Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[59, 59, -3w - 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 4x^{2} - 21x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $-e - 1$ |
5 | $[5, 5, w - 2]$ | $\phantom{-}\frac{1}{9}e^{3} - \frac{2}{9}e^{2} - \frac{10}{9}e + \frac{1}{3}$ |
7 | $[7, 7, w]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{7}{3}e - 1$ |
7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{4}{9}e^{3} + \frac{10}{9}e^{2} - \frac{31}{9}e - \frac{17}{3}$ |
9 | $[9, 3, 3]$ | $-\frac{4}{9}e^{3} - \frac{10}{9}e^{2} + \frac{31}{9}e + \frac{14}{3}$ |
13 | $[13, 13, w + 4]$ | $-\frac{1}{9}e^{3} + \frac{2}{9}e^{2} + \frac{19}{9}e + \frac{5}{3}$ |
13 | $[13, 13, w - 5]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{7}{3}e$ |
23 | $[23, 23, -w - 5]$ | $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} + \frac{8}{3}e + 8$ |
23 | $[23, 23, w - 6]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{14}{3}e - 10$ |
29 | $[29, 29, 2w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{7}{3}e - 6$ |
53 | $[53, 53, 3w - 5]$ | $\phantom{-}\frac{2}{9}e^{3} + \frac{5}{9}e^{2} - \frac{2}{9}e - \frac{22}{3}$ |
53 | $[53, 53, -3w - 2]$ | $-\frac{4}{3}e^{3} - \frac{13}{3}e^{2} + \frac{22}{3}e + 11$ |
59 | $[59, 59, -3w - 1]$ | $\phantom{-}1$ |
59 | $[59, 59, 3w - 4]$ | $-\frac{1}{9}e^{3} - \frac{7}{9}e^{2} + \frac{10}{9}e - \frac{10}{3}$ |
67 | $[67, 67, 3w - 13]$ | $-\frac{10}{9}e^{3} - \frac{7}{9}e^{2} + \frac{91}{9}e - \frac{1}{3}$ |
67 | $[67, 67, -3w - 10]$ | $\phantom{-}\frac{14}{9}e^{3} + \frac{35}{9}e^{2} - \frac{122}{9}e - \frac{55}{3}$ |
71 | $[71, 71, 2w - 11]$ | $-\frac{2}{9}e^{3} + \frac{4}{9}e^{2} + \frac{29}{9}e - \frac{26}{3}$ |
71 | $[71, 71, -2w - 9]$ | $-\frac{5}{3}e^{3} - \frac{17}{3}e^{2} + \frac{26}{3}e + 20$ |
83 | $[83, 83, -w - 9]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{14}{3}e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, -3w - 1]$ | $-1$ |