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 \(21\!\cdots\!30\)\( T_{2}^{293} + \)\(79\!\cdots\!83\)\( T_{2}^{292} - \)\(43\!\cdots\!88\)\( T_{2}^{291} - \)\(91\!\cdots\!55\)\( T_{2}^{290} + \)\(15\!\cdots\!56\)\( T_{2}^{289} + \)\(29\!\cdots\!64\)\( T_{2}^{288} - \)\(89\!\cdots\!29\)\( T_{2}^{287} + \)\(25\!\cdots\!11\)\( T_{2}^{286} - \)\(19\!\cdots\!69\)\( T_{2}^{285} - \)\(35\!\cdots\!23\)\( T_{2}^{284} + \)\(62\!\cdots\!01\)\( T_{2}^{283} + \)\(14\!\cdots\!78\)\( T_{2}^{282} - \)\(35\!\cdots\!24\)\( T_{2}^{281} + \)\(57\!\cdots\!63\)\( T_{2}^{280} - \)\(84\!\cdots\!87\)\( T_{2}^{279} - \)\(10\!\cdots\!78\)\( T_{2}^{278} + \)\(24\!\cdots\!50\)\( T_{2}^{277} + \)\(46\!\cdots\!20\)\( T_{2}^{276} - \)\(13\!\cdots\!84\)\( T_{2}^{275} + \)\(53\!\cdots\!34\)\( T_{2}^{274} - \)\(21\!\cdots\!04\)\( T_{2}^{273} - \)\(19\!\cdots\!33\)\( T_{2}^{272} + \)\(51\!\cdots\!30\)\( T_{2}^{271} + \)\(10\!\cdots\!86\)\( T_{2}^{270} - \)\(32\!\cdots\!58\)\( T_{2}^{269} - \)\(10\!\cdots\!76\)\( T_{2}^{268} + \)\(29\!\cdots\!24\)\( T_{2}^{267} - \)\(30\!\cdots\!18\)\( T_{2}^{266} + \)\(10\!\cdots\!18\)\( T_{2}^{265} + \)\(25\!\cdots\!28\)\( T_{2}^{264} - \)\(82\!\cdots\!12\)\( T_{2}^{263} - \)\(74\!\cdots\!53\)\( T_{2}^{262} + \)\(20\!\cdots\!69\)\( T_{2}^{261} - \)\(40\!\cdots\!99\)\( T_{2}^{260} + \)\(16\!\cdots\!17\)\( T_{2}^{259} + \)\(54\!\cdots\!49\)\( T_{2}^{258} - \)\(19\!\cdots\!79\)\( T_{2}^{257} - \)\(21\!\cdots\!54\)\( T_{2}^{256} + \)\(73\!\cdots\!88\)\( T_{2}^{255} - \)\(59\!\cdots\!07\)\( T_{2}^{254} + \)\(21\!\cdots\!03\)\( T_{2}^{253} + \)\(11\!\cdots\!56\)\( T_{2}^{252} - \)\(38\!\cdots\!93\)\( T_{2}^{251} - \)\(45\!\cdots\!77\)\( T_{2}^{250} + \)\(15\!\cdots\!18\)\( T_{2}^{249} - \)\(81\!\cdots\!00\)\( T_{2}^{248} + \)\(34\!\cdots\!89\)\( T_{2}^{247} + \)\(17\!\cdots\!91\)\( T_{2}^{246} - \)\(69\!\cdots\!47\)\( T_{2}^{245} - \)\(71\!\cdots\!19\)\( T_{2}^{244} + \)\(28\!\cdots\!50\)\( T_{2}^{243} - \)\(11\!\cdots\!22\)\( T_{2}^{242} + \)\(47\!\cdots\!11\)\( T_{2}^{241} + \)\(24\!\cdots\!72\)\( T_{2}^{240} - \)\(10\!\cdots\!15\)\( T_{2}^{239} - \)\(94\!\cdots\!54\)\( T_{2}^{238} + \)\(40\!\cdots\!23\)\( T_{2}^{237} - \)\(12\!