Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} + 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 28x^{4} + 176x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{1}{12}e^{4} + 2e^{2} - \frac{20}{3}$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-\frac{1}{24}e^{5} + \frac{5}{4}e^{3} - \frac{28}{3}e$ |
| 13 | $[13, 13, w^{4} - 5w^{2} + 2]$ | $-\frac{1}{12}e^{5} + 2e^{3} - \frac{29}{3}e$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{5}{2}e^{3} + \frac{50}{3}e$ |
| 32 | $[32, 2, 2]$ | $-\frac{1}{2}e^{2} + 7$ |
| 37 | $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ | $\phantom{-}\frac{1}{4}e^{3} - 4e$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}\frac{1}{12}e^{4} - e^{2} - \frac{4}{3}$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{12}e^{5} - 2e^{3} + \frac{29}{3}e$ |
| 47 | $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ | $\phantom{-}\frac{1}{12}e^{4} - e^{2} + \frac{8}{3}$ |
| 59 | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $\phantom{-}1$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{1}{12}e^{5} + \frac{9}{4}e^{3} - \frac{35}{3}e$ |
| 73 | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $-\frac{1}{6}e^{5} + \frac{17}{4}e^{3} - \frac{67}{3}e$ |
| 73 | $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ | $-\frac{1}{12}e^{5} + \frac{5}{2}e^{3} - \frac{59}{3}e$ |
| 79 | $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ | $-\frac{1}{12}e^{4} + 2e^{2} + \frac{10}{3}$ |
| 79 | $[79, 79, -w^{3} + 5w]$ | $-\frac{1}{12}e^{4} + e^{2} + \frac{28}{3}$ |
| 79 | $[79, 79, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{11}{4}e^{3} + \frac{56}{3}e$ |
| 83 | $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ | $\phantom{-}\frac{1}{6}e^{4} - 3e^{2} - \frac{2}{3}$ |
| 89 | $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{19}{4}e^{3} + \frac{94}{3}e$ |
| 101 | $[101, 101, -w^{4} + 5w^{2} - w - 4]$ | $\phantom{-}\frac{1}{12}e^{4} - 2e^{2} + \frac{14}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $-1$ |