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 \(12\!\cdots\!53\)\( T_{11}^{146} - \)\(58\!\cdots\!96\)\( T_{11}^{145} + \)\(46\!\cdots\!24\)\( T_{11}^{144} - \)\(22\!\cdots\!34\)\( T_{11}^{143} + \)\(17\!\cdots\!00\)\( T_{11}^{142} - \)\(93\!\cdots\!20\)\( T_{11}^{141} + \)\(67\!\cdots\!69\)\( T_{11}^{140} - \)\(32\!\cdots\!36\)\( T_{11}^{139} + \)\(22\!\cdots\!60\)\( T_{11}^{138} - \)\(10\!\cdots\!30\)\( T_{11}^{137} + \)\(70\!\cdots\!33\)\( T_{11}^{136} - \)\(34\!\cdots\!98\)\( T_{11}^{135} + \)\(22\!\cdots\!11\)\( T_{11}^{134} - \)\(11\!\cdots\!24\)\( T_{11}^{133} + \)\(73\!\cdots\!78\)\( T_{11}^{132} - \)\(37\!\cdots\!18\)\( T_{11}^{131} + \)\(22\!\cdots\!79\)\( T_{11}^{130} - \)\(11\!\cdots\!60\)\( T_{11}^{129} + \)\(67\!\cdots\!11\)\( T_{11}^{128} - \)\(34\!\cdots\!42\)\( T_{11}^{127} + \)\(19\!\cdots\!04\)\( T_{11}^{126} - \)\(94\!\cdots\!26\)\( T_{11}^{125} + \)\(51\!\cdots\!59\)\( T_{11}^{124} - \)\(25\!\cdots\!18\)\( T_{11}^{123} + \)\(13\!\cdots\!68\)\( T_{11}^{122} - \)\(63\!\cdots\!32\)\( T_{11}^{121} + \)\(32\!\cdots\!65\)\( T_{11}^{120} - \)\(15\!\cdots\!40\)\( T_{11}^{119} + \)\(76\!\cdots\!90\)\( T_{11}^{118} - \)\(36\!\cdots\!26\)\( T_{11}^{117} + \)\(18\!\cdots\!88\)\( T_{11}^{116} - \)\(86\!\cdots\!86\)\( T_{11}^{115} + \)\(42\!\cdots\!61\)\( T_{11}^{114} - \)\(20\!\cdots\!76\)\( T_{11}^{113} + \)\(96\!\cdots\!49\)\( T_{11}^{112} - \)\(43\!\cdots\!46\)\( T_{11}^{111} + \)\(19\!\cdots\!69\)\( T_{11}^{110} - \)\(85\!\cdots\!30\)\( T_{11}^{109} + \)\(36\!\cdots\!35\)\( T_{11}^{108} - \)\(14\!\cdots\!32\)\( T_{11}^{107} + \)\(60\!\cdots\!42\)\( T_{11}^{106} - \)\(23\!\cdots\!88\)\( T_{11}^{105} + \)\(90\!\cdots\!90\)\( T_{11}^{104} - \)\(33\!\cdots\!28\)\( T_{11}^{103} + \)\(12\!\cdots\!09\)\( T_{11}^{102} - \)\(41\!\cdots\!74\)\( T_{11}^{101} + \)\(14\!\cdots\!43\)\( T_{11}^{100} - \)\(47\!\cdots\!96\)\( T_{11}^{99} + \)\(15\!\cdots\!94\)\( T_{11}^{98} - \)\(47\!\cdots\!16\)\( T_{11}^{97} + \)\(14\!\cdots\!44\)\( T_{11}^{96} - \)\(42\!\cdots\!48\)\( T_{11}^{95} + \)\(13\!\cdots\!94\)\( T_{11}^{94} - \)\(34\!\cdots\!64\)\( T_{11}^{93} + \)\(10\!\cdots\!53\)\( T_{11}^{92} - \)\(26\!\cdots\!20\)\( T_{11}^{91} + \)\(80\!\cdots\!88\)\( T_{11}^{90} - \)\(18\!\cdots\!48\)\( T_{11}^{89} + \)\(61\!\cdots\!15\)\( T_{11}^{88} - \)\(13\!\cdots\!64\)\( T_{11}^{87} + \)\(51\!\cdots\!46\)\( T_{11}^{86} - \)\(11\!\cdots\!34\)\( T_{11}^{85} + \)\(44\!\cdots\!10\)\( T_{11}^{84} - \)\(94\!\cdots\!30\)\( T_{11}^{83} + \)\(38\!\cdots\!78\)\( T_{11}^{82} - \)\(70\!\cdots\!78\)\( T_{11}^{81} + \)\(26\!\cdots\!90\)\( T_{11}^{80} - \)\(31\!\cdots\!62\)\( T_{11}^{79} + \)\(13\!\cdots\!01\)\( T_{11}^{78} - \)\(24\!\cdots\!78\)\( T_{11}^{77} + \)\(72\!\cdots\!65\)\( T_{11}^{76} - \)\(20\!\cdots\!24\)\( T_{11}^{75} + \)\(75\!\cdots\!90\)\( T_{11}^{74} - \)\(91\!