\cdots\!72\)\( T_{2}^{236} + \)\(54\!\cdots\!28\)\( T_{2}^{235} + \)\(27\!\cdots\!08\)\( T_{2}^{234} - \)\(12\!\cdots\!93\)\( T_{2}^{233} - \)\(10\!\cdots\!59\)\( T_{2}^{232} + \)\(44\!\cdots\!35\)\( T_{2}^{231} - \)\(59\!\cdots\!27\)\( T_{2}^{230} + \)\(55\!\cdots\!87\)\( T_{2}^{229} + \)\(23\!\cdots\!02\)\( T_{2}^{228} - \)\(12\!\cdots\!85\)\( T_{2}^{227} - \)\(96\!\cdots\!53\)\( T_{2}^{226} + \)\(44\!\cdots\!18\)\( T_{2}^{225} - \)\(11\!\cdots\!90\)\( T_{2}^{224} + \)\(21\!\cdots\!95\)\( T_{2}^{223} + \)\(19\!\cdots\!22\)\( T_{2}^{222} - \)\(91\!\cdots\!78\)\( T_{2}^{221} - \)\(98\!\cdots\!56\)\( T_{2}^{220} + \)\(38\!\cdots\!35\)\( T_{2}^{219} + \)\(11\!\cdots\!60\)\( T_{2}^{218} - \)\(31\!\cdots\!23\)\( T_{2}^{217} + \)\(13\!\cdots\!57\)\( T_{2}^{216} - \)\(42\!\cdots\!27\)\( T_{2}^{215} - \)\(90\!\cdots\!30\)\( T_{2}^{214} + \)\(23\!\cdots\!95\)\( T_{2}^{213} + \)\(24\!\cdots\!40\)\( T_{2}^{212} - \)\(45\!\cdots\!81\)\( T_{2}^{211} + \)\(26\!\cdots\!21\)\( T_{2}^{210} - \)\(11\!\cdots\!26\)\( T_{2}^{209} - \)\(51\!\cdots\!13\)\( T_{2}^{208} + \)\(11\!\cdots\!58\)\( T_{2}^{207} + \)\(20\!\cdots\!45\)\( T_{2}^{206} - \)\(37\!\cdots\!72\)\( T_{2}^{205} - \)\(16\!\cdots\!44\)\( T_{2}^{204} + \)\(28\!\cdots\!19\)\( T_{2}^{203} - \)\(25\!\cdots\!00\)\( T_{2}^{202} + \)\(34\!\cdots\!43\)\( T_{2}^{201} + \)\(15\!\cdots\!43\)\( T_{2}^{200} - \)\(18\!\cdots\!99\)\( T_{2}^{199} - \)\(39\!\cdots\!80\)\( T_{2}^{198} + \)\(41\!\cdots\!95\)\( T_{2}^{197} - \)\(13\!\cdots\!67\)\( T_{2}^{196} - \)\(17\!\cdots\!33\)\( T_{2}^{195} + \)\(62\!\cdots\!34\)\( T_{2}^{194} - \)\(14\!\cdots\!15\)\( T_{2}^{193} - \)\(28\!\cdots\!74\)\( T_{2}^{192} - \)\(38\!\cdots\!24\)\( T_{2}^{191} + \)\(55\!\cdots\!87\)\( T_{2}^{190} + \)\(32\!\cdots\!52\)\( T_{2}^{189} + \)\(72\!\cdots\!36\)\( T_{2}^{188} + \)\(19\!\cdots\!94\)\( T_{2}^{187} - \)\(78\!\cdots\!09\)\( T_{2}^{186} - \)\(80\!\cdots\!78\)\( T_{2}^{185} + \)\(19\!\cdots\!54\)\( T_{2}^{184} + \)\(33\!\cdots\!95\)\( T_{2}^{183} + \)\(58\!\cdots\!43\)\( T_{2}^{182} - \)\(36\!\cdots\!44\)\( T_{2}^{181} - \)\(15\!\cdots\!16\)\( T_{2}^{180} - \)\(20\!\cdots\!28\)\( T_{2}^{179} + \)\(29\!\cdots\!69\)\( T_{2}^{178} + \)\(94\!