Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11,11,-w^{2} + 2w + 8]$ |
| Dimension: | $7$ |
| 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:
| \(x^{7} + 6x^{6} - 10x^{5} - 104x^{4} - 112x^{3} + 125x^{2} + 129x - 51\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $-\frac{7}{2732}e^{6} - \frac{231}{2732}e^{5} - \frac{703}{2732}e^{4} + \frac{3603}{2732}e^{3} + \frac{13373}{2732}e^{2} + \frac{576}{683}e - \frac{12459}{2732}$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $-\frac{279}{5464}e^{6} - \frac{1011}{5464}e^{5} + \frac{5545}{5464}e^{4} + \frac{17543}{5464}e^{3} - \frac{16903}{5464}e^{2} - \frac{6021}{1366}e + \frac{34989}{5464}$ |
| 11 | $[11, 11, w^{2} - 2w - 8]$ | $-1$ |
| 23 | $[23, 23, w^{2} - 2w - 7]$ | $\phantom{-}\frac{485}{2732}e^{6} + \frac{2345}{2732}e^{5} - \frac{7103}{2732}e^{4} - \frac{40053}{2732}e^{3} - \frac{15631}{2732}e^{2} + \frac{10048}{683}e + \frac{309}{2732}$ |
| 23 | $[23, 23, w^{2} - 3w - 8]$ | $-\frac{399}{5464}e^{6} - \frac{2239}{5464}e^{5} + \frac{3641}{5464}e^{4} + \frac{35987}{5464}e^{3} + \frac{49209}{5464}e^{2} - \frac{659}{683}e - \frac{29895}{5464}$ |
| 23 | $[23, 23, w - 1]$ | $\phantom{-}\frac{579}{5464}e^{6} + \frac{2715}{5464}e^{5} - \frac{8981}{5464}e^{4} - \frac{45895}{5464}e^{3} - \frac{9045}{5464}e^{2} + \frac{4474}{683}e - \frac{24405}{5464}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{203}{2732}e^{6} + \frac{1235}{2732}e^{5} - \frac{1469}{2732}e^{4} - \frac{19795}{2732}e^{3} - \frac{32657}{2732}e^{2} + \frac{371}{683}e + \frac{28007}{2732}$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $\phantom{-}\frac{171}{1366}e^{6} + \frac{431}{683}e^{5} - \frac{2341}{1366}e^{4} - \frac{7370}{683}e^{3} - \frac{8015}{1366}e^{2} + \frac{17383}{1366}e + \frac{1869}{683}$ |
| 29 | $[29, 29, w^{2} - 3w - 10]$ | $-\frac{663}{5464}e^{6} - \frac{2755}{5464}e^{5} + \frac{11473}{5464}e^{4} + \frac{48151}{5464}e^{3} - \frac{5327}{5464}e^{2} - \frac{20477}{1366}e - \frac{18555}{5464}$ |
| 29 | $[29, 29, w - 3]$ | $-\frac{571}{5464}e^{6} - \frac{2451}{5464}e^{5} + \frac{10565}{5464}e^{4} + \frac{44119}{5464}e^{3} - \frac{17947}{5464}e^{2} - \frac{10072}{683}e - \frac{3507}{5464}$ |
| 31 | $[31, 31, w^{2} - 2w - 6]$ | $\phantom{-}\frac{143}{1366}e^{6} + \frac{621}{1366}e^{5} - \frac{2421}{1366}e^{4} - \frac{10573}{1366}e^{3} + \frac{1765}{1366}e^{2} + \frac{6128}{683}e - \frac{12631}{1366}$ |
| 31 | $[31, 31, -w^{2} + 3w + 9]$ | $-\frac{289}{2732}e^{6} - \frac{1341}{2732}e^{5} + \frac{4931}{2732}e^{4} + \frac{23861}{2732}e^{3} - \frac{3653}{2732}e^{2} - \frac{10467}{683}e + \frac{9775}{2732}$ |
| 31 | $[31, 31, w - 2]$ | $\phantom{-}\frac{275}{2732}e^{6} + \frac{879}{2732}e^{5} - \frac{6337}{2732}e^{4} - \frac{16655}{2732}e^{3} + \frac{30399}{2732}e^{2} + \frac{10936}{683}e - \frac{31961}{2732}$ |
| 37 | $[37, 37, -w^{2} + 4w + 7]$ | $-\frac{677}{5464}e^{6} - \frac{3217}{5464}e^{5} + \frac{10067}{5464}e^{4} + \frac{55357}{5464}e^{3} + \frac{21419}{5464}e^{2} - \frac{16593}{1366}e - \frac{32545}{5464}$ |
| 43 | $[43, 43, 2w^{2} - 6w - 13]$ | $-\frac{68}{683}e^{6} - \frac{195}{683}e^{5} + \frac{1562}{683}e^{4} + \frac{3485}{683}e^{3} - \frac{7569}{683}e^{2} - \frac{7280}{683}e + \frac{11179}{683}$ |
| 43 | $[43, 43, 2w^{2} - 4w - 17]$ | $-\frac{475}{2732}e^{6} - \frac{2015}{2732}e^{5} + \frac{7717}{2732}e^{4} + \frac{33735}{2732}e^{3} + \frac{2381}{2732}e^{2} - \frac{8334}{683}e + \frac{3049}{2732}$ |
| 43 | $[43, 43, w^{2} - 2w - 12]$ | $-\frac{671}{5464}e^{6} - \frac{3019}{5464}e^{5} + \frac{9889}{5464}e^{4} + \frac{49927}{5464}e^{3} + \frac{21665}{5464}e^{2} - \frac{9281}{1366}e - \frac{12499}{5464}$ |
| 47 | $[47, 47, w^{2} - 4w - 4]$ | $-\frac{7}{5464}e^{6} - \frac{231}{5464}e^{5} - \frac{703}{5464}e^{4} + \frac{3603}{5464}e^{3} + \frac{16105}{5464}e^{2} + \frac{971}{683}e - \frac{53439}{5464}$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $\phantom{-}\frac{265}{5464}e^{6} + \frac{549}{5464}e^{5} - \frac{6951}{5464}e^{4} - \frac{10337}{5464}e^{3} + \frac{43649}{5464}e^{2} + \frac{8539}{1366}e - \frac{43515}{5464}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-w^{2} + 2w + 8]$ | $1$ |