\cdots\!32\)\( T_{11}^{73} + \)\(65\!\cdots\!07\)\( T_{11}^{72} - \)\(65\!\cdots\!56\)\( T_{11}^{71} + \)\(32\!\cdots\!83\)\( T_{11}^{70} - \)\(94\!\cdots\!26\)\( T_{11}^{69} + \)\(11\!\cdots\!38\)\( T_{11}^{68} + \)\(28\!\cdots\!56\)\( T_{11}^{67} + \)\(64\!\cdots\!62\)\( T_{11}^{66} - \)\(54\!\cdots\!86\)\( T_{11}^{65} + \)\(44\!\cdots\!93\)\( T_{11}^{64} - \)\(51\!\cdots\!26\)\( T_{11}^{63} + \)\(20\!\cdots\!52\)\( T_{11}^{62} - \)\(17\!\cdots\!74\)\( T_{11}^{61} + \)\(71\!\cdots\!02\)\( T_{11}^{60} - \)\(93\!\cdots\!22\)\( T_{11}^{59} + \)\(36\!\cdots\!59\)\( T_{11}^{58} - \)\(67\!\cdots\!56\)\( T_{11}^{57} + \)\(19\!\cdots\!35\)\( T_{11}^{56} - \)\(28\!\cdots\!58\)\( T_{11}^{55} + \)\(62\!\cdots\!80\)\( T_{11}^{54} - \)\(79\!\cdots\!56\)\( T_{11}^{53} + \)\(12\!\cdots\!39\)\( T_{11}^{52} - \)\(15\!\cdots\!36\)\( T_{11}^{51} + \)\(49\!\cdots\!54\)\( T_{11}^{50} - \)\(54\!\cdots\!76\)\( T_{11}^{49} + \)\(17\!\cdots\!09\)\( T_{11}^{48} - \)\(31\!\cdots\!68\)\( T_{11}^{47} + \)\(45\!\cdots\!89\)\( T_{11}^{46} - \)\(70\!\cdots\!04\)\( T_{11}^{45} + \)\(17\!\cdots\!13\)\( T_{11}^{44} - \)\(15\!\cdots\!46\)\( T_{11}^{43} + \)\(38\!\cdots\!48\)\( T_{11}^{42} - \)\(77\!\cdots\!50\)\( T_{11}^{41} + \)\(98\!\cdots\!33\)\( T_{11}^{40} - \)\(15\!\cdots\!34\)\( T_{11}^{39} + \)\(28\!\cdots\!03\)\( T_{11}^{38} - \)\(23\!\cdots\!50\)\( T_{11}^{37} + \)\(29\!\cdots\!01\)\( T_{11}^{36} - \)\(37\!\cdots\!40\)\( T_{11}^{35} + \)\(21\!\cdots\!50\)\( T_{11}^{34} - \)\(11\!\cdots\!34\)\( T_{11}^{33} + \)\(27\!\cdots\!28\)\( T_{11}^{32} + \)\(11\!\cdots\!34\)\( T_{11}^{31} + \)\(12\!\cdots\!51\)\( T_{11}^{30} + \)\(49\!\cdots\!98\)\( T_{11}^{29} + \)\(50\!\cdots\!25\)\( T_{11}^{28} + \)\(25\!\cdots\!04\)\( T_{11}^{27} + \)\(11\!\cdots\!17\)\( T_{11}^{26} + \)\(46\!\cdots\!46\)\( T_{11}^{25} + \)\(58\!\cdots\!73\)\( T_{11}^{24} + \)\(26\!\cdots\!24\)\( T_{11}^{23} + \)\(13\!\cdots\!87\)\( T_{11}^{22} + \)\(64\!\cdots\!26\)\( T_{11}^{21} + \)\(29\!\cdots\!01\)\( T_{11}^{20} + \)\(44\!\cdots\!76\)\( T_{11}^{19} + \)\(17\!\cdots\!76\)\( T_{11}^{18} - \)\(12\!\cdots\!80\)\( T_{11}^{17} + \)\(63\!\cdots\!08\)\( T_{11}^{16} - \)\(49\!\cdots\!48\)\( T_{11}^{15} + \)\(10\!\cdots\!80\)\( T_{11}^{14} - \)\(26\!\cdots\!12\)\( T_{11}^{13} + \)\(11\!\cdots\!12\)\( T_{11}^{12} - \)\(11\!\cdots\!36\)\( T_{11}^{11} + \)\(51\!\cdots\!60\)\( T_{11}^{10} - \)\(84\!\cdots\!52\)\( T_{11}^{9} + \)\(73\!\cdots\!64\)\( T_{11}^{8} - \)\(73\!\cdots\!04\)\( T_{11}^{7} + \)\(91\!\cdots\!16\)\( T_{11}^{6} + \)\(39\!\cdots\!04\)\( T_{11}^{5} + \)\(68\!\cdots\!36\)\( T_{11}^{4} + \)\(41\!\cdots\!56\)\( T_{11}^{3} + \)\(91\!\cdots\!24\)\( T_{11}^{2} + \)\(98\!\cdots\!20\)\( T_{11} + \)\(12\!\cdots\!44\)\( \)">\(T_{11}^{160} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(690, [\chi])\).