Base field 3.3.788.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 8x^{4} + 14x^{2} + 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{3}e^{5} - \frac{1}{3}e^{4} + \frac{7}{3}e^{3} + \frac{4}{3}e^{2} - \frac{10}{3}e + \frac{1}{3}$ |
| 5 | $[5, 5, -w^{2} + 2w + 4]$ | $-\frac{1}{3}e^{5} + \frac{2}{3}e^{4} + \frac{7}{3}e^{3} - \frac{14}{3}e^{2} - \frac{4}{3}e + \frac{13}{3}$ |
| 9 | $[9, 3, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{2}{3}e^{4} - \frac{7}{3}e^{3} + \frac{14}{3}e^{2} + \frac{4}{3}e - \frac{7}{3}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{2}{3}e^{5} + \frac{4}{3}e^{4} + \frac{17}{3}e^{3} - \frac{22}{3}e^{2} - \frac{26}{3}e + \frac{8}{3}$ |
| 13 | $[13, 13, w - 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{2} - 2w - 8]$ | $-\frac{4}{3}e^{5} + \frac{2}{3}e^{4} + \frac{31}{3}e^{3} - \frac{14}{3}e^{2} - \frac{46}{3}e + \frac{4}{3}$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $-\frac{2}{3}e^{5} - \frac{2}{3}e^{4} + \frac{14}{3}e^{3} + \frac{8}{3}e^{2} - \frac{14}{3}e - \frac{4}{3}$ |
| 31 | $[31, 31, 3w^{2} - 5w - 19]$ | $\phantom{-}e^{5} - 2e^{4} - 11e^{3} + 10e^{2} + 24e + 2$ |
| 53 | $[53, 53, 2w^{2} - 3w - 10]$ | $\phantom{-}\frac{13}{3}e^{5} - \frac{2}{3}e^{4} - \frac{88}{3}e^{3} + \frac{26}{3}e^{2} + \frac{100}{3}e + \frac{8}{3}$ |
| 53 | $[53, 53, w^{2} - 3w - 5]$ | $\phantom{-}\frac{10}{3}e^{5} - \frac{2}{3}e^{4} - \frac{64}{3}e^{3} + \frac{26}{3}e^{2} + \frac{64}{3}e - \frac{13}{3}$ |
| 53 | $[53, 53, 2w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 8$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $-\frac{2}{3}e^{5} + \frac{1}{3}e^{4} + \frac{14}{3}e^{3} - \frac{10}{3}e^{2} - \frac{8}{3}e - \frac{1}{3}$ |
| 59 | $[59, 59, 2w^{2} - 6w - 5]$ | $\phantom{-}\frac{13}{3}e^{5} - \frac{8}{3}e^{4} - \frac{94}{3}e^{3} + \frac{56}{3}e^{2} + \frac{112}{3}e - \frac{10}{3}$ |
| 59 | $[59, 59, 2w + 5]$ | $-\frac{4}{3}e^{5} + \frac{5}{3}e^{4} + \frac{22}{3}e^{3} - \frac{38}{3}e^{2} - \frac{4}{3}e + \frac{31}{3}$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $-\frac{1}{3}e^{5} + \frac{8}{3}e^{4} + \frac{19}{3}e^{3} - \frac{38}{3}e^{2} - \frac{64}{3}e + \frac{16}{3}$ |
| 71 | $[71, 71, 2w^{2} - 2w - 13]$ | $-\frac{5}{3}e^{5} - \frac{8}{3}e^{4} + \frac{29}{3}e^{3} + \frac{44}{3}e^{2} - \frac{32}{3}e - \frac{40}{3}$ |
| 73 | $[73, 73, 2w^{2} - 4w - 7]$ | $\phantom{-}\frac{7}{3}e^{5} - \frac{8}{3}e^{4} - \frac{46}{3}e^{3} + \frac{62}{3}e^{2} + \frac{46}{3}e - \frac{40}{3}$ |
| 79 | $[79, 79, -w^{2} + 10]$ | $\phantom{-}\frac{8}{3}e^{5} + \frac{2}{3}e^{4} - \frac{62}{3}e^{3} - \frac{8}{3}e^{2} + \frac{104}{3}e + \frac{16}{3}$ |
| 89 | $[89, 89, 2w^{2} - w - 10]$ | $\phantom{-}3e^{5} + 2e^{4} - 19e^{3} - 4e^{2} + 20e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w - 2]$ | $-1$ |