Newform invariants
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
This newform subspace can be constructed as the kernel of the linear operator \(13\!\cdots\!09\)\( T_{5}^{139} + \)\(26\!\cdots\!42\)\( T_{5}^{138} - \)\(18\!\cdots\!88\)\( T_{5}^{137} + \)\(49\!\cdots\!49\)\( T_{5}^{136} + \)\(22\!\cdots\!99\)\( T_{5}^{135} - \)\(13\!\cdots\!72\)\( T_{5}^{134} - \)\(40\!\cdots\!96\)\( T_{5}^{133} + \)\(13\!\cdots\!38\)\( T_{5}^{132} - \)\(29\!\cdots\!05\)\( T_{5}^{131} + \)\(13\!\cdots\!53\)\( T_{5}^{130} + \)\(41\!\cdots\!99\)\( T_{5}^{129} - \)\(13\!\cdots\!31\)\( T_{5}^{128} - \)\(24\!\cdots\!30\)\( T_{5}^{127} + \)\(20\!\cdots\!67\)\( T_{5}^{126} - \)\(21\!\cdots\!33\)\( T_{5}^{125} - \)\(12\!\cdots\!69\)\( T_{5}^{124} + \)\(60\!\cdots\!96\)\( T_{5}^{123} - \)\(84\!\cdots\!17\)\( T_{5}^{122} - \)\(44\!\cdots\!06\)\( T_{5}^{121} + \)\(22\!\cdots\!81\)\( T_{5}^{120} - \)\(85\!\cdots\!52\)\( T_{5}^{119} - \)\(16\!\cdots\!81\)\( T_{5}^{118} + \)\(51\!\cdots\!20\)\( T_{5}^{117} - \)\(35\!\cdots\!66\)\( T_{5}^{116} - \)\(43\!\cdots\!37\)\( T_{5}^{115} + \)\(18\!\cdots\!39\)\( T_{5}^{114} - \)\(87\!\cdots\!90\)\( T_{5}^{113} - \)\(15\!\cdots\!68\)\( T_{5}^{112} + \)\(31\!\cdots\!24\)\( T_{5}^{111} + \)\(20\!\cdots\!61\)\( T_{5}^{110} - \)\(27\!\cdots\!09\)\( T_{5}^{109} + \)\(83\!\cdots\!14\)\( T_{5}^{108} + \)\(44\!\cdots\!39\)\( T_{5}^{107} - \)\(73\!\cdots\!85\)\( T_{5}^{106} + \)\(92\!\cdots\!75\)\( T_{5}^{105} + \)\(11\!\cdots\!75\)\( T_{5}^{104} - \)\(80\!\cdots\!12\)\( T_{5}^{103} + \)\(12\!\cdots\!67\)\( T_{5}^{102} + \)\(37\!\cdots\!33\)\( T_{5}^{101} - \)\(31\!\cdots\!87\)\( T_{5}^{100} - \)\(64\!\cdots\!80\)\( T_{5}^{99} - \)\(32\!\cdots\!76\)\( T_{5}^{98} + \)\(23\!\cdots\!66\)\( T_{5}^{97} + \)\(35\!\cdots\!43\)\( T_{5}^{96} - \)\(14\!\cdots\!43\)\( T_{5}^{95} - \)\(27\!\cdots\!20\)\( T_{5}^{94} + \)\(64\!\cdots\!00\)\( T_{5}^{93} + \)\(20\!\cdots\!73\)\( T_{5}^{92} + \)\(61\!\cdots\!31\)\( T_{5}^{91} + \)\(86\!\cdots\!82\)\( T_{5}^{90} - \)\(41\!\cdots\!22\)\( T_{5}^{89} - \)\(37\!\cdots\!03\)\( T_{5}^{88} + \)\(19\!\cdots\!50\)\( T_{5}^{87} + \)\(29\!\cdots\!92\)\( T_{5}^{86} - \)\(41\!\cdots\!91\)\( T_{5}^{85} - \)\(10\!\cdots\!57\)\( T_{5}^{84} + \)\(42\!\cdots\!02\)\( T_{5}^{83} + \)\(46\!\cdots\!17\)\( T_{5}^{82} - \)\(26\!\cdots\!87\)\( T_{5}^{81} - \)\(48\!\cdots\!30\)\( T_{5}^{80} + \)\(15\!\cdots\!79\)\( T_{5}^{79} + \)\(37\!\cdots\!95\)\( T_{5}^{78} - \)\(10\!\cdots\!30\)\( T_{5}^{77} - \)\(25\!\cdots\!69\)\( T_{5}^{76} + \)\(48\!\cdots\!53\)\( T_{5}^{75} + \)\(17\!\cdots\!86\)\( T_{5}^{74} - \)\(11\!\cdots\!60\)\( T_{5}^{73} - \)\(99\!\cdots\!54\)\( T_{5}^{72} - \)\(38\!