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 |
|---|---|---|
| $17$ | $[17, 17, w^2 - 2]$ | $-1$ |