Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1\); 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:
| \(x^{6} - x^{5} - 18x^{4} + 18x^{3} + 61x^{2} - 33x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + \frac{15}{2}e^{3} - \frac{49}{2}e^{2} - 5e + 38$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $-\frac{1}{3}e^{5} + e^{4} + 5e^{3} - 16e^{2} - \frac{10}{3}e + \frac{68}{3}$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{2}e^{4} - \frac{11}{2}e^{3} + \frac{17}{2}e^{2} + \frac{65}{6}e - \frac{32}{3}$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $-\frac{1}{2}e^{5} + e^{4} + 8e^{3} - 16e^{2} - \frac{25}{2}e + 20$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $-e^{5} + 2e^{4} + 15e^{3} - 34e^{2} - 14e + 52$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $-\frac{2}{3}e^{5} + \frac{1}{2}e^{4} + \frac{21}{2}e^{3} - \frac{17}{2}e^{2} - \frac{109}{6}e + \frac{22}{3}$ |
| 32 | $[32, 2, -2]$ | $-\frac{2}{3}e^{5} + 11e^{3} - e^{2} - \frac{74}{3}e - \frac{17}{3}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{1}{3}e^{5} - e^{4} - 5e^{3} + 15e^{2} + \frac{10}{3}e - \frac{56}{3}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $-\frac{2}{3}e^{5} + e^{4} + 10e^{3} - 17e^{2} - \frac{26}{3}e + \frac{64}{3}$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $\phantom{-}e^{5} - 2e^{4} - 15e^{3} + 34e^{2} + 14e - 50$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $-\frac{1}{3}e^{5} + 2e^{4} + 5e^{3} - 32e^{2} - \frac{4}{3}e + \frac{170}{3}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $\phantom{-}\frac{2}{3}e^{5} - 11e^{3} + 2e^{2} + \frac{77}{3}e + \frac{2}{3}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $-e - 4$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $-\frac{5}{3}e^{5} + 2e^{4} + 26e^{3} - 34e^{2} - \frac{125}{3}e + \frac{118}{3}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $\phantom{-}\frac{1}{3}e^{5} - 5e^{3} + \frac{22}{3}e + \frac{28}{3}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{3}{2}e^{5} - 4e^{4} - 23e^{3} + 65e^{2} + \frac{49}{2}e - 90$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-\frac{3}{2}e^{5} + e^{4} + 24e^{3} - 16e^{2} - \frac{87}{2}e + 4$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $\phantom{-}\frac{2}{3}e^{5} - 3e^{4} - 10e^{3} + 48e^{2} + \frac{2}{3}e - \frac{214}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{2} - 2]$ | $-1$ |