\cdots\!80\)\( T_{2}^{177} + \)\(57\!\cdots\!37\)\( T_{2}^{176} - \)\(10\!\cdots\!30\)\( T_{2}^{175} - \)\(38\!\cdots\!90\)\( T_{2}^{174} - \)\(45\!\cdots\!83\)\( T_{2}^{173} + \)\(59\!\cdots\!06\)\( T_{2}^{172} + \)\(21\!\cdots\!68\)\( T_{2}^{171} + \)\(12\!\cdots\!27\)\( T_{2}^{170} - \)\(31\!\cdots\!64\)\( T_{2}^{169} - \)\(82\!\cdots\!57\)\( T_{2}^{168} - \)\(54\!\cdots\!09\)\( T_{2}^{167} + \)\(17\!\cdots\!15\)\( T_{2}^{166} + \)\(39\!\cdots\!80\)\( T_{2}^{165} - \)\(90\!\cdots\!15\)\( T_{2}^{164} - \)\(95\!\cdots\!16\)\( T_{2}^{163} - \)\(11\!\cdots\!07\)\( T_{2}^{162} + \)\(63\!\cdots\!04\)\( T_{2}^{161} + \)\(36\!\cdots\!92\)\( T_{2}^{160} + \)\(37\!\cdots\!47\)\( T_{2}^{159} - \)\(48\!\cdots\!98\)\( T_{2}^{158} - \)\(15\!\cdots\!19\)\( T_{2}^{157} - \)\(71\!\cdots\!91\)\( T_{2}^{156} + \)\(23\!\cdots\!54\)\( T_{2}^{155} + \)\(48\!\cdots\!84\)\( T_{2}^{154} + \)\(18\!\cdots\!04\)\( T_{2}^{153} - \)\(91\!\cdots\!49\)\( T_{2}^{152} - \)\(17\!\cdots\!90\)\( T_{2}^{151} - \)\(25\!\cdots\!63\)\( T_{2}^{150} + \)\(34\!\cdots\!76\)\( T_{2}^{149} + \)\(55\!\cdots\!07\)\( T_{2}^{148} + \)\(47\!\cdots\!62\)\( T_{2}^{147} - \)\(12\!\cdots\!50\)\( T_{2}^{146} - \)\(18\!\cdots\!81\)\( T_{2}^{145} + \)\(44\!\cdots\!77\)\( T_{2}^{144} + \)\(43\!\cdots\!86\)\( T_{2}^{143} + \)\(44\!\cdots\!49\)\( T_{2}^{142} - \)\(24\!\cdots\!22\)\( T_{2}^{141} - \)\(11\!\cdots\!28\)\( T_{2}^{140} - \)\(11\!\cdots\!68\)\( T_{2}^{139} + \)\(68\!\cdots\!53\)\( T_{2}^{138} + \)\(28\!\cdots\!40\)\( T_{2}^{137} + \)\(26\!\cdots\!90\)\( T_{2}^{136} - \)\(10\!\cdots\!82\)\( T_{2}^{135} - \)\(67\!\cdots\!78\)\( T_{2}^{134} - \)\(84\!\cdots\!27\)\( T_{2}^{133} + \)\(25\!\cdots\!47\)\( T_{2}^{132} + \)\(19\!\cdots\!54\)\( T_{2}^{131} + \)\(18\!\cdots\!10\)\( T_{2}^{130} - \)\(10\!\cdots\!73\)\( T_{2}^{129} - \)\(43\!\cdots\!55\)\( T_{2}^{128} - \)\(40\!\cdots\!87\)\( T_{2}^{127} + \)\(28\!\cdots\!01\)\( T_{2}^{126} + \)\(95\!\cdots\!27\)\( T_{2}^{125} + \)\(60\!\cdots\!09\)\( T_{2}^{124} - \)\(53\!\cdots\!88\)\( T_{2}^{123} - \)\(15\!\cdots\!26\)\( T_{2}^{122} - \)\(14\!\cdots\!45\)\( T_{2}^{121} + \)\(84\!\cdots\!25\)\( T_{2}^{120} + \)\(33\!\cdots\!82\)\( T_{2}^{119} + \)\(24\!