\cdots\!87\)\( T_{5}^{71} + \)\(33\!\cdots\!98\)\( T_{5}^{70} + \)\(52\!\cdots\!75\)\( T_{5}^{69} - \)\(20\!\cdots\!17\)\( T_{5}^{68} - \)\(23\!\cdots\!86\)\( T_{5}^{67} - \)\(40\!\cdots\!82\)\( T_{5}^{66} + \)\(28\!\cdots\!98\)\( T_{5}^{65} + \)\(20\!\cdots\!31\)\( T_{5}^{64} + \)\(17\!\cdots\!77\)\( T_{5}^{63} - \)\(40\!\cdots\!77\)\( T_{5}^{62} - \)\(96\!\cdots\!83\)\( T_{5}^{61} - \)\(58\!\cdots\!01\)\( T_{5}^{60} + \)\(20\!\cdots\!26\)\( T_{5}^{59} + \)\(22\!\cdots\!01\)\( T_{5}^{58} - \)\(20\!\cdots\!84\)\( T_{5}^{57} - \)\(50\!\cdots\!86\)\( T_{5}^{56} - \)\(12\!\cdots\!03\)\( T_{5}^{55} + \)\(59\!\cdots\!40\)\( T_{5}^{54} + \)\(57\!\cdots\!48\)\( T_{5}^{53} - \)\(18\!\cdots\!37\)\( T_{5}^{52} - \)\(78\!\cdots\!97\)\( T_{5}^{51} - \)\(43\!\cdots\!42\)\( T_{5}^{50} + \)\(26\!\cdots\!91\)\( T_{5}^{49} + \)\(78\!\cdots\!73\)\( T_{5}^{48} + \)\(54\!\cdots\!85\)\( T_{5}^{47} - \)\(28\!\cdots\!35\)\( T_{5}^{46} - \)\(78\!\cdots\!96\)\( T_{5}^{45} - \)\(70\!\cdots\!88\)\( T_{5}^{44} + \)\(15\!\cdots\!21\)\( T_{5}^{43} + \)\(11\!\cdots\!32\)\( T_{5}^{42} + \)\(63\!\cdots\!11\)\( T_{5}^{41} - \)\(67\!\cdots\!68\)\( T_{5}^{40} - \)\(13\!\cdots\!90\)\( T_{5}^{39} - \)\(43\!\cdots\!64\)\( T_{5}^{38} + \)\(66\!\cdots\!16\)\( T_{5}^{37} + \)\(80\!\cdots\!62\)\( T_{5}^{36} + \)\(22\!\cdots\!17\)\( T_{5}^{35} - \)\(45\!\cdots\!32\)\( T_{5}^{34} - \)\(24\!\cdots\!22\)\( T_{5}^{33} + \)\(21\!\cdots\!99\)\( T_{5}^{32} + \)\(32\!\cdots\!53\)\( T_{5}^{31} + \)\(16\!\cdots\!76\)\( T_{5}^{30} + \)\(89\!\cdots\!68\)\( T_{5}^{29} - \)\(29\!\cdots\!08\)\( T_{5}^{28} - \)\(18\!\cdots\!65\)\( T_{5}^{27} + \)\(13\!\cdots\!39\)\( T_{5}^{26} + \)\(72\!\cdots\!21\)\( T_{5}^{25} + \)\(46\!\cdots\!47\)\( T_{5}^{24} - \)\(97\!\cdots\!64\)\( T_{5}^{23} - \)\(68\!\cdots\!47\)\( T_{5}^{22} - \)\(38\!\cdots\!94\)\( T_{5}^{21} - \)\(66\!\cdots\!35\)\( T_{5}^{20} + \)\(30\!\cdots\!73\)\( T_{5}^{19} + \)\(39\!\cdots\!10\)\( T_{5}^{18} + \)\(20\!\cdots\!59\)\( T_{5}^{17} + \)\(12\!\cdots\!59\)\( T_{5}^{16} - \)\(78\!\cdots\!72\)\( T_{5}^{15} - \)\(16\!\cdots\!69\)\( T_{5}^{14} - \)\(83\!\cdots\!31\)\( T_{5}^{13} + \)\(87\!\cdots\!39\)\( T_{5}^{12} + \)\(32\!\cdots\!42\)\( T_{5}^{11} + \)\(52\!\cdots\!22\)\( T_{5}^{10} + \)\(11\!\cdots\!75\)\( T_{5}^{9} + \)\(20\!\cdots\!95\)\( T_{5}^{8} + \)\(13\!\cdots\!45\)\( T_{5}^{7} + \)\(30\!\cdots\!99\)\( T_{5}^{6} + \)\(53\!\cdots\!57\)\( T_{5}^{5} - \)\(11\!\cdots\!20\)\( T_{5}^{4} - \)\(16\!\cdots\!90\)\( T_{5}^{3} + \)\(20\!\cdots\!11\)\( T_{5}^{2} - \)\(17\!\cdots\!59\)\( T_{5} + \)\(18\!\cdots\!81\)\( \)">\(T_{5}^{160} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(966, [\chi])\).
