Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{2} - 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 4x^{8} - 21x^{7} - 94x^{6} + 86x^{5} + 566x^{4} + 39x^{3} - 1006x^{2} - 233x + 482\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{15483}{333160}e^{8} + \frac{48211}{333160}e^{7} - \frac{9031}{8329}e^{6} - \frac{546371}{166580}e^{5} + \frac{544743}{83290}e^{4} + \frac{2961717}{166580}e^{3} - \frac{4415461}{333160}e^{2} - \frac{7352611}{333160}e + \frac{1747909}{166580}$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{423}{41645}e^{8} - \frac{1301}{41645}e^{7} + \frac{1643}{8329}e^{6} + \frac{59119}{83290}e^{5} - \frac{19152}{41645}e^{4} - \frac{154374}{41645}e^{3} - \frac{268313}{83290}e^{2} + \frac{128616}{41645}e + \frac{199712}{41645}$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $-\frac{2743}{66632}e^{8} - \frac{6625}{66632}e^{7} + \frac{8783}{8329}e^{6} + \frac{77229}{33316}e^{5} - \frac{65321}{8329}e^{4} - \frac{448547}{33316}e^{3} + \frac{1418501}{66632}e^{2} + \frac{1299093}{66632}e - \frac{582583}{33316}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1631}{83290}e^{8} + \frac{1376}{41645}e^{7} - \frac{8501}{16658}e^{6} - \frac{62239}{83290}e^{5} + \frac{160972}{41645}e^{4} + \frac{340343}{83290}e^{3} - \frac{403816}{41645}e^{2} - \frac{262726}{41645}e + \frac{121903}{41645}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{6113}{333160}e^{8} - \frac{15651}{333160}e^{7} + \frac{3571}{8329}e^{6} + \frac{174431}{166580}e^{5} - \frac{222483}{83290}e^{4} - \frac{887457}{166580}e^{3} + \frac{2148891}{333160}e^{2} + \frac{1814691}{333160}e - \frac{1266609}{166580}$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $\phantom{-}\frac{549}{16658}e^{8} + \frac{2491}{33316}e^{7} - \frac{13143}{16658}e^{6} - \frac{14619}{8329}e^{5} + \frac{82451}{16658}e^{4} + \frac{85293}{8329}e^{3} - \frac{153637}{16658}e^{2} - \frac{476865}{33316}e + \frac{69529}{16658}$ |
| 19 | $[19, 19, -w + 3]$ | $-\frac{35311}{333160}e^{8} - \frac{96987}{333160}e^{7} + \frac{21385}{8329}e^{6} + \frac{1106947}{166580}e^{5} - \frac{710218}{41645}e^{4} - \frac{6091909}{166580}e^{3} + \frac{13656857}{333160}e^{2} + \frac{15329607}{333160}e - \frac{5927433}{166580}$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $-\frac{12637}{333160}e^{8} - \frac{26659}{333160}e^{7} + \frac{15643}{16658}e^{6} + \frac{298909}{166580}e^{5} - \frac{544427}{83290}e^{4} - \frac{1568143}{166580}e^{3} + \frac{5379419}{333160}e^{2} + \frac{3583339}{333160}e - \frac{1920801}{166580}$ |
| 23 | $[23, 23, w^{2} - 2]$ | $-\frac{81}{33316}e^{8} + \frac{1523}{33316}e^{7} + \frac{792}{8329}e^{6} - \frac{17505}{16658}e^{5} - \frac{8537}{8329}e^{4} + \frac{94737}{16658}e^{3} + \frac{56803}{33316}e^{2} - \frac{164103}{33316}e + \frac{19653}{16658}$ |
| 25 | $[25, 5, w^{2} - 3]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{34783}{333160}e^{8} + \frac{85321}{333160}e^{7} - \frac{21424}{8329}e^{6} - \frac{965631}{166580}e^{5} + \frac{1463193}{83290}e^{4} + \frac{5175067}{166580}e^{3} - \frac{14096041}{333160}e^{2} - \frac{11892401}{333160}e + \frac{5613179}{166580}$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}\frac{24701}{333160}e^{8} + \frac{61007}{333160}e^{7} - \frac{15638}{8329}e^{6} - \frac{716097}{166580}e^{5} + \frac{1122241}{83290}e^{4} + \frac{4215509}{166580}e^{3} - \frac{11296027}{333160}e^{2} - \frac{12205167}{333160}e + \frac{4426693}{166580}$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{12229}{166580}e^{8} - \frac{8197}{41645}e^{7} + \frac{29135}{16658}e^{6} + \frac{183824}{41645}e^{5} - \frac{905063}{83290}e^{4} - \frac{1908371}{83290}e^{3} + \frac{3363953}{166580}e^{2} + \frac{1925019}{83290}e - \frac{430106}{41645}$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $-\frac{2473}{33316}e^{8} - \frac{6149}{33316}e^{7} + \frac{14926}{8329}e^{6} + \frac{68947}{16658}e^{5} - \frac{190489}{16658}e^{4} - \frac{364545}{16658}e^{3} + \frac{740523}{33316}e^{2} + \frac{846623}{33316}e - \frac{248301}{16658}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{10591}{166580}e^{8} + \frac{12687}{166580}e^{7} - \frac{13863}{8329}e^{6} - \frac{146937}{83290}e^{5} + \frac{1055827}{83290}e^{4} + \frac{836829}{83290}e^{3} - \frac{5582037}{166580}e^{2} - \frac{2768077}{166580}e + \frac{2087763}{83290}$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-\frac{8211}{83290}e^{8} - \frac{27617}{83290}e^{7} + \frac{19343}{8329}e^{6} + \frac{318867}{41645}e^{5} - \frac{601447}{41645}e^{4} - \frac{1794249}{41645}e^{3} + \frac{2695537}{83290}e^{2} + \frac{4538987}{83290}e - \frac{1391193}{41645}$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $-\frac{6909}{333160}e^{8} - \frac{49013}{333160}e^{7} + \frac{7403}{16658}e^{6} + \frac{578033}{166580}e^{5} - \frac{203139}{83290}e^{4} - \frac{3426261}{166580}e^{3} + \frac{2521603}{333160}e^{2} + \frac{9805053}{333160}e - \frac{1436867}{166580}$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}\frac{36611}{166580}e^{8} + \frac{44241}{83290}e^{7} - \frac{89699}{16658}e^{6} - \frac{1001837}{83290}e^{5} + \frac{3053717}{83290}e^{4} + \frac{5398169}{83290}e^{3} - \frac{15064137}{166580}e^{2} - \frac{3259953}{41645}e + \frac{3172329}{41645}$ |
| 81 | $[81, 3, -3]$ | $-\frac{17499}{333160}e^{8} - \frac{47323}{333160}e^{7} + \frac{12668}{8329}e^{6} + \frac{593773}{166580}e^{5} - \frac{586372}{41645}e^{4} - \frac{4024261}{166580}e^{3} + \frac{17049313}{333160}e^{2} + \frac{13873863}{333160}e - \frac{8732657}{166580}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{2} - 3]$ | $-1$ |