Base field \(\Q(\zeta_{20})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[61,61,w^{3} - 3w^{2} - 3w + 7]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 15x^{4} + 59x^{2} - 37\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} - w^{2} + 3w + 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{2}e^{2} + \frac{21}{4}$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{31}{4}e$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{5}{2}e^{3} + \frac{13}{4}e$ |
| 19 | $[19, 19, -w^{3} - w^{2} + 3w + 1]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{31}{4}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{3}{2}e^{3} + \frac{21}{2}e$ |
| 41 | $[41, 41, w + 3]$ | $-\frac{3}{4}e^{4} + \frac{11}{2}e^{2} + \frac{5}{4}$ |
| 41 | $[41, 41, -w^{3} + 3w + 3]$ | $-\frac{3}{4}e^{4} + \frac{11}{2}e^{2} + \frac{5}{4}$ |
| 41 | $[41, 41, -w^{3} + 3w - 3]$ | $\phantom{-}2e^{2} - 8$ |
| 41 | $[41, 41, w - 3]$ | $\phantom{-}2e^{2} - 8$ |
| 59 | $[59, 59, 2w^{2} + w - 7]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 17e$ |
| 59 | $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ | $-\frac{3}{4}e^{5} + 9e^{3} - \frac{93}{4}e$ |
| 59 | $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ | $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{49}{4}e$ |
| 59 | $[59, 59, w^{3} - w^{2} - w + 3]$ | $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{49}{4}e$ |
| 61 | $[61, 61, 3w^{2} - w - 8]$ | $\phantom{-}\frac{3}{2}e^{2} - \frac{13}{2}$ |
| 61 | $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ | $\phantom{-}\frac{5}{4}e^{4} - \frac{27}{2}e^{2} + \frac{85}{4}$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ | $-1$ |
| 61 | $[61, 61, -3w^{2} - w + 8]$ | $-\frac{3}{4}e^{4} + 5e^{2} + \frac{11}{4}$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 21e$ |
| 79 | $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}e^{3} - 9e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61,61,w^{3} - 3w^{2} - 3w + 7]$ | $1$ |