Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37,37,-w^{4} + 4w^{3} - w^{2} - 7w + 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 109x^{8} + 3826x^{6} - 45740x^{4} + 69883x^{2} - 2588\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $-\frac{1014876}{33569667991}e^{8} + \frac{121920306}{33569667991}e^{6} - \frac{4667507452}{33569667991}e^{4} + \frac{58383994609}{33569667991}e^{2} - \frac{76713410693}{33569667991}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{29126661}{67139335982}e^{9} + \frac{3196022099}{67139335982}e^{7} - \frac{56599327316}{33569667991}e^{5} + \frac{684415270194}{33569667991}e^{3} - \frac{2142147259903}{67139335982}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $-\frac{3876972}{33569667991}e^{8} + \frac{364535597}{33569667991}e^{6} - \frac{10436115901}{33569667991}e^{4} + \frac{98713192037}{33569667991}e^{2} - \frac{192555228656}{33569667991}$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $-\frac{2057103}{33569667991}e^{8} + \frac{213188752}{33569667991}e^{6} - \frac{6520734762}{33569667991}e^{4} + \frac{49241762880}{33569667991}e^{2} + \frac{53785671563}{33569667991}$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}\frac{7039019}{33569667991}e^{8} - \frac{699350737}{33569667991}e^{6} + \frac{21533824816}{33569667991}e^{4} - \frac{221741115385}{33569667991}e^{2} + \frac{233196667521}{33569667991}$ |
| 37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}1$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $\phantom{-}\frac{33222936}{33569667991}e^{9} - \frac{3635130417}{33569667991}e^{7} + \frac{128232417578}{33569667991}e^{5} - \frac{1543312101017}{33569667991}e^{3} + \frac{2409861365990}{33569667991}e$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $\phantom{-}\frac{33933151}{67139335982}e^{9} - \frac{3673811397}{67139335982}e^{7} + \frac{63990908962}{33569667991}e^{5} - \frac{765773149718}{33569667991}e^{3} + \frac{2679156685595}{67139335982}e$ |
| 64 | $[64, 2, -2]$ | $-\frac{452736}{33569667991}e^{8} + \frac{122263873}{33569667991}e^{6} - \frac{7962314010}{33569667991}e^{4} + \frac{147459615985}{33569667991}e^{2} - \frac{301718185285}{33569667991}$ |
| 71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $-\frac{8448624}{33569667991}e^{9} + \frac{904216451}{33569667991}e^{7} - \frac{31028906075}{33569667991}e^{5} + \frac{365677072043}{33569667991}e^{3} - \frac{638586888902}{33569667991}e$ |
| 71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $-\frac{72802027}{67139335982}e^{9} + \frac{7900278731}{67139335982}e^{7} - \frac{137717489742}{33569667991}e^{5} + \frac{1626302446331}{33569667991}e^{3} - \frac{4643550922929}{67139335982}e$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $\phantom{-}\frac{27770353}{67139335982}e^{9} - \frac{3039435373}{67139335982}e^{7} + \frac{53624653468}{33569667991}e^{5} - \frac{649675583698}{33569667991}e^{3} + \frac{2364294630789}{67139335982}e$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $\phantom{-}\frac{2996041}{33569667991}e^{8} - \frac{308521407}{33569667991}e^{6} + \frac{10045795433}{33569667991}e^{4} - \frac{121716138422}{33569667991}e^{2} + \frac{190184137809}{33569667991}$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $\phantom{-}\frac{10159585}{33569667991}e^{8} - \frac{1091699306}{33569667991}e^{6} + \frac{36678793953}{33569667991}e^{4} - \frac{382802718279}{33569667991}e^{2} + \frac{128232160966}{33569667991}$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $\phantom{-}\frac{17741408}{33569667991}e^{9} - \frac{1913019998}{33569667991}e^{7} + \frac{66084399480}{33569667991}e^{5} - \frac{767405615508}{33569667991}e^{3} + \frac{882278721453}{33569667991}e$ |
| 89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $\phantom{-}\frac{61500727}{67139335982}e^{9} - \frac{6735525943}{67139335982}e^{7} + \frac{118907739120}{33569667991}e^{5} - \frac{1427535215861}{33569667991}e^{3} + \frac{4225043512283}{67139335982}e$ |
| 89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $-\frac{26127315}{67139335982}e^{9} + \frac{2786878507}{67139335982}e^{7} - \frac{47194779356}{33569667991}e^{5} + \frac{525077147677}{33569667991}e^{3} - \frac{758824729815}{67139335982}e$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $-\frac{28669215}{67139335982}e^{9} + \frac{3082718749}{67139335982}e^{7} - \frac{52823666991}{33569667991}e^{5} + \frac{600175093071}{33569667991}e^{3} - \frac{1319986912603}{67139335982}e$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $-\frac{1836395}{67139335982}e^{9} + \frac{248198739}{67139335982}e^{7} - \frac{5548690782}{33569667991}e^{5} + \frac{91491215315}{33569667991}e^{3} - \frac{913018029171}{67139335982}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w^{4} + 4w^{3} - w^{2} - 7w + 3]$ | $-1$ |