Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + w + 4]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 43x^{18} + 762x^{16} - 7243x^{14} + 40390x^{12} - 136052x^{10} + 274255x^{8} - 313426x^{6} + 177576x^{4} - 35924x^{2} + 2304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $-\frac{282311889}{11109605344}e^{19} + \frac{11229092235}{11109605344}e^{17} - \frac{89251608885}{5554802672}e^{15} + \frac{1452712185083}{11109605344}e^{13} - \frac{3226046574827}{5554802672}e^{11} + \frac{3846311520701}{2777401336}e^{9} - \frac{17560008848095}{11109605344}e^{7} + \frac{2776201288913}{5554802672}e^{5} + \frac{385522799999}{1388700668}e^{3} - \frac{149357119803}{2777401336}e$ |
| 11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $-\frac{24194657}{347175167}e^{18} + \frac{1950290689}{694350334}e^{16} - \frac{15811071802}{347175167}e^{14} + \frac{132758641625}{347175167}e^{12} - \frac{1243101944407}{694350334}e^{10} + \frac{3268480922915}{694350334}e^{8} - \frac{4622656996337}{694350334}e^{6} + \frac{1554818196974}{347175167}e^{4} - \frac{367857704769}{347175167}e^{2} + \frac{28563790338}{347175167}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{329700391}{16664408016}e^{19} - \frac{13248653653}{16664408016}e^{17} + \frac{35654327117}{2777401336}e^{15} - \frac{1785713165389}{16664408016}e^{13} + \frac{4144683034793}{8332204008}e^{11} - \frac{5379261739559}{4166102004}e^{9} + \frac{29784655736905}{16664408016}e^{7} - \frac{9540387484931}{8332204008}e^{5} + \frac{153578737231}{694350334}e^{3} - \frac{33264546083}{4166102004}e$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{54587871}{694350334}e^{18} - \frac{2193715957}{694350334}e^{16} + \frac{17710223026}{347175167}e^{14} - \frac{295558519525}{694350334}e^{12} + \frac{685197604125}{347175167}e^{10} - \frac{1773312429017}{347175167}e^{8} + \frac{4877811161789}{694350334}e^{6} - \frac{1546536216302}{347175167}e^{4} + \frac{303158953205}{347175167}e^{2} - \frac{16503358648}{347175167}$ |
| 17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}\frac{493129375}{5554802672}e^{19} - \frac{19674243533}{5554802672}e^{17} + \frac{157137250619}{2777401336}e^{15} - \frac{2579047470501}{5554802672}e^{13} + \frac{5817538396993}{2777401336}e^{11} - \frac{7171010858033}{1388700668}e^{9} + \frac{35757248436265}{5554802672}e^{7} - \frac{8649853454079}{2777401336}e^{5} - \frac{49444868243}{694350334}e^{3} + \frac{91905374337}{1388700668}e$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-1$ |
| 19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1467771307}{33328816032}e^{19} - \frac{59172684265}{33328816032}e^{17} + \frac{160016328789}{5554802672}e^{15} - \frac{8075298841849}{33328816032}e^{13} + \frac{18981194495273}{16664408016}e^{11} - \frac{25201999019939}{8332204008}e^{9} + \frac{146103916346389}{33328816032}e^{7} - \frac{52374198857987}{16664408016}e^{5} + \frac{1241454420673}{1388700668}e^{3} - \frac{626146522751}{8332204008}e$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $\phantom{-}\frac{66930575}{694350334}e^{19} - \frac{1356691005}{347175167}e^{17} + \frac{22186164906}{347175167}e^{15} - \frac{377456323897}{694350334}e^{13} + \frac{1804177994907}{694350334}e^{11} - \frac{4910744173141}{694350334}e^{9} + \frac{3692849526480}{347175167}e^{7} - \frac{2804377100998}{347175167}e^{5} + \frac{875389194339}{347175167}e^{3} - \frac{77968788302}{347175167}e$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $\phantom{-}\frac{779949265}{16664408016}e^{19} - \frac{31558750867}{16664408016}e^{17} + \frac{85794264527}{2777401336}e^{15} - \frac{4363971383611}{16664408016}e^{13} + \frac{10383573248207}{8332204008}e^{11} - \frac{14058110805047}{4166102004}e^{9} + \frac{84182440148983}{16664408016}e^{7} - \frac{31958112752945}{8332204008}e^{5} + \frac{840494346599}{694350334}e^{3} - \frac{407914118033}{4166102004}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}\frac{2446911259}{16664408016}e^{19} - \frac{98954304121}{16664408016}e^{17} + \frac{268759198881}{2777401336}e^{15} - \frac{13646966001817}{16664408016}e^{13} + \frac{32362832575073}{8332204008}e^{11} - \frac{43517635610921}{4166102004}e^{9} + \frac{256853749906045}{16664408016}e^{7} - \frac{94486604357879}{8332204008}e^{5} + \frac{2329396208491}{694350334}e^{3} - \frac{1229531770415}{4166102004}e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $-\frac{2013876161}{33328816032}e^{19} + \frac{81543532235}{33328816032}e^{17} - \frac{221877153687}{5554802672}e^{15} + \frac{11298305825003}{33328816032}e^{13} - \frac{26916925440211}{16664408016}e^{11} + \frac{36484452053041}{8332204008}e^{9} - \frac{218580685891679}{33328816032}e^{7} + \frac{83002106586961}{16664408016}e^{5} - \frac{2217174857979}{1388700668}e^{3} + \frac{1363694585605}{8332204008}e$ |
