Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 6x^{6} - 27x^{5} + 222x^{4} - 110x^{3} - 1492x^{2} + 2825x - 1408\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $\phantom{-}\frac{1317}{17894}e^{6} - \frac{4091}{17894}e^{5} - \frac{45855}{17894}e^{4} + \frac{79159}{8947}e^{3} + \frac{126274}{8947}e^{2} - \frac{1167801}{17894}e + \frac{444564}{8947}$ |
| 19 | $[19, 19, w^{3} - 3w - 1]$ | $\phantom{-}\frac{141}{8947}e^{6} - \frac{10}{8947}e^{5} - \frac{5643}{8947}e^{4} + \frac{890}{8947}e^{3} + \frac{58424}{8947}e^{2} + \frac{1760}{8947}e - \frac{119557}{8947}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $-\frac{205}{17894}e^{6} - \frac{310}{8947}e^{5} + \frac{4007}{8947}e^{4} + \frac{9696}{8947}e^{3} - \frac{90717}{17894}e^{2} - \frac{150343}{17894}e + \frac{167784}{8947}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{758}{8947}e^{6} + \frac{3163}{8947}e^{5} + \frac{25006}{8947}e^{4} - \frac{120461}{8947}e^{3} - \frac{97005}{8947}e^{2} + \frac{883779}{8947}e - \frac{739428}{8947}$ |
| 31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{703}{17894}e^{6} + \frac{1992}{8947}e^{5} + \frac{23947}{17894}e^{4} - \frac{148795}{17894}e^{3} - \frac{87287}{17894}e^{2} + \frac{553055}{8947}e - \frac{468193}{8947}$ |
| 41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $\phantom{-}\frac{277}{8947}e^{6} - \frac{908}{8947}e^{5} - \frac{9563}{8947}e^{4} + \frac{36077}{8947}e^{3} + \frac{47642}{8947}e^{2} - \frac{287542}{8947}e + \frac{245662}{8947}$ |
| 49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $-\frac{72}{8947}e^{6} + \frac{1528}{8947}e^{5} + \frac{1549}{8947}e^{4} - \frac{55469}{8947}e^{3} + \frac{34128}{8947}e^{2} + \frac{402097}{8947}e - \frac{384396}{8947}$ |
| 59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{836}{8947}e^{6} + \frac{1836}{8947}e^{5} + \frac{30412}{8947}e^{4} - \frac{73934}{8947}e^{3} - \frac{212132}{8947}e^{2} + \frac{553670}{8947}e - \frac{198528}{8947}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $-1$ |
| 59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $-\frac{831}{17894}e^{6} + \frac{1362}{8947}e^{5} + \frac{28689}{17894}e^{4} - \frac{108231}{17894}e^{3} - \frac{151873}{17894}e^{2} + \frac{422366}{8947}e - \frac{305864}{8947}$ |
| 61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $\phantom{-}\frac{72}{8947}e^{6} - \frac{1528}{8947}e^{5} - \frac{1549}{8947}e^{4} + \frac{55469}{8947}e^{3} - \frac{34128}{8947}e^{2} - \frac{402097}{8947}e + \frac{402290}{8947}$ |
| 64 | $[64, 2, -2]$ | $-\frac{419}{17894}e^{6} - \frac{1049}{17894}e^{5} + \frac{8670}{8947}e^{4} + \frac{39679}{17894}e^{3} - \frac{97531}{8947}e^{2} - \frac{167151}{8947}e + \frac{269045}{8947}$ |
| 71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $-\frac{341}{8947}e^{6} + \frac{278}{8947}e^{5} + \frac{11934}{8947}e^{4} - \frac{15795}{8947}e^{3} - \frac{79935}{8947}e^{2} + \frac{138959}{8947}e - \frac{65439}{8947}$ |
| 79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $\phantom{-}\frac{1453}{8947}e^{6} - \frac{4989}{8947}e^{5} - \frac{49775}{8947}e^{4} + \frac{193505}{8947}e^{3} + \frac{250713}{8947}e^{2} - \frac{1439209}{8947}e + \frac{1129089}{8947}$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $-\frac{2347}{17894}e^{6} + \frac{4525}{8947}e^{5} + \frac{78701}{17894}e^{4} - \frac{349153}{17894}e^{3} - \frac{345883}{17894}e^{2} + \frac{1306145}{8947}e - \frac{1081080}{8947}$ |
| 79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-\frac{1040}{8947}e^{6} + \frac{3183}{8947}e^{5} + \frac{36292}{8947}e^{4} - \frac{122241}{8947}e^{3} - \frac{204906}{8947}e^{2} + \frac{871312}{8947}e - \frac{598731}{8947}$ |
| 81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $\phantom{-}\frac{763}{8947}e^{6} - \frac{2275}{8947}e^{5} - \frac{26729}{8947}e^{4} + \frac{86164}{8947}e^{3} + \frac{157264}{8947}e^{2} - \frac{610611}{8947}e + \frac{379910}{8947}$ |
| 89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $-\frac{477}{17894}e^{6} + \frac{588}{8947}e^{5} + \frac{7927}{8947}e^{4} - \frac{25491}{8947}e^{3} - \frac{87047}{17894}e^{2} + \frac{428261}{17894}e - \frac{143753}{8947}$ |
| 101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $\phantom{-}\frac{413}{8947}e^{6} - \frac{1806}{8947}e^{5} - \frac{13483}{8947}e^{4} + \frac{71264}{8947}e^{3} + \frac{45807}{8947}e^{2} - \frac{541056}{8947}e + \frac{485623}{8947}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $1$ |