Base field 4.4.11661.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25,5,-w^{3} + w^{2} + 3w - 1]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 6x^{15} - 12x^{14} - 128x^{13} - 31x^{12} + 1031x^{11} + 1051x^{10} - 3828x^{9} - 5696x^{8} + 6123x^{7} + 12576x^{6} - 1815x^{5} - 10952x^{4} - 3792x^{3} + 1950x^{2} + 1362x + 213\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{8940}{163}e^{15} + \frac{66982}{163}e^{14} - \frac{7678}{163}e^{13} - \frac{1158250}{163}e^{12} - \frac{2003896}{163}e^{11} + \frac{6271605}{163}e^{10} + \frac{18808939}{163}e^{9} - \frac{6429077}{163}e^{8} - \frac{61101535}{163}e^{7} - \frac{35886196}{163}e^{6} + \frac{60947037}{163}e^{5} + \frac{75069847}{163}e^{4} + \frac{11623314}{163}e^{3} - \frac{18222741}{163}e^{2} - \frac{9418544}{163}e - \frac{1349900}{163}$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{13535}{163}e^{15} + \frac{101017}{163}e^{14} - \frac{14366}{163}e^{13} - \frac{1751859}{163}e^{12} - \frac{2983969}{163}e^{11} + \frac{9558016}{163}e^{10} + \frac{28170895}{163}e^{9} - \frac{10404915}{163}e^{8} - \frac{91896197}{163}e^{7} - \frac{51963831}{163}e^{6} + \frac{92684374}{163}e^{5} + \frac{110801250}{163}e^{4} + \frac{15710370}{163}e^{3} - \frac{27186224}{163}e^{2} - \frac{13663365}{163}e - \frac{1921675}{163}$ |
| 16 | $[16, 2, 2]$ | $-\frac{132230}{163}e^{15} - \frac{987868}{163}e^{14} + \frac{133361}{163}e^{13} + \frac{17118647}{163}e^{12} + \frac{29279246}{163}e^{11} - \frac{93210925}{163}e^{10} - \frac{275998917}{163}e^{9} + \frac{99904571}{163}e^{8} + \frac{899374775}{163}e^{7} + \frac{513811095}{163}e^{6} - \frac{904570355}{163}e^{5} - \frac{1089942912}{163}e^{4} - \frac{158094776}{163}e^{3} + \frac{266754446}{163}e^{2} + \frac{134947239}{163}e + \frac{19056532}{163}$ |
| 23 | $[23, 23, -w^{3} + 4w + 1]$ | $-\frac{221477}{163}e^{15} - \frac{1654954}{163}e^{14} + \frac{220990}{163}e^{13} + \frac{28674035}{163}e^{12} + \frac{49084344}{163}e^{11} - \frac{156066431}{163}e^{10} - \frac{462548331}{163}e^{9} + \frac{166741356}{163}e^{8} + \frac{1506942118}{163}e^{7} + \frac{862693790}{163}e^{6} - \frac{1514791881}{163}e^{5} - \frac{1828137997}{163}e^{4} - \frac{266372983}{163}e^{3} + \frac{447208973}{163}e^{2} + \frac{226530092}{163}e + \frac{32011986}{163}$ |
| 25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{56868}{163}e^{15} + \frac{424561}{163}e^{14} - \frac{59371}{163}e^{13} - \frac{7360824}{163}e^{12} - \frac{12555140}{163}e^{11} + \frac{40131617}{163}e^{10} + \frac{118468863}{163}e^{9} - \frac{43449121}{163}e^{8} - \frac{386308597}{163}e^{7} - \frac{219256063}{163}e^{6} + \frac{389220527}{163}e^{5} + \frac{466650170}{163}e^{4} + \frac{66735511}{163}e^{3} - \frac{114381763}{163}e^{2} - \frac{57632367}{163}e - \frac{8120336}{163}$ |
| 25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $\phantom{-}\frac{47210}{163}e^{15} + \frac{352347}{163}e^{14} - \frac{49984}{163}e^{13} - \frac{6109890}{163}e^{12} - \frac{10409900}{163}e^{11} + \frac{33326760}{163}e^{10} + \frac{98265403}{163}e^{9} - \frac{36210068}{163}e^{8} - \frac{320502092}{163}e^{7} - \frac{181498366}{163}e^{6} + \frac{323085085}{163}e^{5} + \frac{386744281}{163}e^{4} + \frac{55091004}{163}e^{3} - \frac{94839349}{163}e^{2} - \frac{47738258}{163}e - \frac{6721929}{163}$ |
