Base field 4.4.12357.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 2]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 18x^{6} + 92x^{4} - 148x^{2} + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{3}{14}e^{6} - \frac{22}{7}e^{4} + \frac{67}{7}e^{2} - \frac{22}{7}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $\phantom{-}\frac{1}{7}e^{7} - \frac{17}{7}e^{5} + \frac{75}{7}e^{3} - \frac{73}{7}e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{14}e^{6} - \frac{5}{7}e^{4} - \frac{8}{7}e^{2} + \frac{37}{7}$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{28}e^{7} - \frac{6}{7}e^{5} + \frac{45}{7}e^{3} - \frac{90}{7}e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{3}{14}e^{6} + \frac{22}{7}e^{4} - \frac{74}{7}e^{2} + \frac{50}{7}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{3}{14}e^{7} + \frac{22}{7}e^{5} - \frac{67}{7}e^{3} + \frac{29}{7}e$ |
| 31 | $[31, 31, w^{3} - w^{2} - 3w + 1]$ | $-\frac{3}{14}e^{6} + \frac{22}{7}e^{4} - \frac{67}{7}e^{2} + \frac{22}{7}$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{1}{28}e^{7} - \frac{1}{7}e^{5} + \frac{53}{7}e^{3} - \frac{155}{7}e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}\frac{1}{7}e^{6} - \frac{10}{7}e^{4} - \frac{2}{7}e^{2} + \frac{32}{7}$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}\frac{11}{28}e^{7} - \frac{45}{7}e^{5} + \frac{187}{7}e^{3} - \frac{220}{7}e$ |
| 53 | $[53, 53, -w^{2} - w + 4]$ | $\phantom{-}\frac{5}{28}e^{7} - \frac{23}{7}e^{5} + \frac{127}{7}e^{3} - \frac{233}{7}e$ |
| 59 | $[59, 59, -w^{3} + 4w - 2]$ | $-\frac{3}{14}e^{7} + \frac{22}{7}e^{5} - \frac{60}{7}e^{3} - \frac{20}{7}e$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ | $\phantom{-}\frac{9}{14}e^{6} - \frac{66}{7}e^{4} + \frac{187}{7}e^{2} - \frac{10}{7}$ |
| 89 | $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ | $-\frac{23}{28}e^{7} + \frac{89}{7}e^{5} - \frac{321}{7}e^{3} + \frac{257}{7}e$ |
| 89 | $[89, 89, w^{3} - 5w + 1]$ | $-\frac{3}{28}e^{7} + \frac{18}{7}e^{5} - \frac{135}{7}e^{3} + \frac{326}{7}e$ |
| 97 | $[97, 97, w^{3} - 6w - 1]$ | $\phantom{-}\frac{5}{14}e^{6} - \frac{32}{7}e^{4} + \frac{58}{7}e^{2} + \frac{52}{7}$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ | $-\frac{5}{14}e^{6} + \frac{39}{7}e^{4} - \frac{142}{7}e^{2} + \frac{88}{7}$ |
| 101 | $[101, 101, -w^{3} + 6w - 2]$ | $-\frac{1}{4}e^{7} + 5e^{5} - 29e^{3} + 47e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 2]$ | $1$ |