Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, w + 1]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - x^{16} - 25x^{15} + 22x^{14} + 253x^{13} - 190x^{12} - 1335x^{11} + 836x^{10} + 3912x^{9} - 2023x^{8} - 6207x^{7} + 2682x^{6} + 4688x^{5} - 1775x^{4} - 1124x^{3} + 441x^{2} + 25x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{2241025}{11675351}e^{16} + \frac{3193095}{11675351}e^{15} + \frac{51364618}{11675351}e^{14} - \frac{63516692}{11675351}e^{13} - \frac{470245887}{11675351}e^{12} + \frac{469978776}{11675351}e^{11} + \frac{2221378385}{11675351}e^{10} - \frac{1608052430}{11675351}e^{9} - \frac{5763860122}{11675351}e^{8} + \frac{2451263708}{11675351}e^{7} + \frac{7967094062}{11675351}e^{6} - \frac{976376476}{11675351}e^{5} - \frac{5071930655}{11675351}e^{4} - \frac{763494380}{11675351}e^{3} + \frac{894225048}{11675351}e^{2} + \frac{186638737}{11675351}e - \frac{14125971}{11675351}$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{616267}{35026053}e^{16} - \frac{6747100}{35026053}e^{15} + \frac{29257229}{35026053}e^{14} + \frac{47905264}{11675351}e^{13} - \frac{437801317}{35026053}e^{12} - \frac{1184133073}{35026053}e^{11} + \frac{2998194826}{35026053}e^{10} + \frac{1598806730}{11675351}e^{9} - \frac{3501680139}{11675351}e^{8} - \frac{9823111742}{35026053}e^{7} + \frac{18828863282}{35026053}e^{6} + \frac{9051431131}{35026053}e^{5} - \frac{5133317879}{11675351}e^{4} - \frac{2386674406}{35026053}e^{3} + \frac{1293993990}{11675351}e^{2} - \frac{10034326}{11675351}e - \frac{106279480}{35026053}$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{2723654}{35026053}e^{16} + \frac{8463430}{35026053}e^{15} + \frac{54824512}{35026053}e^{14} - \frac{59429329}{11675351}e^{13} - \frac{412378175}{35026053}e^{12} + \frac{1441148935}{35026053}e^{11} + \frac{1433771471}{35026053}e^{10} - \frac{1892172791}{11675351}e^{9} - \frac{723025613}{11675351}e^{8} + \frac{11227525763}{35026053}e^{7} + \frac{630504733}{35026053}e^{6} - \frac{9975696754}{35026053}e^{5} + \frac{359321758}{11675351}e^{4} + \frac{2532727948}{35026053}e^{3} - \frac{101194918}{11675351}e^{2} + \frac{38361924}{11675351}e - \frac{5977919}{35026053}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{6965828}{35026053}e^{16} - \frac{11322001}{35026053}e^{15} - \frac{160958791}{35026053}e^{14} + \frac{77694988}{11675351}e^{13} + \frac{1493663015}{35026053}e^{12} - \frac{1821935173}{35026053}e^{11} - \frac{7217977976}{35026053}e^{10} + \frac{2279232204}{11675351}e^{9} + \frac{6484912014}{11675351}e^{8} - \frac{12538720127}{35026053}e^{7} - \frac{28667845900}{35026053}e^{6} + \frac{9569823025}{35026053}e^{5} + \frac{6813785853}{11675351}e^{4} - \frac{1237957030}{35026053}e^{3} - \frac{1594987348}{11675351}e^{2} - \frac{21038707}{11675351}e + \frac{210506396}{35026053}$ |
| 11 | $[11, 11, w + 1]$ | $-1$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}\frac{3883246}{35026053}e^{16} - \frac{2834849}{35026053}e^{15} - \frac{98823245}{35026053}e^{14} + \frac{19226346}{11675351}e^{13} + \frac{1029331339}{35026053}e^{12} - \frac{442036160}{35026053}e^{11} - \frac{5664176203}{35026053}e^{10} + \frac{538649324}{11675351}e^{9} + \frac{5847555701}{11675351}e^{8} - \frac{2893418404}{35026053}e^{7} - \frac{29733352610}{35026053}e^{6} + \frac{2304593099}{35026053}e^{5} + \frac{8012356584}{11675351}e^{4} - \frac{842930948}{35026053}e^{3} - \frac{2011157109}{11675351}e^{2} + \frac{214520755}{11675351}e + \frac{249595804}{35026053}$ |
| 17 | $[17, 17, -3w + 17]$ | $-\frac{5480387}{35026053}e^{16} + \frac{28683181}{35026053}e^{15} + \frac{78308824}{35026053}e^{14} - \frac{200384086}{11675351}e^{13} - \frac{178264151}{35026053}e^{12} + \frac{4857026947}{35026053}e^{11} - \frac{2168100145}{35026053}e^{10} - \frac{6448987907}{11675351}e^{9} + \frac{4884165984}{11675351}e^{8} + \frac{39659702006}{35026053}e^{7} - \frac{34682550641}{35026053}e^{6} - \frac{38807012560}{35026053}e^{5} + \frac{11010852368}{11675351}e^{4} + \frac{13883128531}{35026053}e^{3} - \frac{2934125389}{11675351}e^{2} - \frac{239287643}{11675351}e + \frac{377352532}{35026053}$ |