| 41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $-\frac{1665654449}{16664408016}e^{19} + \frac{66593790539}{16664408016}e^{17} - \frac{177795618271}{2777401336}e^{15} + \frac{8787828492731}{16664408016}e^{13} - \frac{19922967461467}{8332204008}e^{11} + \frac{24708592839421}{4166102004}e^{9} - \frac{123849481792895}{16664408016}e^{7} + \frac{29733313052689}{8332204008}e^{5} + \frac{106922524065}{694350334}e^{3} - \frac{351707084615}{4166102004}e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $\phantom{-}\frac{175084515}{1388700668}e^{18} - \frac{7027501045}{1388700668}e^{16} + \frac{56632138333}{694350334}e^{14} - \frac{942495883913}{1388700668}e^{12} + \frac{2175180895905}{694350334}e^{10} - \frac{2792493001238}{347175167}e^{8} + \frac{15118926001473}{1388700668}e^{6} - \frac{4595684486233}{694350334}e^{4} + \frac{370698746937}{347175167}e^{2} - \frac{11852918221}{347175167}$ |
| 59 | $[59, 59, w - 4]$ | $\phantom{-}\frac{71952147}{1388700668}e^{18} - \frac{2904647325}{1388700668}e^{16} + \frac{23621482815}{694350334}e^{14} - \frac{399174030549}{1388700668}e^{12} + \frac{946799726161}{694350334}e^{10} - \frac{1280760350605}{347175167}e^{8} + \frac{7722137603785}{1388700668}e^{6} - \frac{3008525937725}{694350334}e^{4} + \frac{508376178470}{347175167}e^{2} - \frac{48281590415}{347175167}$ |
| 67 | $[67, 67, 2w^{2} - 3w - 8]$ | $-\frac{49591407}{1388700668}e^{18} + \frac{1995334567}{1388700668}e^{16} - \frac{16134149843}{694350334}e^{14} + \frac{269816011093}{1388700668}e^{12} - \frac{313585997955}{347175167}e^{10} + \frac{1627864417013}{694350334}e^{8} - \frac{4483474465091}{1388700668}e^{6} + \frac{1406611722403}{694350334}e^{4} - \frac{122897092319}{347175167}e^{2} + \frac{3714896253}{347175167}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $-\frac{129040279}{11109605344}e^{19} + \frac{5463803805}{11109605344}e^{17} - \frac{47389445851}{5554802672}e^{15} + \frac{874191660029}{11109605344}e^{13} - \frac{2334715854853}{5554802672}e^{11} + \frac{3694082725419}{2777401336}e^{9} - \frac{27147468906841}{11109605344}e^{7} + \frac{13405446387599}{5554802672}e^{5} - \frac{1449755802879}{1388700668}e^{3} + \frac{245263104219}{2777401336}e$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $-\frac{1773349555}{33328816032}e^{19} + \frac{69582797137}{33328816032}e^{17} - \frac{180458616861}{5554802672}e^{15} + \frac{8498871104977}{33328816032}e^{13} - \frac{17630025900329}{16664408016}e^{11} + \frac{18008186581415}{8332204008}e^{9} - \frac{46541221795837}{33328816032}e^{7} - \frac{25524497979973}{16664408016}e^{5} + \frac{2889897149859}{1388700668}e^{3} - \frac{2517914687737}{8332204008}e$ |
| 97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $\phantom{-}\frac{267977581}{694350334}e^{18} - \frac{10794132803}{694350334}e^{16} + \frac{87442619872}{347175167}e^{14} - \frac{1467168038739}{694350334}e^{12} + \frac{3431967536198}{347175167}e^{10} - \frac{9025516928030}{347175167}e^{8} + \frac{25622860640567}{694350334}e^{6} - \frac{8744908732908}{347175167}e^{4} + \frac{2179856202885}{347175167}e^{2} - \frac{170457752184}{347175167}$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{216371799}{5554802672}e^{19} - \frac{8756345645}{5554802672}e^{17} + \frac{71427472011}{2777401336}e^{15} - \frac{1211328106509}{5554802672}e^{13} + \frac{2882775718445}{2777401336}e^{11} - \frac{3902946370839}{1388700668}e^{9} + \frac{23360977272569}{5554802672}e^{7} - \frac{8875626723175}{2777401336}e^{5} + \frac{722840827439}{694350334}e^{3} - \frac{173370389127}{1388700668}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + w + 4]$ | $1$ |