Base field 3.3.940.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[16, 4, w^{2} - 7]$ |
Dimension: | $5$ |
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:
\(x^{5} + 2x^{4} - 7x^{3} - 13x^{2} + 4x + 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
5 | $[5, 5, -w^{2} + w + 7]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 4e^{2} - \frac{5}{2}e + \frac{7}{2}$ |
5 | $[5, 5, -w^{2} + w + 5]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 3e^{2} + \frac{7}{2}e + \frac{1}{2}$ |
17 | $[17, 17, -w^{2} + 3w + 1]$ | $-\frac{3}{2}e^{4} - \frac{3}{2}e^{3} + 11e^{2} + \frac{17}{2}e - \frac{13}{2}$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}e^{4} - 7e^{2} + 6$ |
27 | $[27, 3, 3]$ | $-e^{3} + e^{2} + 7e - 3$ |
29 | $[29, 29, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 4e^{2} - \frac{9}{2}e + \frac{11}{2}$ |
37 | $[37, 37, w^{2} + w + 1]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - 9e^{2} - \frac{5}{2}e - \frac{1}{2}$ |
41 | $[41, 41, w^{2} - w - 9]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - e^{2} - \frac{19}{2}e - \frac{11}{2}$ |
43 | $[43, 43, -3w^{2} + 3w + 17]$ | $-e^{4} + e^{3} + 8e^{2} - 5e - 7$ |
47 | $[47, 47, 2w^{2} - 2w - 13]$ | $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 17e + 3$ |
47 | $[47, 47, -2w + 5]$ | $-2e^{3} + 14e + 4$ |
53 | $[53, 53, 3w^{2} - w - 19]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{5}{2}e^{3} - 10e^{2} - \frac{23}{2}e + \frac{15}{2}$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}e^{4} - 9e^{2} - 2e + 14$ |
67 | $[67, 67, w^{2} + w - 5]$ | $-e^{3} - e^{2} + 7e + 7$ |
71 | $[71, 71, -3w^{2} + w + 21]$ | $\phantom{-}e^{4} - 9e^{2} - 4e + 12$ |
79 | $[79, 79, 3w^{2} - w - 23]$ | $-e^{4} - 2e^{3} + 7e^{2} + 12e$ |
89 | $[89, 89, 2w^{2} - 4w - 7]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 4e^{2} + \frac{17}{2}e - \frac{1}{2}$ |
89 | $[89, 89, -2w^{2} - 2w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{3}{2}e^{3} - 5e^{2} - \frac{23}{2}e + \frac{17}{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 1]$ | $-1$ |