| 29 | $[29, 29, w + 11]$ | $-\frac{8252786}{11675351}e^{16} + \frac{11231014}{11675351}e^{15} + \frac{194190620}{11675351}e^{14} - \frac{228491576}{11675351}e^{13} - \frac{1839013107}{11675351}e^{12} + \frac{1756982892}{11675351}e^{11} + \frac{9063968836}{11675351}e^{10} - \frac{6459781849}{11675351}e^{9} - \frac{24798620457}{11675351}e^{8} + \frac{11604508988}{11675351}e^{7} + \frac{36634653182}{11675351}e^{6} - \frac{8888552731}{11675351}e^{5} - \frac{25351563766}{11675351}e^{4} + \frac{1702869410}{11675351}e^{3} + \frac{5015703022}{11675351}e^{2} - \frac{335508075}{11675351}e - \frac{67743706}{11675351}$ |
| 29 | $[29, 29, w + 18]$ | $-\frac{12142747}{35026053}e^{16} + \frac{2063525}{35026053}e^{15} + \frac{320449967}{35026053}e^{14} - \frac{11473190}{11675351}e^{13} - \frac{3422317540}{35026053}e^{12} + \frac{149163998}{35026053}e^{11} + \frac{18977038738}{35026053}e^{10} + \frac{90613424}{11675351}e^{9} - \frac{19342706746}{11675351}e^{8} - \frac{3521720681}{35026053}e^{7} + \frac{94993619630}{35026053}e^{6} + \frac{8694643279}{35026053}e^{5} - \frac{24073835920}{11675351}e^{4} - \frac{7158338716}{35026053}e^{3} + \frac{5319830832}{11675351}e^{2} + \frac{84015662}{11675351}e - \frac{582963856}{35026053}$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{10213716}{11675351}e^{16} - \frac{5103843}{11675351}e^{15} - \frac{258221801}{11675351}e^{14} + \frac{96716660}{11675351}e^{13} + \frac{2634903913}{11675351}e^{12} - \frac{651619183}{11675351}e^{11} - \frac{13937222786}{11675351}e^{10} + \frac{1847579423}{11675351}e^{9} + \frac{40581923542}{11675351}e^{8} - \frac{1725151987}{11675351}e^{7} - \frac{63215917977}{11675351}e^{6} - \frac{859298476}{11675351}e^{5} + \frac{46058381336}{11675351}e^{4} + \frac{1208257092}{11675351}e^{3} - \frac{10190308840}{11675351}e^{2} + \frac{556777646}{11675351}e + \frac{246787166}{11675351}$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{8057824}{35026053}e^{16} + \frac{9329270}{35026053}e^{15} + \frac{191373140}{35026053}e^{14} - \frac{64938618}{11675351}e^{13} - \frac{1826692111}{35026053}e^{12} + \frac{1551440657}{35026053}e^{11} + \frac{9044978050}{35026053}e^{10} - \frac{2000082194}{11675351}e^{9} - \frac{8266200224}{11675351}e^{8} + \frac{11726772943}{35026053}e^{7} + \frac{36866691881}{35026053}e^{6} - \frac{10759390121}{35026053}e^{5} - \frac{8837252047}{11675351}e^{4} + \frac{3770215499}{35026053}e^{3} + \frac{2208861213}{11675351}e^{2} - \frac{232885317}{11675351}e - \frac{264438448}{35026053}$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{14961682}{35026053}e^{16} + \frac{10852930}{35026053}e^{15} - \frac{425019317}{35026053}e^{14} - \frac{76311848}{11675351}e^{13} + \frac{4808491924}{35026053}e^{12} + \frac{1884295522}{35026053}e^{11} - \frac{27716080318}{35026053}e^{10} - \frac{2564002346}{11675351}e^{9} + \frac{28832735760}{11675351}e^{8} + \frac{15821068409}{35026053}e^{7} - \frac{142323158450}{35026053}e^{6} - \frac{13886836666}{35026053}e^{5} + \frac{35992963516}{11675351}e^{4} + \frac{1685909341}{35026053}e^{3} - \frac{8135037705}{11675351}e^{2} + \frac{647111698}{11675351}e + \frac{608822494}{35026053}$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{16430369}{35026053}e^{16} - \frac{15481474}{35026053}e^{15} - \frac{390224635}{35026053}e^{14} + \frac{95771369}{11675351}e^{13} + \frac{3731253572}{35026053}e^{12} - \frac{1872030343}{35026053}e^{11} - \frac{18535656017}{35026053}e^{10} + \frac{1612175836}{11675351}e^{9} + \frac{16968181135}{11675351}e^{8} - \frac{1894208780}{35026053}e^{7} - \frac{75089077591}{35026053}e^{6} - \frac{11059031438}{35026053}e^{5} + \frac{17308738663}{11675351}e^{4} + \frac{13690063886}{35026053}e^{3} - \frac{3634699756}{11675351}e^{2} - \frac{693498574}{11675351}e + \frac{433516829}{35026053}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{25850066}{35026053}e^{16} - \frac{39475879}{35026053}e^{15} - \frac{603265543}{35026053}e^{14} + \frac{275078695}{11675351}e^{13} + \frac{5660614679}{35026053}e^{12} - \frac{6598042942}{35026053}e^{11} - \frac{27656920886}{35026053}e^{10} + \frac{8559133797}{11675351}e^{9} + \frac{25083609921}{11675351}e^{8} - \frac{50428004075}{35026053}e^{7} - \frac{111429235558}{35026053}e^{6} + \frac{45874381483}{35026053}e^{5} + \frac{26245146021}{11675351}e^{4} - \frac{15219340372}{35026053}e^{3} - \frac{5698241774}{11675351}e^{2} + \frac{945181351}{11675351}e + \frac{424844423}{35026053}$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}\frac{3600395}{11675351}e^{16} + \frac{2129657}{11675351}e^{15} - \frac{97277054}{11675351}e^{14} - \frac{52455439}{11675351}e^{13} + \frac{1052994246}{11675351}e^{12} + \frac{527996059}{11675351}e^{11} - \frac{5837122620}{11675351}e^{10} - \frac{2774658894}{11675351}e^{9} + \frac{17560518043}{11675351}e^{8} + \frac{7984414001}{11675351}e^{7} - \frac{27783691935}{11675351}e^{6} - \frac{12012668639}{11675351}e^{5} + \frac{19951761522}{11675351}e^{4} + \frac{7936446964}{11675351}e^{3} - \frac{3835557748}{11675351}e^{2} - \frac{1070569649}{11675351}e + \frac{92210340}{11675351}$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}\frac{1388768}{11675351}e^{16} - \frac{6574564}{11675351}e^{15} - \frac{20947963}{11675351}e^{14} + \frac{134294854}{11675351}e^{13} + \frac{68053893}{11675351}e^{12} - \frac{1050907035}{11675351}e^{11} + \frac{369048598}{11675351}e^{10} + \frac{4042613463}{11675351}e^{9} - \frac{3032031596}{11675351}e^{8} - \frac{8065726878}{11675351}e^{7} + \frac{7507369811}{11675351}e^{6} + \frac{7968233105}{11675351}e^{5} - \frac{7222812830}{11675351}e^{4} - \frac{3210317839}{11675351}e^{3} + \frac{1749366775}{11675351}e^{2} + \frac{165835039}{11675351}e + \frac{29934558}{11675351}$ |
| 89 | $[89, 89, 2w - 15]$ | $-\frac{5874869}{35026053}e^{16} - \frac{8845037}{35026053}e^{15} + \frac{183788326}{35026053}e^{14} + \frac{63755094}{11675351}e^{13} - \frac{2256057719}{35026053}e^{12} - \frac{1632623309}{35026053}e^{11} + \frac{13972807796}{35026053}e^{10} + \frac{2372166810}{11675351}e^{9} - \frac{15521754941}{11675351}e^{8} - \frac{16809984259}{35026053}e^{7} + \frac{81062645107}{35026053}e^{6} + \frac{20550624815}{35026053}e^{5} - \frac{20941985596}{11675351}e^{4} - \frac{10362562637}{35026053}e^{3} + \frac{3815394621}{11675351}e^{2} + \frac{29841416}{11675351}e + \frac{95353045}{35026053}$ |
| 89 | $[89, 89, -2w - 15]$ | $-\frac{8167738}{35026053}e^{16} + \frac{19030646}{35026053}e^{15} + \frac{166571915}{35026053}e^{14} - \frac{127490129}{11675351}e^{13} - \frac{1266515656}{35026053}e^{12} + \frac{2875130306}{35026053}e^{11} + \frac{4361026366}{35026053}e^{10} - \frac{3357385382}{11675351}e^{9} - \frac{1938816689}{11675351}e^{8} + \frac{15971904601}{35026053}e^{7} - \frac{1631751964}{35026053}e^{6} - \frac{7130371157}{35026053}e^{5} + \frac{2663668870}{11675351}e^{4} - \frac{5240027170}{35026053}e^{3} - \frac{521810966}{11675351}e^{2} + \frac{876754824}{11675351}e - \frac{191403928}{35026053}$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}\frac{5941756}{35026053}e^{16} - \frac{12498725}{35026053}e^{15} - \frac{126011207}{35026053}e^{14} + \frac{85903075}{11675351}e^{13} + \frac{1055152384}{35026053}e^{12} - \frac{2044806323}{35026053}e^{11} - \frac{4581989728}{35026053}e^{10} + \frac{2684455998}{11675351}e^{9} + \frac{3792014274}{11675351}e^{8} - \frac{16732243996}{35026053}e^{7} - \frac{16736839445}{35026053}e^{6} + \frac{17707394642}{35026053}e^{5} + \frac{4710207267}{11675351}e^{4} - \frac{8165172338}{35026053}e^{3} - \frac{1803676860}{11675351}e^{2} + \frac{319025456}{11675351}e + \frac{296367019}{35026053}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w + 1]$ | $1$ |