Base field 4.4.2624.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 3x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[71, 71, 2w - 3]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 4x^{4} - 8x^{3} + 38x^{2} - 9x - 14\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - \frac{9}{4}e^{2} + \frac{25}{4}e + \frac{1}{2}$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}2$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} - 3]$ | $-\frac{3}{4}e^{4} + \frac{3}{4}e^{3} + \frac{31}{4}e^{2} - \frac{21}{4}e - \frac{5}{2}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{1}{4}e^{3} - \frac{31}{4}e^{2} - \frac{5}{4}e + \frac{11}{2}$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{3}{2}e^{3} - \frac{31}{2}e^{2} + \frac{21}{2}e + 7$ |
| 25 | $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ | $-e^{4} + 11e^{2} + 2e - 6$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $-2e^{4} + 2e^{3} + 20e^{2} - 14e - 6$ |
| 47 | $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{13}{2}e^{2} + \frac{11}{2}e - 7$ |
| 47 | $[47, 47, 2w^{3} - 4w^{2} - 5w]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{13}{4}e^{2} - \frac{41}{4}e + \frac{11}{2}$ |
| 49 | $[49, 7, w^{2} - 4w - 1]$ | $-2e^{4} + 3e^{3} + 20e^{2} - 23e - 6$ |
| 71 | $[71, 71, 2w - 3]$ | $-1$ |
| 71 | $[71, 71, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{9}{4}e^{4} + \frac{5}{4}e^{3} + \frac{93}{4}e^{2} - \frac{35}{4}e - \frac{3}{2}$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}\frac{5}{4}e^{4} - \frac{1}{4}e^{3} - \frac{49}{4}e^{2} - \frac{5}{4}e + \frac{11}{2}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ | $-\frac{9}{4}e^{4} + \frac{11}{4}e^{3} + \frac{85}{4}e^{2} - \frac{73}{4}e - \frac{5}{2}$ |
| 73 | $[73, 73, -w^{3} + 3w^{2} - 5]$ | $-\frac{7}{4}e^{4} + \frac{7}{4}e^{3} + \frac{75}{4}e^{2} - \frac{53}{4}e - \frac{29}{2}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{11}{4}e^{4} - \frac{5}{4}e^{3} - \frac{115}{4}e^{2} + \frac{15}{4}e + \frac{31}{2}$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{5}{4}e^{3} - \frac{17}{4}e^{2} - \frac{47}{4}e + \frac{9}{2}$ |
| 79 | $[79, 79, 2w^{3} - 3w^{2} - 5w]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{5}{4}e^{3} - \frac{13}{4}e^{2} + \frac{51}{4}e + \frac{15}{2}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}2e^{4} - e^{3} - 22e^{2} + 5e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71, 71, 2w - 3]$ | $1$ |