# Properties

 Label 966.2.be.b Level $966$ Weight $2$ Character orbit 966.be Analytic conductor $7.714$ Analytic rank $0$ Dimension $320$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.be (of order $$66$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.71354883526$$ Analytic rank: $$0$$ Dimension: $$320$$ Relative dimension: $$16$$ over $$\Q(\zeta_{66})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$320q + 16q^{2} + 16q^{4} - 32q^{8} - 16q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$320q + 16q^{2} + 16q^{4} - 32q^{8} - 16q^{9} + 22q^{14} + 16q^{16} - 66q^{17} - 16q^{18} + 36q^{23} + 24q^{25} + 12q^{26} + 44q^{28} + 8q^{29} - 48q^{31} + 16q^{32} - 46q^{35} + 32q^{36} - 22q^{37} + 66q^{38} + 8q^{39} + 176q^{43} - 8q^{46} + 120q^{47} - 24q^{49} - 48q^{50} - 22q^{51} - 12q^{52} - 44q^{53} + 44q^{57} + 18q^{58} + 12q^{59} - 32q^{64} - 108q^{70} - 48q^{71} - 16q^{72} + 252q^{73} + 22q^{74} - 36q^{75} - 42q^{77} - 16q^{78} + 44q^{79} + 16q^{81} + 12q^{82} - 22q^{84} - 76q^{85} + 22q^{86} + 24q^{87} - 22q^{88} + 16q^{92} + 12q^{94} + 26q^{95} + 2q^{98} + 88q^{99} + O(q^{100})$$

## Embeddings

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.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
19.1 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −2.88028 + 1.48489i 0.755750 0.654861i −2.06769 + 1.65065i −0.959493 0.281733i −0.0475819 0.998867i 3.00838 1.20438i
19.2 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −2.11320 + 1.08943i 0.755750 0.654861i 0.852549 2.50463i −0.959493 0.281733i −0.0475819 0.998867i 2.20719 0.883624i
19.3 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −1.73698 + 0.895474i 0.755750 0.654861i 0.815740 + 2.51686i −0.959493 0.281733i −0.0475819 0.998867i 1.81423 0.726309i
19.4 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −1.35389 + 0.697977i 0.755750 0.654861i −2.16100 + 1.52646i −0.959493 0.281733i −0.0475819 0.998867i 1.41410 0.566121i
19.5 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 0.157815 0.0813595i 0.755750 0.654861i −1.34398 2.27897i −0.959493 0.281733i −0.0475819 0.998867i −0.164835 + 0.0659898i
19.6 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 0.505673 0.260692i 0.755750 0.654861i 2.07574 1.64052i −0.959493 0.281733i −0.0475819 0.998867i −0.528163 + 0.211445i
19.7 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 2.27295 1.17179i 0.755750 0.654861i 2.41464 + 1.08144i −0.959493 0.281733i −0.0475819 0.998867i −2.37404 + 0.950422i
19.8 −0.995472 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 2.93697 1.51411i 0.755750 0.654861i −2.06506 1.65394i −0.959493 0.281733i −0.0475819 0.998867i −3.06760 + 1.22808i
