Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, 2w^{2} + w - 19]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 20x^{6} + 110x^{4} - 116x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}\frac{1}{6}e^{7} - \frac{19}{6}e^{5} + \frac{47}{3}e^{3} - \frac{29}{3}e$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}\frac{1}{12}e^{6} - \frac{4}{3}e^{4} + \frac{29}{6}e^{2} - \frac{1}{3}$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{2}e^{5} + \frac{55}{4}e^{3} - \frac{27}{2}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{12}e^{6} + \frac{4}{3}e^{4} - \frac{29}{6}e^{2} - \frac{2}{3}$ |
| 13 | $[13, 13, -w]$ | $\phantom{-}\frac{1}{24}e^{7} - \frac{2}{3}e^{5} + \frac{35}{12}e^{3} - \frac{25}{6}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{2}e^{5} + \frac{55}{4}e^{3} - \frac{33}{2}e$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $-\frac{1}{6}e^{6} + \frac{8}{3}e^{4} - \frac{32}{3}e^{2} + \frac{26}{3}$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $\phantom{-}\frac{1}{12}e^{7} - \frac{11}{6}e^{5} + \frac{71}{6}e^{3} - \frac{58}{3}e$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $\phantom{-}2e$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $-\frac{1}{8}e^{7} + \frac{5}{2}e^{5} - \frac{51}{4}e^{3} + \frac{15}{2}e$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}\frac{1}{4}e^{7} - 5e^{5} + \frac{53}{2}e^{3} - 18e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{7} - 5e^{5} + \frac{53}{2}e^{3} - 18e$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $\phantom{-}\frac{1}{3}e^{6} - \frac{19}{3}e^{4} + \frac{94}{3}e^{2} - \frac{52}{3}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{6}e^{7} - \frac{19}{6}e^{5} + \frac{47}{3}e^{3} - \frac{17}{3}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $-\frac{5}{24}e^{7} + \frac{13}{3}e^{5} - \frac{283}{12}e^{3} + \frac{83}{6}e$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{5}{2}e^{5} + \frac{47}{4}e^{3} + \frac{7}{2}e$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $\phantom{-}\frac{1}{4}e^{6} - 5e^{4} + \frac{51}{2}e^{2} - 9$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $-\frac{1}{12}e^{7} + \frac{11}{6}e^{5} - \frac{71}{6}e^{3} + \frac{55}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 2]$ | $-1$ |