\cdots\!76\)\( T_{2}^{118} - \)\(15\!\cdots\!84\)\( T_{2}^{117} - \)\(60\!\cdots\!60\)\( T_{2}^{116} - \)\(54\!\cdots\!21\)\( T_{2}^{115} + \)\(52\!\cdots\!71\)\( T_{2}^{114} + \)\(13\!\cdots\!80\)\( T_{2}^{113} + \)\(27\!\cdots\!04\)\( T_{2}^{112} - \)\(14\!\cdots\!21\)\( T_{2}^{111} - \)\(15\!\cdots\!89\)\( T_{2}^{110} + \)\(33\!\cdots\!78\)\( T_{2}^{109} + \)\(26\!\cdots\!69\)\( T_{2}^{108} + \)\(15\!\cdots\!05\)\( T_{2}^{107} - \)\(27\!\cdots\!44\)\( T_{2}^{106} - \)\(31\!\cdots\!94\)\( T_{2}^{105} + \)\(11\!\cdots\!10\)\( T_{2}^{104} + \)\(33\!\cdots\!26\)\( T_{2}^{103} + \)\(19\!\cdots\!60\)\( T_{2}^{102} - \)\(22\!\cdots\!20\)\( T_{2}^{101} - \)\(47\!\cdots\!50\)\( T_{2}^{100} + \)\(61\!\cdots\!82\)\( T_{2}^{99} + \)\(50\!\cdots\!28\)\( T_{2}^{98} + \)\(64\!\cdots\!97\)\( T_{2}^{97} - \)\(23\!\cdots\!18\)\( T_{2}^{96} - \)\(11\!\cdots\!65\)\( T_{2}^{95} - \)\(99\!\cdots\!11\)\( T_{2}^{94} + \)\(14\!\cdots\!24\)\( T_{2}^{93} + \)\(19\!\cdots\!87\)\( T_{2}^{92} - \)\(16\!\cdots\!96\)\( T_{2}^{91} + \)\(34\!\cdots\!18\)\( T_{2}^{90} + \)\(11\!\cdots\!73\)\( T_{2}^{89} - \)\(30\!\cdots\!01\)\( T_{2}^{88} + \)\(54\!\cdots\!36\)\( T_{2}^{87} + \)\(30\!\cdots\!22\)\( T_{2}^{86} - \)\(25\!\cdots\!55\)\( T_{2}^{85} - \)\(25\!\cdots\!09\)\( T_{2}^{84} + \)\(32\!\cdots\!84\)\( T_{2}^{83} - \)\(28\!\cdots\!06\)\( T_{2}^{82} - \)\(20\!\cdots\!20\)\( T_{2}^{81} + \)\(39\!\cdots\!23\)\( T_{2}^{80} + \)\(17\!\cdots\!99\)\( T_{2}^{79} - \)\(28\!\cdots\!41\)\( T_{2}^{78} + \)\(10\!\cdots\!48\)\( T_{2}^{77} + \)\(10\!\cdots\!17\)\( T_{2}^{76} - \)\(11\!\cdots\!66\)\( T_{2}^{75} + \)\(21\!\cdots\!44\)\( T_{2}^{74} + \)\(58\!\cdots\!54\)\( T_{2}^{73} - \)\(56\!\cdots\!87\)\( T_{2}^{72} - \)\(15\!\cdots\!72\)\( T_{2}^{71} + \)\(41\!\cdots\!07\)\( T_{2}^{70} + \)\(88\!\cdots\!52\)\( T_{2}^{69} - \)\(18\!\cdots\!38\)\( T_{2}^{68} + \)\(27\!\cdots\!81\)\( T_{2}^{67} + \)\(60\!\cdots\!77\)\( T_{2}^{66} + \)\(40\!\cdots\!90\)\( T_{2}^{65} - \)\(19\!\cdots\!16\)\( T_{2}^{64} - \)\(38\!\cdots\!07\)\( T_{2}^{63} + \)\(79\!\cdots\!19\)\( T_{2}^{62} + \)\(11\!\cdots\!63\)\( T_{2}^{61} - \)\(30\!\cdots\!81\)\( T_{2}^{60} + \)\(80\!\cdots\!82\)\( T_{2}^{59} + \)\(10\!