2} + 4w + 25]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{7}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, 2w^{2} - 2w - 9]$ | $-1$ |