Base field 3.3.321.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[31, 31, 2w - 3]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 9x^{3} + 8x^{2} + 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{4}e^{3} - \frac{9}{4}e^{2} + e + 3$ |
7 | $[7, 7, w^{2} - 2]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{9}{2}e^{2} + 3e - 6$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{7}{2}e^{2} + 3e + 2$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{11}{4}e^{2} + \frac{3}{2}e - 3$ |
23 | $[23, 23, -w - 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + 5$ |
29 | $[29, 29, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + 4e + 6$ |
31 | $[31, 31, 2w - 3]$ | $\phantom{-}1$ |
41 | $[41, 41, -2w^{2} + 3w + 6]$ | $\phantom{-}\frac{5}{4}e^{4} + \frac{1}{4}e^{3} - \frac{39}{4}e^{2} - \frac{7}{2}e + 11$ |
43 | $[43, 43, w^{2} - 3w + 3]$ | $\phantom{-}e^{4} - 8e^{2} + e + 2$ |
47 | $[47, 47, w^{2} + w - 4]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{9}{2}e^{2} - 4e - 2$ |
49 | $[49, 7, 2w^{2} - 3w - 3]$ | $\phantom{-}e^{3} + e^{2} - 7e - 2$ |
53 | $[53, 53, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{5}{4}e^{2} + 11e + 1$ |
59 | $[59, 59, 2w^{2} - w - 5]$ | $-\frac{3}{2}e^{4} + e^{3} + 11e^{2} - \frac{9}{2}e - 3$ |
59 | $[59, 59, w^{2} - w - 7]$ | $-\frac{3}{4}e^{4} + \frac{3}{4}e^{3} + \frac{19}{4}e^{2} - 2e + 1$ |
59 | $[59, 59, -w^{2} - w + 7]$ | $\phantom{-}\frac{5}{4}e^{4} + \frac{5}{4}e^{3} - \frac{47}{4}e^{2} - \frac{17}{2}e + 17$ |
67 | $[67, 67, 2w^{2} - 3w - 7]$ | $\phantom{-}e^{4} + e^{3} - 9e^{2} - 6e + 6$ |
73 | $[73, 73, -w^{2} + 4w - 5]$ | $\phantom{-}e^{4} - \frac{1}{2}e^{3} - \frac{17}{2}e^{2} + \frac{13}{2}e + 5$ |
79 | $[79, 79, w^{2} - 8]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 6e$ |
79 | $[79, 79, w^{2} - 5w + 5]$ | $-2e^{4} - \frac{1}{2}e^{3} + \frac{39}{2}e^{2} + \frac{11}{2}e - 25$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, 2w - 3]$ | $-1$ |