Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, w^{2} - 2w - 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - x^{7} - 19x^{6} + 19x^{5} + 108x^{4} - 116x^{3} - 180x^{2} + 183x + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{38}{291}e^{7} + \frac{31}{291}e^{6} - \frac{704}{291}e^{5} - \frac{541}{291}e^{4} + \frac{1232}{97}e^{3} + \frac{2150}{291}e^{2} - \frac{1770}{97}e - \frac{656}{97}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{20}{97}e^{7} + \frac{1}{97}e^{6} - \frac{345}{97}e^{5} - \frac{55}{97}e^{4} + \frac{1690}{97}e^{3} + \frac{182}{97}e^{2} - \frac{2371}{97}e - \frac{76}{97}$ |
| 7 | $[7, 7, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{29}{291}e^{7} + \frac{16}{291}e^{6} - \frac{476}{291}e^{5} - \frac{298}{291}e^{4} + \frac{736}{97}e^{3} + \frac{875}{291}e^{2} - \frac{1070}{97}e + \frac{112}{97}$ |
| 8 | $[8, 2, 2]$ | $-\frac{20}{97}e^{7} - \frac{1}{97}e^{6} + \frac{345}{97}e^{5} + \frac{55}{97}e^{4} - \frac{1690}{97}e^{3} - \frac{279}{97}e^{2} + \frac{2274}{97}e + \frac{561}{97}$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{20}{291}e^{7} + \frac{1}{291}e^{6} - \frac{248}{291}e^{5} - \frac{55}{291}e^{4} + \frac{143}{97}e^{3} - \frac{109}{291}e^{2} + \frac{309}{97}e + \frac{298}{97}$ |
| 17 | $[17, 17, w - 2]$ | $-\frac{49}{97}e^{7} - \frac{17}{97}e^{6} + \frac{821}{97}e^{5} + \frac{353}{97}e^{4} - \frac{3801}{97}e^{3} - \frac{1251}{97}e^{2} + \frac{4902}{97}e + \frac{1098}{97}$ |
| 25 | $[25, 5, -w^{2} - w + 3]$ | $\phantom{-}\frac{2}{291}e^{7} - \frac{29}{291}e^{6} - \frac{83}{291}e^{5} + \frac{431}{291}e^{4} + \frac{315}{97}e^{3} - \frac{1495}{291}e^{2} - \frac{813}{97}e + \frac{670}{97}$ |
| 29 | $[29, 29, w^{2} - 2w - 6]$ | $\phantom{-}\frac{30}{97}e^{7} + \frac{50}{97}e^{6} - \frac{566}{97}e^{5} - \frac{713}{97}e^{4} + \frac{2923}{97}e^{3} + \frac{2116}{97}e^{2} - \frac{3993}{97}e - \frac{1278}{97}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}\frac{107}{291}e^{7} + \frac{49}{291}e^{6} - \frac{1967}{291}e^{5} - \frac{658}{291}e^{4} + \frac{3418}{97}e^{3} + \frac{1061}{291}e^{2} - \frac{4841}{97}e + \frac{52}{97}$ |
| 37 | $[37, 37, -w^{2} - 2w + 2]$ | $-\frac{208}{291}e^{7} - \frac{185}{291}e^{6} + \frac{3685}{291}e^{5} + \frac{2900}{291}e^{4} - \frac{6085}{97}e^{3} - \frac{8935}{291}e^{2} + \frac{8601}{97}e + \frac{1906}{97}$ |
| 41 | $[41, 41, w^{2} - 8]$ | $\phantom{-}\frac{15}{97}e^{7} + \frac{25}{97}e^{6} - \frac{283}{97}e^{5} - \frac{308}{97}e^{4} + \frac{1413}{97}e^{3} + \frac{476}{97}e^{2} - \frac{1560}{97}e + \frac{234}{97}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{232}{291}e^{7} - \frac{128}{291}e^{6} + \frac{4099}{291}e^{5} + \frac{2093}{291}e^{4} - \frac{6761}{97}e^{3} - \frac{5836}{291}e^{2} + \frac{9045}{97}e + \frac{1432}{97}$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-\frac{79}{97}e^{7} - \frac{67}{97}e^{6} + \frac{1387}{97}e^{5} + \frac{1066}{97}e^{4} - \frac{6821}{97}e^{3} - \frac{3270}{97}e^{2} + \frac{9477}{97}e + \frac{1794}{97}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{3}{97}e^{7} + \frac{5}{97}e^{6} + \frac{21}{97}e^{5} - \frac{178}{97}e^{4} - \frac{571}{97}e^{3} + \frac{1104}{97}e^{2} + \frac{1143}{97}e - \frac{768}{97}$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $-\frac{42}{97}e^{7} - \frac{70}{97}e^{6} + \frac{773}{97}e^{5} + \frac{940}{97}e^{4} - \frac{3840}{97}e^{3} - \frac{2167}{97}e^{2} + \frac{4950}{97}e + \frac{276}{97}$ |
| 61 | $[61, 61, -w^{2} + 2w + 12]$ | $\phantom{-}\frac{32}{97}e^{7} + \frac{21}{97}e^{6} - \frac{552}{97}e^{5} - \frac{379}{97}e^{4} + \frac{2704}{97}e^{3} + \frac{1397}{97}e^{2} - \frac{3910}{97}e - \frac{1402}{97}$ |
| 67 | $[67, 67, -2w^{2} + 6w + 3]$ | $\phantom{-}\frac{122}{291}e^{7} - \frac{23}{291}e^{6} - \frac{2153}{291}e^{5} + \frac{101}{291}e^{4} + \frac{3598}{97}e^{3} + \frac{179}{291}e^{2} - \frac{4682}{97}e - \frac{452}{97}$ |
| 71 | $[71, 71, w^{2} - w - 11]$ | $\phantom{-}\frac{52}{97}e^{7} + \frac{22}{97}e^{6} - \frac{897}{97}e^{5} - \frac{337}{97}e^{4} + \frac{4297}{97}e^{3} + \frac{609}{97}e^{2} - \frac{5796}{97}e - \frac{120}{97}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{2} - 2w - 4]$ | $-1$ |