19.9 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −3.62091 + 1.86671i −0.755750 + 0.654861i −2.61175 0.422774i −0.959493 0.281733i −0.0475819 0.998867i 3.78196 1.51407i
19.10 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −2.00286 + 1.03255i −0.755750 + 0.654861i 1.87452 1.86713i −0.959493 0.281733i −0.0475819 0.998867i 2.09194 0.837488i
19.11 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −1.84849 + 0.952964i −0.755750 + 0.654861i 1.16229 + 2.37678i −0.959493 0.281733i −0.0475819 0.998867i 1.93071 0.772938i
19.12 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −0.0836058 + 0.0431018i −0.755750 + 0.654861i −1.37599 2.25979i −0.959493 0.281733i −0.0475819 0.998867i 0.0873243 0.0349594i
19.13 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 0.0713145 0.0367652i −0.755750 + 0.654861i −2.59984 0.490747i −0.959493 0.281733i −0.0475819 0.998867i −0.0744863 + 0.0298198i
19.14 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 0.951099 0.490326i −0.755750 + 0.654861i 1.44395 + 2.21698i −0.959493 0.281733i −0.0475819 0.998867i −0.993401 + 0.397698i
19.15 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 3.08964 1.59282i −0.755750 + 0.654861i 1.21125 2.35221i −0.959493 0.281733i −0.0475819 0.998867i −3.22705 + 1.29192i
19.16 −0.995472 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 3.91984 2.02082i −0.755750 + 0.654861i −0.423103 + 2.61170i −0.959493 0.281733i −0.0475819 0.998867i −4.09418 + 1.63906i
61.1 −0.786053 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −2.69832 + 0.520058i 0.281733 + 0.959493i 1.79038 1.94796i 0.415415 0.909632i 0.327068 + 0.945001i 2.44250 + 1.25920i
61.2 −0.786053 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −2.30347 + 0.443957i 0.281733 + 0.959493i −2.21609 + 1.44532i 0.415415 0.909632i 0.327068 + 0.945001i 2.08508 + 1.07494i
61.3 −0.786053 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −2.22749 + 0.429313i 0.281733 + 0.959493i −1.35585 2.27193i 0.415415 0.909632i 0.327068 + 0.945001i 2.01631 + 1.03948i
61.4 −0.786053 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i 1.21776 0.234705i 0.281733 + 0.959493i −1.70399 2.02396i 0.415415 0.909632i 0.327068 + 0.945001i −1.10231 0.568281i
See next 80 embeddings (of 320 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 871.16 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner
23.d odd 22 1 inner
161.o even 66 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 966.2.be.b 320
7.d odd 6 1 inner 966.2.be.b 320
23.d odd 22 1 inner 966.2.be.b 320
161.o even 66 1 inner 966.2.be.b 320

