Base field 4.4.2525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[71,71,3w^{2} - 4w - 7]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 16x^{5} + 64x^{4} + 52x^{3} - 240x^{2} - 18x + 162\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $-\frac{1}{9}e^{6} + \frac{2}{9}e^{5} + 2e^{4} - \frac{22}{9}e^{3} - \frac{65}{9}e^{2} + 4e + 2$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} + 4]$ | $\phantom{-}\frac{2}{9}e^{6} - \frac{2}{9}e^{5} - \frac{14}{3}e^{4} + \frac{13}{9}e^{3} + \frac{68}{3}e^{2} + e - 18$ |
| 11 | $[11, 11, w^{2} - 2w - 3]$ | $-\frac{1}{9}e^{4} + \frac{2}{9}e^{3} + \frac{10}{9}e^{2} - \frac{4}{3}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{9}e^{6} + \frac{2}{9}e^{5} + \frac{19}{9}e^{4} - \frac{8}{3}e^{3} - \frac{28}{3}e^{2} + \frac{22}{3}e + 7$ |
| 29 | $[29, 29, w^{3} - 4w - 1]$ | $-\frac{4}{9}e^{6} + \frac{7}{9}e^{5} + \frac{26}{3}e^{4} - \frac{77}{9}e^{3} - \frac{116}{3}e^{2} + \frac{43}{3}e + 32$ |
| 29 | $[29, 29, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{2}{3}e^{6} - \frac{10}{9}e^{5} - \frac{116}{9}e^{4} + \frac{34}{3}e^{3} + \frac{508}{9}e^{2} - \frac{46}{3}e - 42$ |
| 41 | $[41, 41, w^{3} - 2w^{2} - w + 4]$ | $-\frac{4}{9}e^{6} + \frac{2}{3}e^{5} + \frac{26}{3}e^{4} - \frac{20}{3}e^{3} - \frac{328}{9}e^{2} + \frac{28}{3}e + 18$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w + 2]$ | $\phantom{-}\frac{2}{9}e^{5} - \frac{2}{9}e^{4} - 4e^{3} + \frac{10}{9}e^{2} + 12e + 2$ |
| 59 | $[59, 59, -2w^{3} + 4w^{2} + 4w - 7]$ | $-\frac{2}{9}e^{6} + \frac{2}{9}e^{5} + \frac{44}{9}e^{4} - \frac{20}{9}e^{3} - \frac{236}{9}e^{2} + 6e + 32$ |
| 59 | $[59, 59, -3w^{2} + 2w + 7]$ | $\phantom{-}\frac{2}{9}e^{6} - \frac{2}{9}e^{5} - \frac{14}{3}e^{4} + \frac{16}{9}e^{3} + 22e^{2} - \frac{1}{3}e - 14$ |
| 61 | $[61, 61, -w^{3} + 4w^{2} - 6]$ | $-\frac{2}{3}e^{6} + \frac{10}{9}e^{5} + \frac{118}{9}e^{4} - \frac{106}{9}e^{3} - \frac{182}{3}e^{2} + 20e + 50$ |
| 61 | $[61, 61, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}\frac{8}{9}e^{6} - \frac{4}{3}e^{5} - \frac{160}{9}e^{4} + \frac{122}{9}e^{3} + \frac{248}{3}e^{2} - \frac{64}{3}e - 66$ |
| 71 | $[71, 71, w^{3} + w^{2} - 4w - 6]$ | $-\frac{2}{9}e^{4} + \frac{4}{9}e^{3} + \frac{38}{9}e^{2} - \frac{14}{3}e - 12$ |
| 71 | $[71, 71, 3w^{2} - 2w - 8]$ | $\phantom{-}\frac{4}{9}e^{6} - \frac{2}{3}e^{5} - \frac{76}{9}e^{4} + \frac{53}{9}e^{3} + \frac{314}{9}e^{2} - \frac{7}{3}e - 22$ |
| 71 | $[71, 71, 3w^{2} - 4w - 7]$ | $-1$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + w + 8]$ | $\phantom{-}\frac{4}{9}e^{6} - \frac{7}{9}e^{5} - \frac{26}{3}e^{4} + \frac{71}{9}e^{3} + 40e^{2} - \frac{29}{3}e - 34$ |
| 79 | $[79, 79, -2w^{3} + 3w^{2} + 5w - 2]$ | $-\frac{2}{9}e^{6} + \frac{4}{9}e^{5} + \frac{40}{9}e^{4} - \frac{52}{9}e^{3} - \frac{188}{9}e^{2} + \frac{46}{3}e + 12$ |
| 79 | $[79, 79, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{2}{9}e^{6} - \frac{5}{9}e^{5} - 4e^{4} + \frac{64}{9}e^{3} + 16e^{2} - \frac{49}{3}e - 12$ |
| 79 | $[79, 79, 2w^{2} - w - 8]$ | $-\frac{8}{9}e^{6} + \frac{4}{3}e^{5} + \frac{158}{9}e^{4} - \frac{118}{9}e^{3} - \frac{706}{9}e^{2} + \frac{50}{3}e + 52$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71,71,3w^{2} - 4w - 7]$ | $1$ |