Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w - 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 13x^{6} + 44x^{4} - 35x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{6}e^{7} - \frac{13}{6}e^{5} + 7e^{3} - \frac{25}{6}e$ |
| 7 | $[7, 7, w - 3]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{3}e^{6} + \frac{13}{3}e^{4} - 14e^{2} + \frac{19}{3}$ |
| 9 | $[9, 3, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{11}{3}e^{3} + \frac{26}{3}e$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{8}{3}e^{2} + \frac{5}{3}$ |
| 13 | $[13, 13, -w + 2]$ | $-\frac{1}{3}e^{4} + \frac{8}{3}e^{2} - \frac{11}{3}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $-\frac{2}{3}e^{7} + \frac{25}{3}e^{5} - \frac{76}{3}e^{3} + 12e$ |
| 23 | $[23, 23, w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{14}{3}e^{4} + \frac{50}{3}e^{2} - 10$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}\frac{5}{6}e^{7} - \frac{21}{2}e^{5} + \frac{97}{3}e^{3} - \frac{109}{6}e$ |
| 31 | $[31, 31, w^{2} - 2w - 9]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{14}{3}e^{5} + \frac{56}{3}e^{3} - 23e$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{3}{2}e^{7} - \frac{115}{6}e^{5} + \frac{184}{3}e^{3} - \frac{215}{6}e$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-\frac{5}{3}e^{7} + \frac{62}{3}e^{5} - 62e^{3} + \frac{92}{3}e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{43}{6}e^{5} + \frac{88}{3}e^{3} - \frac{191}{6}e$ |
| 41 | $[41, 41, w^{2} - w - 10]$ | $-\frac{1}{3}e^{6} + \frac{11}{3}e^{4} - \frac{26}{3}e^{2} + 1$ |
| 43 | $[43, 43, -2w - 3]$ | $\phantom{-}\frac{2}{3}e^{5} - \frac{25}{3}e^{3} + \frac{61}{3}e$ |
| 47 | $[47, 47, -w^{2} - w + 4]$ | $-\frac{1}{3}e^{4} + \frac{2}{3}e^{2} + \frac{10}{3}$ |
| 49 | $[49, 7, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{2}{3}e^{6} - \frac{25}{3}e^{4} + \frac{79}{3}e^{2} - 13$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $-\frac{4}{3}e^{7} + 17e^{5} - \frac{163}{3}e^{3} + \frac{92}{3}e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{5}{3}e^{3} - \frac{13}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 3]$ | $1$ |