| 29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}\frac{152586}{163}e^{15} + \frac{1139730}{163}e^{14} - \frac{155405}{163}e^{13} - \frac{19753123}{163}e^{12} - \frac{33759203}{163}e^{11} + \frac{107596366}{163}e^{10} + \frac{318321515}{163}e^{9} - \frac{115662763}{163}e^{8} - \frac{1037512612}{163}e^{7} - \frac{591587559}{163}e^{6} + \frac{1044120196}{163}e^{5} + \frac{1256165989}{163}e^{4} + \frac{181303419}{163}e^{3} - \frac{307636086}{163}e^{2} - \frac{155369314}{163}e - \frac{21911316}{163}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{67448}{163}e^{15} + \frac{505109}{163}e^{14} - \frac{59479}{163}e^{13} - \frac{8736951}{163}e^{12} - \frac{15090133}{163}e^{11} + \frac{47345290}{163}e^{10} + \frac{141730684}{163}e^{9} - \frac{48843918}{163}e^{8} - \frac{460632950}{163}e^{7} - \frac{269528886}{163}e^{6} + \frac{460048676}{163}e^{5} + \frac{564923575}{163}e^{4} + \frac{86609189}{163}e^{3} - \frac{137326030}{163}e^{2} - \frac{70717304}{163}e - \frac{10107299}{163}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $-\frac{238740}{163}e^{15} - \frac{1784239}{163}e^{14} + \frac{236094}{163}e^{13} + \frac{30909661}{163}e^{12} + \frac{52947787}{163}e^{11} - \frac{168172549}{163}e^{10} - \frac{498817552}{163}e^{9} + \frac{179161616}{163}e^{8} + \frac{1624725368}{163}e^{7} + \frac{931899226}{163}e^{6} - \frac{1632080409}{163}e^{5} - \frac{1972876997}{163}e^{4} - \frac{289164361}{163}e^{3} + \frac{482212795}{163}e^{2} + \frac{244801526}{163}e + \frac{34660240}{163}$ |
| 61 | $[61, 61, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{442770}{163}e^{15} + \frac{3308510}{163}e^{14} - \frac{441903}{163}e^{13} - \frac{57323766}{163}e^{12} - \frac{98125256}{163}e^{11} + \frac{311999777}{163}e^{10} + \frac{924686388}{163}e^{9} - \frac{333337329}{163}e^{8} - \frac{3012506605}{163}e^{7} - \frac{1724645395}{163}e^{6} + \frac{3028020874}{163}e^{5} + \frac{3654625791}{163}e^{4} + \frac{532845684}{163}e^{3} - \frac{893878208}{163}e^{2} - \frac{452956412}{163}e - \frac{64040686}{163}$ |
| 61 | $[61, 61, w^{2} - 5]$ | $\phantom{-}\frac{303011}{163}e^{15} + \frac{2263461}{163}e^{14} - \frac{307559}{163}e^{13} - \frac{39226830}{163}e^{12} - \frac{67059087}{163}e^{11} + \frac{213640655}{163}e^{10} + \frac{632245610}{163}e^{9} - \frac{229407042}{163}e^{8} - \frac{2060520433}{163}e^{7} - \frac{1175757222}{163}e^{6} + \frac{2073153839}{163}e^{5} + \frac{2495657259}{163}e^{4} + \frac{360937968}{163}e^{3} - \frac{611019249}{163}e^{2} - \frac{308814694}{163}e - \frac{43577330}{163}$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ | $\phantom{-}\frac{314278}{163}e^{15} + \frac{2347969}{163}e^{14} - \frac{316543}{163}e^{13} - \frac{40686713}{163}e^{12} - \frac{69597083}{163}e^{11} + \frac{221525147}{163}e^{10} + \frac{656025613}{163}e^{9} - \frac{237317505}{163}e^{8} - \frac{2137667219}{163}e^{7} - \frac{1221647921}{163}e^{6} + \frac{2149822786}{163}e^{5} + \frac{2591064457}{163}e^{4} + \frac{376104052}{163}e^{3} - \frac{634098392}{163}e^{2} - \frac{320847096}{163}e - \frac{45313072}{163}$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 4]$ | $-\frac{487040}{163}e^{15} - \frac{3640362}{163}e^{14} + \frac{478825}{163}e^{13} + \frac{63060288}{163}e^{12} + \frac{108068722}{163}e^{11} - \frac{343035061}{163}e^{10} - \frac{1017956236}{163}e^{9} + \frac{364928656}{163}e^{8} + \frac{3315373181}{163}e^{7} + \frac{1903240159}{163}e^{6} - \frac{3329825039}{163}e^{5} - \frac{4027478027}{163}e^{4} - \frac{590959908}{163}e^{3} + \frac{984327535}{163}e^{2} + \frac{499783610}{163}e + \frac{70755538}{163}$ |
| 101 | $[101, 101, -w^{3} + 3w^{2} + w - 7]$ | $-\frac{281831}{163}e^{15} - \frac{2105225}{163}e^{14} + \frac{286297}{163}e^{13} + \frac{36485116}{163}e^{12} + \frac{62367501}{163}e^{11} - \frac{198716955}{163}e^{10} - \frac{588026855}{163}e^{9} + \frac{213453861}{163}e^{8} + \frac{1916443361}{163}e^{7} + \frac{1093296095}{163}e^{6} - \frac{1928283240}{163}e^{5} - \frac{2320863902}{163}e^{4} - \frac{335547251}{163}e^{3} + \frac{568221385}{163}e^{2} + \frac{287177619}{163}e + \frac{40527822}{163}$ |
| 101 | $[101, 101, w^{3} - 4w - 4]$ | $\phantom{-}\frac{533133}{163}e^{15} + \frac{3985528}{163}e^{14} - \frac{519443}{163}e^{13} - \frac{69030227}{163}e^{12} - \frac{118381349}{163}e^{11} + \frac{375379345}{163}e^{10} + \frac{1114810761}{163}e^{9} - \frac{398239172}{163}e^{8} - \frac{3630132033}{163}e^{7} - \frac{2087637975}{163}e^{6} + \frac{3644100979}{163}e^{5} + \frac{4413791675}{163}e^{4} + \frac{650288187}{163}e^{3} - \frac{1078245543}{163}e^{2} - \frac{548147022}{163}e - \frac{77662581}{163}$ |
| 103 | $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ | $-\frac{399099}{163}e^{15} - \frac{2983911}{163}e^{14} + \frac{386422}{163}e^{13} + \frac{51678256}{163}e^{12} + \frac{88664906}{163}e^{11} - \frac{280967613}{163}e^{10} - \frac{834836482}{163}e^{9} + \frac{297626334}{163}e^{8} + \frac{2718227099}{163}e^{7} + \frac{1564629317}{163}e^{6} - \frac{2728202458}{163}e^{5} - \frac{3306490106}{163}e^{4} - \frac{487715882}{163}e^{3} + \frac{807679528}{163}e^{2} + \frac{410669953}{163}e + \frac{58180114}{163}$ |
| 103 | $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ | $-\frac{9654}{163}e^{15} - \frac{71808}{163}e^{14} + \frac{11926}{163}e^{13} + \frac{1248315}{163}e^{12} + \frac{2097529}{163}e^{11} - \frac{6853362}{163}e^{10} - \frac{19900978}{163}e^{9} + \frac{7816906}{163}e^{8} + \frac{65135722}{163}e^{7} + \frac{35655974}{163}e^{6} - \frac{66248478}{163}e^{5} - \frac{77317637}{163}e^{4} - \frac{10181730}{163}e^{3} + \frac{19131855}{163}e^{2} + \frac{9411811}{163}e + \frac{1301431}{163}$ |
| 107 | $[107, 107, 2w^{2} - 3w - 4]$ | $-\frac{62347}{163}e^{15} - \frac{466007}{163}e^{14} + \frac{61259}{163}e^{13} + \frac{8072105}{163}e^{12} + \frac{13834305}{163}e^{11} - \frac{43906140}{163}e^{10} - \frac{130305751}{163}e^{9} + \frac{46671507}{163}e^{8} + \frac{424351791}{163}e^{7} + \frac{243763627}{163}e^{6} - \frac{426054809}{163}e^{5} - \frac{515685650}{163}e^{4} - \frac{75910830}{163}e^{3} + \frac{125982175}{163}e^{2} + \frac{64048061}{163}e + \frac{9076758}{163}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25,5,-w^{3} + w^{2} + 3w - 1]$ | $-1$ |