Base field 4.4.15529.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[18, 6, -w^{2} + w + 4]$ |
| 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:
| \(x^{8} - 4x^{7} - 18x^{6} + 77x^{5} + 39x^{4} - 263x^{3} + 14x^{2} + 176x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{499}{4072}e^{7} + \frac{477}{1018}e^{6} + \frac{4647}{2036}e^{5} - \frac{36327}{4072}e^{4} - \frac{26765}{4072}e^{3} + \frac{116341}{4072}e^{2} + \frac{17835}{2036}e - \frac{6441}{509}$ |
| 9 | $[9, 3, -w^{3} + w^{2} + 5w + 1]$ | $\phantom{-}\frac{479}{1018}e^{7} - \frac{826}{509}e^{6} - \frac{4779}{509}e^{5} + \frac{31613}{1018}e^{4} + \frac{36521}{1018}e^{3} - \frac{105721}{1018}e^{2} - \frac{26019}{509}e + \frac{27410}{509}$ |
| 9 | $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{2277}{4072}e^{7} - \frac{1891}{1018}e^{6} - \frac{23045}{2036}e^{5} + \frac{145217}{4072}e^{4} + \frac{184379}{4072}e^{3} - \frac{494451}{4072}e^{2} - \frac{133385}{2036}e + \frac{33560}{509}$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $\phantom{-}\frac{533}{2036}e^{7} - \frac{484}{509}e^{6} - \frac{5237}{1018}e^{5} + \frac{37113}{2036}e^{4} + \frac{39091}{2036}e^{3} - \frac{124215}{2036}e^{2} - \frac{33037}{1018}e + \frac{15504}{509}$ |
| 29 | $[29, 29, w^{2} - 3w - 1]$ | $\phantom{-}\frac{2199}{4072}e^{7} - \frac{1845}{1018}e^{6} - \frac{21931}{2036}e^{5} + \frac{140779}{4072}e^{4} + \frac{166641}{4072}e^{3} - \frac{469321}{4072}e^{2} - \frac{114199}{2036}e + \frac{31780}{509}$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{171}{1018}e^{7} + \frac{280}{509}e^{6} + \frac{1620}{509}e^{5} - \frac{10121}{1018}e^{4} - \frac{9835}{1018}e^{3} + \frac{26667}{1018}e^{2} + \frac{5766}{509}e - \frac{3080}{509}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 5w + 1]$ | $-\frac{374}{509}e^{7} + \frac{1326}{509}e^{6} + \frac{7381}{509}e^{5} - \frac{25443}{509}e^{4} - \frac{27169}{509}e^{3} + \frac{85596}{509}e^{2} + \frac{38715}{509}e - \frac{44108}{509}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{1427}{2036}e^{7} - \frac{1207}{509}e^{6} - \frac{14403}{1018}e^{5} + \frac{92991}{2036}e^{4} + \frac{114441}{2036}e^{3} - \frac{319997}{2036}e^{2} - \frac{82149}{1018}e + \frac{44326}{509}$ |
| 47 | $[47, 47, -w^{2} + 2w + 5]$ | $-\frac{269}{1018}e^{7} + \frac{500}{509}e^{6} + \frac{2602}{509}e^{5} - \frac{19273}{1018}e^{4} - \frac{17817}{1018}e^{3} + \frac{65471}{1018}e^{2} + \frac{12696}{509}e - \frac{16698}{509}$ |
| 47 | $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ | $\phantom{-}\frac{1437}{4072}e^{7} - \frac{1239}{1018}e^{6} - \frac{14337}{2036}e^{5} + \frac{95857}{4072}e^{4} + \frac{109563}{4072}e^{3} - \frac{337523}{4072}e^{2} - \frac{78057}{2036}e + \frac{24884}{509}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ | $-\frac{1417}{2036}e^{7} + \frac{1175}{509}e^{6} + \frac{14469}{1018}e^{5} - \frac{90125}{2036}e^{4} - \frac{119319}{2036}e^{3} + \frac{304507}{2036}e^{2} + \frac{88277}{1018}e - \frac{39902}{509}$ |
| 59 | $[59, 59, -w - 3]$ | $-\frac{1405}{1018}e^{7} + \frac{2375}{509}e^{6} + \frac{14141}{509}e^{5} - \frac{91165}{1018}e^{4} - \frac{111735}{1018}e^{3} + \frac{309333}{1018}e^{2} + \frac{84229}{509}e - \frac{82624}{509}$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}\frac{103}{2036}e^{7} - \frac{126}{509}e^{6} - \frac{949}{1018}e^{5} + \frac{9567}{2036}e^{4} + \frac{6561}{2036}e^{3} - \frac{30261}{2036}e^{2} - \frac{10483}{1018}e + \frac{3422}{509}$ |
| 73 | $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ | $\phantom{-}\frac{1735}{2036}e^{7} - \frac{1480}{509}e^{6} - \frac{17053}{1018}e^{5} + \frac{112447}{2036}e^{4} + \frac{121785}{2036}e^{3} - \frac{367493}{2036}e^{2} - \frac{74407}{1018}e + \frac{45802}{509}$ |
| 79 | $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ | $\phantom{-}\frac{709}{1018}e^{7} - \frac{1280}{509}e^{6} - \frac{6824}{509}e^{5} + \frac{48667}{1018}e^{4} + \frac{45469}{1018}e^{3} - \frac{158627}{1018}e^{2} - \frac{30140}{509}e + \frac{39530}{509}$ |
| 97 | $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ | $\phantom{-}\frac{17}{1018}e^{7} - \frac{7}{509}e^{6} - \frac{295}{509}e^{5} + \frac{393}{1018}e^{4} + \frac{6163}{1018}e^{3} - \frac{1901}{1018}e^{2} - \frac{8619}{509}e + \frac{586}{509}$ |
| 101 | $[101, 101, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{2347}{4072}e^{7} - \frac{2115}{1018}e^{6} - \frac{22583}{2036}e^{5} + \frac{161207}{4072}e^{4} + \frac{148197}{4072}e^{3} - \frac{527549}{4072}e^{2} - \frac{89471}{2036}e + \frac{33774}{509}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $9$ | $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ | $-1$ |