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.2.be.b 320 1.a even 1 1 trivial
966.2.be.b 320 7.d odd 6 1 inner
966.2.be.b 320 23.d odd 22 1 inner
966.2.be.b 320 161.o even 66 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$17\!\cdots\!04$$$$T_{5}^{302} -$$$$57\!\cdots\!70$$$$T_{5}^{301} +$$$$39\!\cdots\!63$$$$T_{5}^{300} -$$$$11\!\cdots\!72$$$$T_{5}^{299} -$$$$41\!\cdots\!67$$$$T_{5}^{298} +$$$$20\!\cdots\!08$$$$T_{5}^{297} +$$$$15\!\cdots\!79$$$$T_{5}^{296} -$$$$39\!\cdots\!72$$$$T_{5}^{295} +$$$$19\!\cdots\!02$$$$T_{5}^{294} +$$$$16\!\cdots\!40$$$$T_{5}^{293} -$$$$56\!\cdots\!82$$$$T_{5}^{292} +$$$$53\!\cdots\!54$$$$T_{5}^{291} +$$$$73\!\cdots\!10$$$$T_{5}^{290} -$$$$62\!\cdots\!78$$$$T_{5}^{289} +$$$$90\!\cdots\!03$$$$T_{5}^{288} -$$$$14\!\cdots\!78$$$$T_{5}^{287} -$$$$47\!\cdots\!65$$$$T_{5}^{286} +$$$$50\!\cdots\!92$$$$T_{5}^{285} +$$$$20\!\cdots\!35$$$$T_{5}^{284} -$$$$63\!\cdots\!92$$$$T_{5}^{283} +$$$$24\!\cdots\!50$$$$T_{5}^{282} +$$$$10\!\cdots\!62$$$$T_{5}^{281} -$$$$71\!\cdots\!46$$$$T_{5}^{280} +$$$$12\!\cdots\!12$$$$T_{5}^{279} +$$$$84\!\cdots\!65$$$$T_{5}^{278} -$$$$35\!\cdots\!94$$$$T_{5}^{277} +$$$$39\!\cdots\!98$$$$T_{5}^{276} +$$$$54\!\cdots\!32$$$$T_{5}^{275} -$$$$18\!\cdots\!72$$$$T_{5}^{274} -$$$$42\!\cdots\!32$$$$T_{5}^{273} +$$$$34\!\cdots\!61$$$$T_{5}^{272} -$$$$32\!\cdots\!42$$$$T_{5}^{271} -$$$$32\!\cdots\!03$$$$T_{5}^{270} +$$$$14\!\cdots\!48$$$$T_{5}^{269} +$$$$25\!\cdots\!36$$$$T_{5}^{268} -$$$$19\!\cdots\!88$$$$T_{5}^{267} +$$$$44\!\cdots\!00$$$$T_{5}^{266} +$$$$10\!\cdots\!10$$$$T_{5}^{265} -$$$$76\!\cdots\!24$$$$T_{5}^{264} +$$$$94\!\cdots\!68$$$$T_{5}^{263} +$$$$59\!\cdots\!37$$$$T_{5}^{262} -$$$$26\!\cdots\!68$$$$T_{5}^{261} +$$$$10\!\cdots\!03$$$$T_{5}^{260} +$$$$25\!\cdots\!64$$$$T_{5}^{259} -$$$$80\!\cdots\!25$$$$T_{5}^{258} -$$$$50\!\cdots\!76$$$$T_{5}^{257} +$$$$88\!\cdots\!51$$$$T_{5}^{256} -$$$$20\!\cdots\!36$$$$T_{5}^{255} -$$$$20\!\cdots\!82$$$$T_{5}^{254} +$$$$29\!\cdots\!18$$$$T_{5}^{253} -$$$$60\!\cdots\!91$$$$T_{5}^{252} -$$$$13\!\cdots\!84$$$$T_{5}^{251} +$$$$82\!\cdots\!47$$$$T_{5}^{250} -$$$$14\!\cdots\!10$$$$T_{5}^{249} -$$$$34\!\cdots\!51$$$$T_{5}^{248} +$$$$27\!\cdots\!20$$$$T_{5}^{247} -$$$$36\!\cdots\!80$$$$T_{5}^{246} -$$$$14\!\cdots\!12$$$$T_{5}^{245} +$$$$70\!\cdots\!67$$$$T_{5}^{244} -$$$$69\!\cdots\!72$$$$T_{5}^{243} -$$$$41\!\cdots\!38$$$$T_{5}^{242} +$$$$17\!\cdots\!48$$$$T_{5}^{241} -$$$$18\!\cdots\!19$$$$T_{5}^{240} -$$$$12\!\cdots\!70$$$$T_{5}^{239} +$$$$45\!\cdots\!06$$$$T_{5}^{238} -$$$$35\!\cdots\!96$$$$T_{5}^{237} -$$$$22\!\cdots\!91$$$$T_{5}^{236} +$$$$87\!\cdots\!50$$$$T_{5}^{235} -$$$$11\!\cdots\!48$$$$T_{5}^{234} -$$$$67\!\cdots\!36$$$$T_{5}^{233} +$$$$22\!