Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 3x^{5} - 12x^{4} + 26x^{3} + 38x^{2} - 9x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{1}{6}e^{5} + 2e^{3} + \frac{2}{3}e^{2} - \frac{7}{3}e - \frac{1}{2}$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{1}{6}e^{5} + e^{4} + 2e^{3} - \frac{28}{3}e^{2} - \frac{28}{3}e + \frac{5}{2}$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{1}{6}e^{5} - e^{3} - \frac{5}{3}e^{2} - \frac{17}{3}e - \frac{1}{2}$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + \frac{5}{2}e^{3} - 4e^{2} - \frac{3}{2}e + \frac{15}{4}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{6}e^{5} - 2e^{3} - \frac{2}{3}e^{2} + \frac{7}{3}e - \frac{1}{2}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{5}{12}e^{5} - \frac{1}{2}e^{4} + \frac{11}{2}e^{3} + \frac{20}{3}e^{2} - \frac{53}{6}e - \frac{11}{4}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} - 4e^{2} + 2e + \frac{9}{2}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{1}{2}e^{4} - \frac{17}{2}e^{3} + e^{2} + \frac{25}{2}e + \frac{7}{4}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-e^{5} + e^{4} + 10e^{3} - 5e^{2} - 5e + 6$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{1}{6}e^{5} - 2e^{4} - 2e^{3} + \frac{61}{3}e^{2} + \frac{40}{3}e - \frac{13}{2}$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{5}{12}e^{5} - \frac{3}{2}e^{4} - \frac{7}{2}e^{3} + \frac{40}{3}e^{2} + \frac{23}{6}e - \frac{41}{4}$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $\phantom{-}\frac{1}{3}e^{5} - e^{4} - 3e^{3} + \frac{23}{3}e^{2} + \frac{11}{3}e - 5$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{3}{2}e^{4} - \frac{7}{2}e^{3} + 14e^{2} + \frac{37}{2}e - \frac{3}{4}$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}e^{3} - e^{2} - 9e - 3$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}e^{5} - 2e^{4} - 11e^{3} + 14e^{2} + 22e - 3$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{1}{2}e^{5} - 2e^{4} + 7e^{3} + 24e^{2} - 9e - \frac{35}{2}$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $-\frac{1}{2}e^{5} + 6e^{3} + 2e^{2} - 11e + \frac{3}{2}$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{5}{6}e^{5} - 3e^{4} - 8e^{3} + \frac{80}{3}e^{2} + \frac{47}{3}e - \frac{31}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $-1$ |