Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 8, w - 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 12x^{3} - 6x^{2} + 11x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{13}{4}e^{2} + \frac{15}{4}e - \frac{3}{2}$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{2}e + 4$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} - 4e + 4$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{13}{4}e^{2} + \frac{19}{4}e - \frac{5}{2}$ |
| 13 | $[13, 13, -2w + 1]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + \frac{9}{4}e^{2} - \frac{3}{4}e + \frac{1}{2}$ |
| 19 | $[19, 19, 2w^{2} - w - 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{2}e + 2$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{4}e^{3} - \frac{13}{4}e^{2} + \frac{15}{4}e + \frac{15}{2}$ |
| 27 | $[27, 3, 3]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{7}{2}e - 3$ |
| 31 | $[31, 31, w^{2} - 2w - 1]$ | $\phantom{-}e^{4} - e^{3} - 11e^{2} + 3e + 8$ |
| 37 | $[37, 37, -3w^{2} + 2w + 23]$ | $\phantom{-}\frac{3}{4}e^{4} + \frac{3}{4}e^{3} - \frac{35}{4}e^{2} - \frac{45}{4}e + \frac{11}{2}$ |
| 41 | $[41, 41, -2w - 1]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{1}{4}e^{3} - \frac{39}{4}e^{2} - \frac{1}{4}e + \frac{17}{2}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{11}{2}e - 3$ |
| 49 | $[49, 7, w^{2} - 2w - 5]$ | $-e^{4} + 12e^{2} + 4e - 11$ |
| 59 | $[59, 59, 2w - 3]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{1}{2}e^{3} - \frac{33}{2}e^{2} - \frac{5}{2}e + 12$ |
| 67 | $[67, 67, w - 5]$ | $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + \frac{35}{2}e^{2} + \frac{23}{2}e - 7$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{7}{2}e + 3$ |
| 73 | $[73, 73, w^{2} + 1]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e + 3$ |
| 83 | $[83, 83, -4w^{2} + 3w + 27]$ | $\phantom{-}e^{4} - e^{3} - 11e^{2} + 3e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $-1$ |