\cdots\!20$$$$T_{5}^{232} -$$$$63\!\cdots\!46$$$$T_{5}^{231} -$$$$11\!\cdots\!11$$$$T_{5}^{230} +$$$$41\!\cdots\!06$$$$T_{5}^{229} -$$$$55\!\cdots\!71$$$$T_{5}^{228} -$$$$28\!\cdots\!30$$$$T_{5}^{227} +$$$$14\!\cdots\!54$$$$T_{5}^{226} +$$$$11\!\cdots\!10$$$$T_{5}^{225} -$$$$74\!\cdots\!50$$$$T_{5}^{224} +$$$$13\!\cdots\!02$$$$T_{5}^{223} -$$$$24\!\cdots\!76$$$$T_{5}^{222} -$$$$10\!\cdots\!92$$$$T_{5}^{221} +$$$$29\!\cdots\!25$$$$T_{5}^{220} +$$$$24\!\cdots\!36$$$$T_{5}^{219} -$$$$68\!\cdots\!71$$$$T_{5}^{218} +$$$$50\!\cdots\!22$$$$T_{5}^{217} -$$$$44\!\cdots\!64$$$$T_{5}^{216} -$$$$12\!\cdots\!92$$$$T_{5}^{215} +$$$$29\!\cdots\!17$$$$T_{5}^{214} +$$$$35\!\cdots\!62$$$$T_{5}^{213} -$$$$26\!\cdots\!49$$$$T_{5}^{212} -$$$$71\!\cdots\!66$$$$T_{5}^{211} -$$$$23\!\cdots\!89$$$$T_{5}^{210} +$$$$28\!\cdots\!92$$$$T_{5}^{209} +$$$$10\!\cdots\!55$$$$T_{5}^{208} -$$$$16\!\cdots\!22$$$$T_{5}^{207} -$$$$83\!\cdots\!38$$$$T_{5}^{206} -$$$$29\!\cdots\!84$$$$T_{5}^{205} +$$$$65\!\cdots\!13$$$$T_{5}^{204} +$$$$17\!\cdots\!30$$$$T_{5}^{203} +$$$$13\!\cdots\!81$$$$T_{5}^{202} -$$$$10\!\cdots\!00$$$$T_{5}^{201} -$$$$50\!\cdots\!17$$$$T_{5}^{200} -$$$$60\!\cdots\!88$$$$T_{5}^{199} +$$$$14\!\cdots\!92$$$$T_{5}^{198} +$$$$60\!\cdots\!46$$$$T_{5}^{197} +$$$$97\!\cdots\!72$$$$T_{5}^{196} -$$$$92\!\cdots\!72$$$$T_{5}^{195} -$$$$96\!\cdots\!82$$$$T_{5}^{194} -$$$$76\!\cdots\!86$$$$T_{5}^{193} +$$$$74\!\cdots\!33$$$$T_{5}^{192} +$$$$20\!\cdots\!34$$$$T_{5}^{191} -$$$$16\!\cdots\!79$$$$T_{5}^{190} -$$$$22\!\cdots\!66$$$$T_{5}^{189} -$$$$51\!\cdots\!92$$$$T_{5}^{188} +$$$$40\!\cdots\!16$$$$T_{5}^{187} +$$$$49\!\cdots\!82$$$$T_{5}^{186} +$$$$97\!\cdots\!32$$$$T_{5}^{185} -$$$$80\!\cdots\!19$$$$T_{5}^{184} -$$$$82\!\cdots\!44$$$$T_{5}^{183} -$$$$14\!\cdots\!99$$$$T_{5}^{182} +$$$$21\!\cdots\!46$$$$T_{5}^{181} +$$$$15\!\cdots\!96$$$$T_{5}^{180} +$$$$23\!\cdots\!54$$$$T_{5}^{179} -$$$$54\!\cdots\!68$$$$T_{5}^{178} -$$$$33\!\cdots\!96$$$$T_{5}^{177} -$$$$56\!\cdots\!61$$$$T_{5}^{176} +$$$$82\!\cdots\!28$$$$T_{5}^{175} +$$$$66\!\cdots\!14$$$$T_{5}^{174} +$$$$13\!\cdots\!18$$$$T_{5}^{173} -$$$$70\!\cdots\!86$$$$T_{5}^{172} -$$$$10\!\cdots\!74$$$$T_{5}^{171} -$$$$25\!\cdots\!13$$$$T_{5}^{170} -$$$$17\!\cdots\!26$$$$T_{5}^{169} +$$$$15\!\cdots\!07$$$$T_{5}^{168} +$$$$41\!\cdots\!56$$$$T_{5}^{167} +$$$$21\!\cdots\!70$$$$T_{5}^{166} -$$$$19\!\cdots\!06$$$$T_{5}^{165} -$$$$65\!\cdots\!97$$$$T_{5}^{164} -$$$$64\!\cdots\!56$$$$T_{5}^{163} +$$$$20\!\cdots\!27$$$$T_{5}^{162} +$$$$95\!\cdots\!32$$$$T_{5}^{161} +$$$$14\!\cdots\!96$$$$T_{5}^{160} -$$$$12\!\cdots\!84$$$$T_{5}^{159} -$$$$11\!\cdots\!49$$$$T_{5}^{158} -$$$$23\!