Base field 6.6.434581.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 41x^{3} + 35x^{2} + 448x + 506\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + w + 2]$ | $-\frac{25}{161}e^{4} + \frac{5}{7}e^{3} + \frac{841}{161}e^{2} - \frac{2285}{161}e - \frac{300}{7}$ |
| 27 | $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}\frac{40}{161}e^{4} - \frac{8}{7}e^{3} - \frac{1249}{161}e^{2} + \frac{3334}{161}e + \frac{438}{7}$ |
| 27 | $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ | $-\frac{45}{161}e^{4} + \frac{9}{7}e^{3} + \frac{1385}{161}e^{2} - \frac{3791}{161}e - \frac{470}{7}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ | $-\frac{68}{161}e^{4} + \frac{15}{7}e^{3} + \frac{2075}{161}e^{2} - \frac{6505}{161}e - \frac{739}{7}$ |
| 29 | $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ | $\phantom{-}\frac{53}{161}e^{4} - \frac{12}{7}e^{3} - \frac{1667}{161}e^{2} + \frac{5456}{161}e + \frac{650}{7}$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ | $-\frac{13}{161}e^{4} + \frac{4}{7}e^{3} + \frac{418}{161}e^{2} - \frac{2122}{161}e - \frac{191}{7}$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ | $-\frac{50}{161}e^{4} + \frac{10}{7}e^{3} + \frac{1682}{161}e^{2} - \frac{4570}{161}e - \frac{593}{7}$ |
| 49 | $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ | $\phantom{-}\frac{9}{23}e^{4} - 2e^{3} - \frac{277}{23}e^{2} + \frac{887}{23}e + 98$ |
| 64 | $[64, 2, -2]$ | $-\frac{4}{23}e^{4} + e^{3} + \frac{118}{23}e^{2} - \frac{453}{23}e - 45$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $-1$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ | $\phantom{-}\frac{10}{161}e^{4} - \frac{2}{7}e^{3} - \frac{272}{161}e^{2} + \frac{592}{161}e + \frac{92}{7}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}\frac{18}{161}e^{4} - \frac{5}{7}e^{3} - \frac{393}{161}e^{2} + \frac{1935}{161}e + \frac{97}{7}$ |
| 71 | $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ | $\phantom{-}\frac{45}{161}e^{4} - \frac{9}{7}e^{3} - \frac{1385}{161}e^{2} + \frac{3791}{161}e + \frac{442}{7}$ |
| 83 | $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ | $\phantom{-}\frac{93}{161}e^{4} - \frac{20}{7}e^{3} - \frac{2916}{161}e^{2} + \frac{8951}{161}e + \frac{1095}{7}$ |
| 83 | $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ | $\phantom{-}\frac{38}{161}e^{4} - \frac{9}{7}e^{3} - \frac{1098}{161}e^{2} + \frac{3763}{161}e + \frac{428}{7}$ |
| 83 | $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ | $\phantom{-}\frac{15}{161}e^{4} - \frac{3}{7}e^{3} - \frac{569}{161}e^{2} + \frac{1693}{161}e + \frac{215}{7}$ |
| 83 | $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ | $-\frac{15}{161}e^{4} + \frac{3}{7}e^{3} + \frac{569}{161}e^{2} - \frac{1371}{161}e - \frac{222}{7}$ |
| 97 | $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ | $\phantom{-}\frac{14}{23}e^{4} - 3e^{3} - \frac{436}{23}e^{2} + \frac{1367}{23}e + 154$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ | $-\frac{88}{161}e^{4} + \frac{19}{7}e^{3} + \frac{2619}{161}e^{2} - \frac{8011}{161}e - \frac{909}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $1$ |