Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 3 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{2} - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 18 x^{4} + 18 x^{3} + 61 x^{2} - 33 x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6 w^{2} - 2 w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5 w^{2} - w - 4]$ | $-\frac{1}{2} e^{5} + \frac{3}{2} e^{4} + \frac{15}{2} e^{3} - \frac{49}{2} e^{2} - 5 e + 38$ |
| 11 | $[11, 11, -2 w^{4} + w^{3} + 10 w^{2} + w - 3]$ | $-\frac{1}{3} e^{5} + e^{4} + 5 e^{3} - 16 e^{2} - \frac{10}{3} e + \frac{68}{3}$ |
| 11 | $[11, 11, w^{4} - 6 w^{2} - 3 w + 3]$ | $\phantom{-}\frac{1}{3} e^{5} - \frac{1}{2} e^{4} - \frac{11}{2} e^{3} + \frac{17}{2} e^{2} + \frac{65}{6} e - \frac{32}{3}$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3 w]$ | $-\frac{1}{2} e^{5} + e^{4} + 8 e^{3} - 16 e^{2} - \frac{25}{2} e + 20$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4 w^{2} + 2 w - 1]$ | $-e^{5} + 2 e^{4} + 15 e^{3} - 34 e^{2} - 14 e + 52$ |
| 29 | $[29, 29, 2 w^{4} - 2 w^{3} - 9 w^{2} + 2 w + 3]$ | $-\frac{2}{3} e^{5} + \frac{1}{2} e^{4} + \frac{21}{2} e^{3} - \frac{17}{2} e^{2} - \frac{109}{6} e + \frac{22}{3}$ |
| 32 | $[32, 2, -2]$ | $-\frac{2}{3} e^{5} + 11 e^{3} - e^{2} - \frac{74}{3} e - \frac{17}{3}$ |
| 47 | $[47, 47, w^{4} - 2 w^{3} - 3 w^{2} + 5 w]$ | $\phantom{-}\frac{1}{3} e^{5} - e^{4} - 5 e^{3} + 15 e^{2} + \frac{10}{3} e - \frac{56}{3}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4 w - 1]$ | $-\frac{2}{3} e^{5} + e^{4} + 10 e^{3} - 17 e^{2} - \frac{26}{3} e + \frac{64}{3}$ |
| 53 | $[53, 53, -w^{4} + 7 w^{2} - 3]$ | $\phantom{-}e^{5} - 2 e^{4} - 15 e^{3} + 34 e^{2} + 14 e - 50$ |
| 53 | $[53, 53, 2 w^{4} - 2 w^{3} - 9 w^{2} + 2 w + 2]$ | $-\frac{1}{3} e^{5} + 2 e^{4} + 5 e^{3} - 32 e^{2} - \frac{4}{3} e + \frac{170}{3}$ |
| 53 | $[53, 53, 3 w^{4} - 2 w^{3} - 16 w^{2} + 8]$ | $\phantom{-}\frac{2}{3} e^{5} - 11 e^{3} + 2 e^{2} + \frac{77}{3} e + \frac{2}{3}$ |
| 67 | $[67, 67, -w^{4} + 6 w^{2} + 4 w - 3]$ | $-e - 4$ |
| 73 | $[73, 73, 2 w^{4} - 12 w^{2} - 4 w + 5]$ | $-\frac{5}{3} e^{5} + 2 e^{4} + 26 e^{3} - 34 e^{2} - \frac{125}{3} e + \frac{118}{3}$ |
| 83 | $[83, 83, w^{4} - 5 w^{2} - 3 w + 3]$ | $\phantom{-}\frac{1}{3} e^{5} - 5 e^{3} + \frac{22}{3} e + \frac{28}{3}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5 w^{2} - 3 w - 3]$ | $\phantom{-}\frac{3}{2} e^{5} - 4 e^{4} - 23 e^{3} + 65 e^{2} + \frac{49}{2} e - 90$ |
| 103 | $[103, 103, 2 w^{3} - 3 w^{2} - 7 w + 3]$ | $-\frac{3}{2} e^{5} + e^{4} + 24 e^{3} - 16 e^{2} - \frac{87}{2} e + 4$ |
| 109 | $[109, 109, -3 w^{4} + 2 w^{3} + 14 w^{2} + w - 6]$ | $\phantom{-}\frac{2}{3} e^{5} - 3 e^{4} - 10 e^{3} + 48 e^{2} + \frac{2}{3} e - \frac{214}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{2} - 2]$ | $-1$ |