\cdots\!39\)\( T_{2}^{58} - \)\(20\!\cdots\!56\)\( T_{2}^{57} - \)\(33\!\cdots\!55\)\( T_{2}^{56} + \)\(16\!\cdots\!47\)\( T_{2}^{55} + \)\(71\!\cdots\!20\)\( T_{2}^{54} - \)\(91\!\cdots\!64\)\( T_{2}^{53} + \)\(10\!\cdots\!50\)\( T_{2}^{52} + \)\(26\!\cdots\!21\)\( T_{2}^{51} - \)\(17\!\cdots\!75\)\( T_{2}^{50} - \)\(74\!\cdots\!67\)\( T_{2}^{49} + \)\(60\!\cdots\!71\)\( T_{2}^{48} - \)\(22\!\cdots\!01\)\( T_{2}^{47} - \)\(66\!\cdots\!39\)\( T_{2}^{46} + \)\(78\!\cdots\!26\)\( T_{2}^{45} - \)\(14\!\cdots\!78\)\( T_{2}^{44} - \)\(10\!\cdots\!31\)\( T_{2}^{43} + \)\(65\!\cdots\!96\)\( T_{2}^{42} - \)\(10\!\cdots\!86\)\( T_{2}^{41} - \)\(11\!\cdots\!47\)\( T_{2}^{40} + \)\(33\!\cdots\!54\)\( T_{2}^{39} + \)\(18\!\cdots\!40\)\( T_{2}^{38} - \)\(11\!\cdots\!59\)\( T_{2}^{37} - \)\(17\!\cdots\!48\)\( T_{2}^{36} + \)\(27\!\cdots\!09\)\( T_{2}^{35} - \)\(62\!\cdots\!16\)\( T_{2}^{34} - \)\(36\!\cdots\!93\)\( T_{2}^{33} + \)\(23\!\cdots\!59\)\( T_{2}^{32} - \)\(27\!\cdots\!27\)\( T_{2}^{31} - \)\(26\!\cdots\!94\)\( T_{2}^{30} + \)\(13\!\cdots\!39\)\( T_{2}^{29} - \)\(13\!\cdots\!49\)\( T_{2}^{28} - \)\(82\!\cdots\!33\)\( T_{2}^{27} + \)\(46\!\cdots\!59\)\( T_{2}^{26} - \)\(68\!\cdots\!12\)\( T_{2}^{25} - \)\(80\!\cdots\!79\)\( T_{2}^{24} + \)\(85\!\cdots\!91\)\( T_{2}^{23} - \)\(17\!\cdots\!82\)\( T_{2}^{22} + \)\(10\!\cdots\!77\)\( T_{2}^{21} + \)\(81\!\cdots\!18\)\( T_{2}^{20} - \)\(22\!\cdots\!74\)\( T_{2}^{19} + \)\(31\!\cdots\!70\)\( T_{2}^{18} + \)\(27\!\cdots\!36\)\( T_{2}^{17} - \)\(12\!\cdots\!65\)\( T_{2}^{16} + \)\(27\!\cdots\!08\)\( T_{2}^{15} - \)\(23\!\cdots\!73\)\( T_{2}^{14} - \)\(38\!\cdots\!64\)\( T_{2}^{13} + \)\(12\!\cdots\!27\)\( T_{2}^{12} - \)\(22\!\cdots\!24\)\( T_{2}^{11} - \)\(30\!\cdots\!43\)\( T_{2}^{10} + \)\(35\!\cdots\!81\)\( T_{2}^{9} + \)\(53\!\cdots\!89\)\( T_{2}^{8} + \)\(15\!\cdots\!22\)\( T_{2}^{7} + \)\(66\!\cdots\!50\)\( T_{2}^{6} + \)\(40\!\cdots\!55\)\( T_{2}^{5} + \)\(83\!\cdots\!32\)\( T_{2}^{4} + \)\(50\!\cdots\!36\)\( T_{2}^{3} + \)\(14\!\cdots\!53\)\( T_{2}^{2} + \)\(95\!\cdots\!06\)\( T_{2} + \)\(15\!\cdots\!01\)\( \)">\(T_{2}^{320} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\).