Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $45$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} + 13x^{13} + 28x^{12} - 241x^{11} - 843x^{10} + 1914x^{9} + 7178x^{8} - 10514x^{7} - 25093x^{6} + 40266x^{5} + 21529x^{4} - 65766x^{3} + 41057x^{2} - 9965x + 834\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $\phantom{-}\frac{1300077791817908}{11740084447674443}e^{13} + \frac{17620497781090628}{11740084447674443}e^{12} + \frac{46155996663430139}{11740084447674443}e^{11} - \frac{287563477060754101}{11740084447674443}e^{10} - \frac{1253290293117140842}{11740084447674443}e^{9} + \frac{1793771264066031402}{11740084447674443}e^{8} + \frac{10283284408555325961}{11740084447674443}e^{7} - \frac{8001208580374602120}{11740084447674443}e^{6} - \frac{36677481351130235820}{11740084447674443}e^{5} + \frac{32181297333217554309}{11740084447674443}e^{4} + \frac{2600207897236453234}{690593202804379}e^{3} - \frac{8676484943511018071}{1677154921096349}e^{2} + \frac{22337545864619187310}{11740084447674443}e - \frac{2512473149784518790}{11740084447674443}$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{923877184114725}{11740084447674443}e^{13} + \frac{12576104620695292}{11740084447674443}e^{12} + \frac{33626095470063427}{11740084447674443}e^{11} - \frac{201167148172124874}{11740084447674443}e^{10} - \frac{898349260982791623}{11740084447674443}e^{9} + \frac{1210191029444875696}{11740084447674443}e^{8} + \frac{7298168905967052353}{11740084447674443}e^{7} - \frac{5261945114595930791}{11740084447674443}e^{6} - \frac{25901306925407505931}{11740084447674443}e^{5} + \frac{21555584029609168523}{11740084447674443}e^{4} + \frac{1850826858456126287}{690593202804379}e^{3} - \frac{5923206280505830110}{1677154921096349}e^{2} + \frac{14699851307540189114}{11740084447674443}e - \frac{1625872357777830875}{11740084447674443}$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $-\frac{3304487171449109}{11740084447674443}e^{13} - \frac{45071443157403099}{11740084447674443}e^{12} - \frac{121448619462242657}{11740084447674443}e^{11} + \frac{717025749529569049}{11740084447674443}e^{10} + \frac{3236695067929491479}{11740084447674443}e^{9} - \frac{4241137351000550513}{11740084447674443}e^{8} - \frac{26279393425911084967}{11740084447674443}e^{7} + \frac{17991371406609378635}{11740084447674443}e^{6} + \frac{93361949919980010009}{11740084447674443}e^{5} - \frac{73852259217014471357}{11740084447674443}e^{4} - \frac{6750493761462917757}{690593202804379}e^{3} + \frac{20551648863337321985}{1677154921096349}e^{2} - \frac{48730243702047064861}{11740084447674443}e + \frac{5096225784530740158}{11740084447674443}$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $\phantom{-}\frac{2769274014080312}{11740084447674443}e^{13} + \frac{37742193006469720}{11740084447674443}e^{12} + \frac{101393357234364833}{11740084447674443}e^{11} - \frac{602136914320439609}{11740084447674443}e^{10} - \frac{2709659631332769541}{11740084447674443}e^{9} + \frac{3573769595570789402}{11740084447674443}e^{8} + \frac{22035754324715023782}{11740084447674443}e^{7} - \frac{15140410749706586093}{11740084447674443}e^{6} - \frac{78358804287710723012}{11740084447674443}e^{5} + \frac{61867575290666520143}{11740084447674443}e^{4} + \frac{5674124889787301179}{690593202804379}e^{3} - \frac{17194739839539149093}{1677154921096349}e^{2} + \frac{40481409175270607937}{11740084447674443}e - \frac{4190169889888650251}{11740084447674443}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $\phantom{-}\frac{4335580997322944}{11740084447674443}e^{13} + \frac{59663908313978574}{11740084447674443}e^{12} + \frac{166648827580627808}{11740084447674443}e^{11} - \frac{920257166866648293}{11740084447674443}e^{10} - \frac{4360738537981042368}{11740084447674443}e^{9} + \frac{5015491709010082130}{11740084447674443}e^{8} + \frac{35082321289269104105}{11740084447674443}e^{7} - \frac{19102096425469833996}{11740084447674443}e^{6} - \frac{124467669035300704632}{11740084447674443}e^{5} + \frac{80656061479564771848}{11740084447674443}e^{4} + \frac{9331300435905360321}{690593202804379}e^{3} - \frac{23851443930311221311}{1677154921096349}e^{2} + \frac{45955265562771910306}{11740084447674443}e - \frac{3779470278399799062}{11740084447674443}$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $\phantom{-}\frac{1666557579908553}{11740084447674443}e^{13} + \frac{22897303692351936}{11740084447674443}e^{12} + \frac{63535386433757160}{11740084447674443}e^{11} - \frac{355471957396651684}{11740084447674443}e^{10} - \frac{1670331780410619432}{11740084447674443}e^{9} + \frac{1965159585651844879}{11740084447674443}e^{8} + \frac{13476326972000327322}{11740084447674443}e^{7} - \frac{7593103681437974461}{11740084447674443}e^{6} - \frac{47890095284896262442}{11740084447674443}e^{5} + \frac{31774521441149530653}{11740084447674443}e^{4} + \frac{3586887148575084325}{690593202804379}e^{3} - \frac{9307783472354884963}{1677154921096349}e^{2} + \frac{18027933202279232168}{11740084447674443}e - \frac{1410108933571880112}{11740084447674443}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $-\frac{423081521685948}{1677154921096349}e^{13} - \frac{5790239080204981}{1677154921096349}e^{12} - \frac{15820173034419099}{1677154921096349}e^{11} + \frac{91074684764889619}{1677154921096349}e^{10} + \frac{418983238105316824}{1677154921096349}e^{9} - \frac{522089051125876097}{1677154921096349}e^{8} - \frac{3392332696184160794}{1677154921096349}e^{7} + \frac{2122202298624029583}{1677154921096349}e^{6} + \frac{12056542270788122592}{1677154921096349}e^{5} - \frac{8774313416769322341}{1677154921096349}e^{4} - \frac{887318231670229990}{98656171829197}e^{3} + \frac{17482911261050613725}{1677154921096349}e^{2} - \frac{5432289559079104981}{1677154921096349}e + \frac{524086334725059312}{1677154921096349}$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $-\frac{2336291884190097}{11740084447674443}e^{13} - \frac{31943390402663969}{11740084447674443}e^{12} - \frac{86884590845897399}{11740084447674443}e^{11} + \frac{505356547628333714}{11740084447674443}e^{10} + \frac{2315667164802225869}{11740084447674443}e^{9} - \frac{2910334484901221239}{11740084447674443}e^{8} - \frac{18837478384114916500}{11740084447674443}e^{7} + \frac{11705983827053085908}{11740084447674443}e^{6} + \frac{67234110159472832236}{11740084447674443}e^{5} - \frac{47785858247611062969}{11740084447674443}e^{4} - \frac{5002160812665991004}{690593202804379}e^{3} + \frac{13605559766456774126}{1677154921096349}e^{2} - \frac{27856394793103044779}{11740084447674443}e + \frac{2382605249658246948}{11740084447674443}$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $-\frac{655553663372065}{11740084447674443}e^{13} - \frac{8656745135882649}{11740084447674443}e^{12} - \frac{20109368529299979}{11740084447674443}e^{11} + \frac{153906821118429401}{11740084447674443}e^{10} + \frac{582167943798339970}{11740084447674443}e^{9} - \frac{1143509925504164928}{11740084447674443}e^{8} - \frac{4913196404695770596}{11740084447674443}e^{7} + \frac{6010957576690925746}{11740084447674443}e^{6} + \frac{17538094871600669004}{11740084447674443}e^{5} - \frac{23430856593366397568}{11740084447674443}e^{4} - \frac{1085281811383340472}{690593202804379}e^{3} + \frac{5760639235258157103}{1677154921096349}e^{2} - \frac{19433227536054085494}{11740084447674443}e + \frac{2624468892002251039}{11740084447674443}$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $\phantom{-}\frac{1991640123942}{98656171829197}e^{13} + \frac{25750287900383}{98656171829197}e^{12} + \frac{52369087056392}{98656171829197}e^{11} - \frac{507661642085585}{98656171829197}e^{10} - \frac{1738576331060394}{98656171829197}e^{9} + \frac{4129487996486197}{98656171829197}e^{8} + \frac{15858196091555233}{98656171829197}e^{7} - \frac{21258301527533669}{98656171829197}e^{6} - \frac{59925137816709083}{98656171829197}e^{5} + \frac{76069059365425583}{98656171829197}e^{4} + \frac{70372983273529147}{98656171829197}e^{3} - \frac{125334519484691590}{98656171829197}e^{2} + \frac{50459830463368679}{98656171829197}e - \frac{5981082975631641}{98656171829197}$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $-\frac{5389283537097361}{11740084447674443}e^{13} - \frac{73846766883617702}{11740084447674443}e^{12} - \frac{202853071315241002}{11740084447674443}e^{11} + \frac{1154988375942704018}{11740084447674443}e^{10} + \frac{5347916919777816379}{11740084447674443}e^{9} - \frac{6552145243483637972}{11740084447674443}e^{8} - \frac{43165535334738073794}{11740084447674443}e^{7} + \frac{26460140316966147944}{11740084447674443}e^{6} + \frac{153073596042406646765}{11740084447674443}e^{5} - \frac{110313433540626348692}{11740084447674443}e^{4} - \frac{11251270713345764981}{690593202804379}e^{3} + \frac{31595461507613257344}{1677154921096349}e^{2} - \frac{68889411865432130320}{11740084447674443}e + \frac{6567663023941385542}{11740084447674443}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $-\frac{4148567626318132}{11740084447674443}e^{13} - \frac{56494480224347320}{11740084447674443}e^{12} - \frac{150971031024601101}{11740084447674443}e^{11} + \frac{907769510428039127}{11740084447674443}e^{10} + \frac{4062280741909794755}{11740084447674443}e^{9} - \frac{5438630947996305783}{11740084447674443}e^{8} - \frac{33202959511068737991}{11740084447674443}e^{7} + \frac{23044320073427258934}{11740084447674443}e^{6} + \frac{118522415136468210758}{11740084447674443}e^{5} - \frac{93307029248993172782}{11740084447674443}e^{4} - \frac{8627287546332524782}{690593202804379}e^{3} + \frac{25841699461702616416}{1677154921096349}e^{2} - \frac{59786027539231066401}{11740084447674443}e + \frac{6034543954829356383}{11740084447674443}$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $\phantom{-}\frac{58247683359325}{1677154921096349}e^{13} + \frac{829495733054006}{1677154921096349}e^{12} + \frac{2625572400948261}{1677154921096349}e^{11} - \frac{11247060732665732}{1677154921096349}e^{10} - \frac{64309492278502037}{1677154921096349}e^{9} + \frac{38933471089893846}{1677154921096349}e^{8} + \frac{499334104558453696}{1677154921096349}e^{7} - \frac{32231201179539588}{1677154921096349}e^{6} - \frac{1764135622384364369}{1677154921096349}e^{5} + \frac{295785265781204759}{1677154921096349}e^{4} + \frac{149656238902937871}{98656171829197}e^{3} - \frac{1206984242591175471}{1677154921096349}e^{2} - \frac{304767029804490151}{1677154921096349}e + \frac{107502878935321315}{1677154921096349}$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $-\frac{6891926847633633}{11740084447674443}e^{13} - \frac{94362710673759925}{11740084447674443}e^{12} - \frac{258054596244693488}{11740084447674443}e^{11} + \frac{1484791755280355226}{11740084447674443}e^{10} + \frac{6841846726635187062}{11740084447674443}e^{9} - \frac{8490993954961042554}{11740084447674443}e^{8} - \frac{55450002859036250075}{11740084447674443}e^{7} + \frac{34265829396636649191}{11740084447674443}e^{6} + \frac{197205767396198451446}{11740084447674443}e^{5} - \frac{141596187246358414351}{11740084447674443}e^{4} - \frac{14547246206250010052}{690593202804379}e^{3} + \frac{40449081816211967424}{1677154921096349}e^{2} - \frac{87001345253861792378}{11740084447674443}e + \frac{8262699722656207387}{11740084447674443}$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{3214129281487526}{11740084447674443}e^{13} + \frac{43952373039504441}{11740084447674443}e^{12} + \frac{119545463410359573}{11740084447674443}e^{11} - \frac{695300114385144017}{11740084447674443}e^{10} - \frac{3182304812312622067}{11740084447674443}e^{9} + \frac{4020149754980577851}{11740084447674443}e^{8} + \frac{25856580744992757115}{11740084447674443}e^{7} - \frac{16380279024629798326}{11740084447674443}e^{6} - \frac{92091889863449005217}{11740084447674443}e^{5} + \frac{67219534119246961516}{11740084447674443}e^{4} + \frac{6784954182108442038}{690593202804379}e^{3} - \frac{19058403791497449134}{1677154921096349}e^{2} + \frac{41326690692953707117}{11740084447674443}e - \frac{4024338777754130469}{11740084447674443}$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $-\frac{37886812596272}{690593202804379}e^{13} - \frac{502746672791126}{690593202804379}e^{12} - \frac{1210416043846120}{690593202804379}e^{11} + \frac{8632465288736605}{690593202804379}e^{10} + \frac{33879088937347725}{690593202804379}e^{9} - \frac{61012064318963068}{690593202804379}e^{8} - \frac{279561027051040811}{690593202804379}e^{7} + \frac{312859509779323632}{690593202804379}e^{6} + \frac{982813429069991430}{690593202804379}e^{5} - \frac{1240316872237718976}{690593202804379}e^{4} - \frac{1034011857311389814}{690593202804379}e^{3} + \frac{310664803423308717}{98656171829197}e^{2} - \frac{1049055231580543389}{690593202804379}e + \frac{143574886194207094}{690593202804379}$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $\phantom{-}\frac{100851646109530}{11740084447674443}e^{13} + \frac{1368251830589040}{11740084447674443}e^{12} + \frac{3492660522500088}{11740084447674443}e^{11} - \frac{23424533179602301}{11740084447674443}e^{10} - \frac{98806157883924426}{11740084447674443}e^{9} + \frac{159221986465692914}{11740084447674443}e^{8} + \frac{844129433964866366}{11740084447674443}e^{7} - \frac{758433916670093932}{11740084447674443}e^{6} - \frac{3136835516237938833}{11740084447674443}e^{5} + \frac{2974376677203188759}{11740084447674443}e^{4} + \frac{232164716799509258}{690593202804379}e^{3} - \frac{790705415712299992}{1677154921096349}e^{2} + \frac{1853209457880539663}{11740084447674443}e - \frac{3507824072508132}{11740084447674443}$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $-\frac{2661183753045245}{11740084447674443}e^{13} - \frac{36257337144081030}{11740084447674443}e^{12} - \frac{97200940144379227}{11740084447674443}e^{11} + \frac{580109528313092629}{11740084447674443}e^{10} + \frac{2604777893892234030}{11740084447674443}e^{9} - \frac{3456880794452802760}{11740084447674443}e^{8} - \frac{21231896740929366795}{11740084447674443}e^{7} + \frac{14646164047694805418}{11740084447674443}e^{6} + \frac{75680142017666411816}{11740084447674443}e^{5} - \frac{59573889576292828322}{11740084447674443}e^{4} - \frac{5507049065560400052}{690593202804379}e^{3} + \frac{16528754404563735060}{1677154921096349}e^{2} - \frac{38183085563504255257}{11740084447674443}e + \frac{3767244600885359789}{11740084447674443}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $-1$ |