Base field 3.3.1957.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 8, w^{2} + w + 6]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 8x^{3} + 24x^{2} + 7x - 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2}]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{2} + w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{5}{2}e + \frac{25}{4}$ |
| 11 | $[11, 11, 10w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{7}{2}e + \frac{7}{2}$ |
| 13 | $[13, 13, 12w^{2} + w + 7]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + \frac{3}{2}e + 7$ |
| 17 | $[17, 17, w + 1]$ | $\phantom{-}\frac{1}{4}e^{4} - 3e^{2} + e + \frac{31}{4}$ |
| 17 | $[17, 17, 16w^{2} + 16]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{11}{2}e^{2} - \frac{7}{2}e - 8$ |
| 17 | $[17, 17, 16w^{2} + 16w + 8]$ | $-\frac{1}{4}e^{4} + 4e^{2} + e - \frac{43}{4}$ |
| 19 | $[19, 19, 18w^{2} + 18w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 5e^{2} + 5e + \frac{21}{2}$ |
| 19 | $[19, 19, -w^{2} + 7]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + \frac{3}{2}e + 7$ |
| 25 | $[25, 5, 4w^{2} + w + 4]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{7}{2}e^{2} + \frac{9}{2}e + \frac{29}{4}$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{7}{2}e^{2} + \frac{17}{2}e + 4$ |
| 29 | $[29, 29, w + 7]$ | $-\frac{3}{4}e^{4} + e^{3} + 7e^{2} - 4e - \frac{53}{4}$ |
| 41 | $[41, 41, 40w^{2} + 18]$ | $-\frac{1}{2}e^{4} + e^{3} + 4e^{2} - 5e - \frac{3}{2}$ |
| 43 | $[43, 43, w^{2} - 11]$ | $-e^{4} + 2e^{3} + 8e^{2} - 10e - 7$ |
| 47 | $[47, 47, 2w^{2} + 2w - 13]$ | $-e^{4} + e^{3} + 10e^{2} - 5e - 19$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-e^{4} + \frac{1}{2}e^{3} + \frac{25}{2}e^{2} - \frac{7}{2}e - \frac{49}{2}$ |
| 73 | $[73, 73, w^{2} + 2w - 1]$ | $-\frac{3}{4}e^{4} + \frac{3}{2}e^{3} + \frac{9}{2}e^{2} - \frac{19}{2}e + \frac{9}{4}$ |
| 79 | $[79, 79, w^{2} + 37]$ | $\phantom{-}2e^{4} - \frac{5}{2}e^{3} - \frac{39}{2}e^{2} + \frac{27}{2}e + \frac{69}{2}$ |
| 97 | $[97, 97, w^{2} + 2w - 7]$ | $-\frac{5}{4}e^{4} + \frac{3}{2}e^{3} + \frac{23}{2}e^{2} - \frac{19}{2}e - \frac{57}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2}]$ | $-1$ |