Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, -w - 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 2x^{6} - 24x^{5} + 59x^{4} + 110x^{3} - 437x^{2} + 387x - 81\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{1}{18}e^{6} + \frac{1}{9}e^{5} + \frac{11}{6}e^{4} - \frac{34}{9}e^{3} - \frac{127}{9}e^{2} + \frac{545}{18}e - \frac{15}{2}$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{5}{18}e^{6} - \frac{1}{18}e^{5} - \frac{20}{3}e^{4} + \frac{35}{9}e^{3} + \frac{329}{9}e^{2} - \frac{871}{18}e + 12$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{7}{18}e^{6} - \frac{5}{18}e^{5} - \frac{28}{3}e^{4} + \frac{85}{9}e^{3} + \frac{466}{9}e^{2} - \frac{1493}{18}e + 20$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{3}e^{6} + \frac{1}{6}e^{5} + \frac{15}{2}e^{4} - \frac{17}{3}e^{3} - \frac{113}{3}e^{2} + \frac{158}{3}e - \frac{21}{2}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{9}e^{6} + \frac{2}{9}e^{5} + \frac{8}{3}e^{4} - \frac{50}{9}e^{3} - \frac{128}{9}e^{2} + \frac{320}{9}e - 13$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{5}{9}e^{6} + \frac{1}{9}e^{5} + \frac{40}{3}e^{4} - \frac{70}{9}e^{3} - \frac{667}{9}e^{2} + \frac{862}{9}e - 15$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{5}{6}e^{6} + \frac{1}{6}e^{5} + 20e^{4} - \frac{35}{3}e^{3} - \frac{332}{3}e^{2} + \frac{877}{6}e - 27$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{2}{3}e^{6} - \frac{1}{3}e^{5} - 16e^{4} + \frac{43}{3}e^{3} + \frac{262}{3}e^{2} - \frac{439}{3}e + 46$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}e^{4} - 2e^{3} - 14e^{2} + 26e - 3$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{11}{9}e^{6} - \frac{4}{9}e^{5} - \frac{91}{3}e^{4} + \frac{217}{9}e^{3} + \frac{1570}{9}e^{2} - \frac{2431}{9}e + 74$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{4}{9}e^{6} - \frac{1}{9}e^{5} + \frac{32}{3}e^{4} - \frac{29}{9}e^{3} - \frac{521}{9}e^{2} + \frac{668}{9}e - 25$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{7}{18}e^{6} - \frac{2}{9}e^{5} + \frac{59}{6}e^{4} - \frac{13}{9}e^{3} - \frac{520}{9}e^{2} + \frac{1277}{18}e - \frac{39}{2}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{25}{2}e^{4} + 7e^{3} + 72e^{2} - \frac{209}{2}e + \frac{69}{2}$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}\frac{2}{3}e^{6} - \frac{1}{3}e^{5} - 16e^{4} + \frac{40}{3}e^{3} + \frac{265}{3}e^{2} - \frac{400}{3}e + 36$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{3}e^{6} + \frac{1}{3}e^{5} - 9e^{4} - \frac{4}{3}e^{3} + \frac{173}{3}e^{2} - \frac{161}{3}e + 3$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{3}{2}e^{6} + \frac{73}{2}e^{4} - 17e^{3} - 205e^{2} + \frac{535}{2}e - \frac{125}{2}$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $\phantom{-}\frac{5}{3}e^{6} - \frac{1}{3}e^{5} - 40e^{4} + \frac{73}{3}e^{3} + \frac{661}{3}e^{2} - \frac{916}{3}e + 72$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{4}{9}e^{6} + \frac{1}{9}e^{5} - \frac{35}{3}e^{4} + \frac{38}{9}e^{3} + \frac{665}{9}e^{2} - \frac{785}{9}e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w - 1]$ | $-1$ |