\cdots\!38$$$$T_{5}^{157} -$$$$71\!\cdots\!07$$$$T_{5}^{156} +$$$$90\!\cdots\!06$$$$T_{5}^{155} +$$$$25\!\cdots\!04$$$$T_{5}^{154} +$$$$25\!\cdots\!30$$$$T_{5}^{153} -$$$$45\!\cdots\!41$$$$T_{5}^{152} -$$$$20\!\cdots\!44$$$$T_{5}^{151} -$$$$29\!\cdots\!01$$$$T_{5}^{150} +$$$$11\!\cdots\!78$$$$T_{5}^{149} +$$$$13\!\cdots\!60$$$$T_{5}^{148} +$$$$25\!\cdots\!00$$$$T_{5}^{147} +$$$$59\!\cdots\!02$$$$T_{5}^{146} -$$$$80\!\cdots\!76$$$$T_{5}^{145} -$$$$19\!\cdots\!64$$$$T_{5}^{144} -$$$$11\!\cdots\!12$$$$T_{5}^{143} +$$$$44\!\cdots\!09$$$$T_{5}^{142} +$$$$12\!\cdots\!90$$$$T_{5}^{141} +$$$$10\!\cdots\!92$$$$T_{5}^{140} -$$$$21\!\cdots\!60$$$$T_{5}^{139} -$$$$72\!\cdots\!73$$$$T_{5}^{138} -$$$$66\!\cdots\!80$$$$T_{5}^{137} +$$$$99\!\cdots\!79$$$$T_{5}^{136} +$$$$36\!\cdots\!94$$$$T_{5}^{135} +$$$$33\!\cdots\!90$$$$T_{5}^{134} -$$$$38\!\cdots\!86$$$$T_{5}^{133} -$$$$13\!\cdots\!22$$$$T_{5}^{132} -$$$$10\!\cdots\!50$$$$T_{5}^{131} +$$$$17\!\cdots\!66$$$$T_{5}^{130} +$$$$51\!\cdots\!06$$$$T_{5}^{129} +$$$$40\!\cdots\!71$$$$T_{5}^{128} -$$$$43\!\cdots\!56$$$$T_{5}^{127} -$$$$13\!\cdots\!09$$$$T_{5}^{126} -$$$$11\!\cdots\!92$$$$T_{5}^{125} +$$$$10\!\cdots\!09$$$$T_{5}^{124} +$$$$38\!\cdots\!50$$$$T_{5}^{123} +$$$$41\!\cdots\!73$$$$T_{5}^{122} -$$$$43\!\cdots\!88$$$$T_{5}^{121} -$$$$77\!\cdots\!97$$$$T_{5}^{120} -$$$$95\!\cdots\!26$$$$T_{5}^{119} +$$$$27\!\cdots\!46$$$$T_{5}^{118} +$$$$23\!\cdots\!20$$$$T_{5}^{117} +$$$$26\!\cdots\!79$$$$T_{5}^{116} -$$$$16\!\cdots\!58$$$$T_{5}^{115} -$$$$82\!\cdots\!08$$$$T_{5}^{114} -$$$$97\!\cdots\!88$$$$T_{5}^{113} -$$$$60\!\cdots\!56$$$$T_{5}^{112} +$$$$13\!\cdots\!76$$$$T_{5}^{111} +$$$$19\!\cdots\!03$$$$T_{5}^{110} +$$$$13\!\cdots\!74$$$$T_{5}^{109} +$$$$50\!\cdots\!12$$$$T_{5}^{108} +$$$$56\!\cdots\!70$$$$T_{5}^{107} +$$$$18\!\cdots\!44$$$$T_{5}^{106} +$$$$28\!\cdots\!36$$$$T_{5}^{105} +$$$$92\!\cdots\!11$$$$T_{5}^{104} -$$$$92\!\cdots\!18$$$$T_{5}^{103} -$$$$20\!\cdots\!65$$$$T_{5}^{102} -$$$$18\!\cdots\!44$$$$T_{5}^{101} +$$$$18\!\cdots\!38$$$$T_{5}^{100} +$$$$22\!\cdots\!16$$$$T_{5}^{99} +$$$$15\!\cdots\!75$$$$T_{5}^{98} -$$$$10\!\cdots\!68$$$$T_{5}^{97} -$$$$90\!\cdots\!61$$$$T_{5}^{96} +$$$$41\!\cdots\!02$$$$T_{5}^{95} +$$$$95\!\cdots\!45$$$$T_{5}^{94} +$$$$80\!\cdots\!72$$$$T_{5}^{93} -$$$$18\!\cdots\!95$$$$T_{5}^{92} -$$$$13\!\cdots\!90$$$$T_{5}^{91} -$$$$17\!\cdots\!82$$$$T_{5}^{90} -$$$$59\!\cdots\!74$$$$T_{5}^{89} +$$$$17\!\cdots\!46$$$$T_{5}^{88} +$$$$31\!\cdots\!76$$$$T_{5}^{87} +$$$$11\!\cdots\!73$$$$T_{5}^{86} -$$$$36\!\cdots\!58$$$$T_{5}^{85} -$$$$63\!\cdots\!68$$$$T_{5}^{84} -$$$$24\!\cdots\!56$$$$T_{5}^{83} +$$$$58\!\cdots\!29$$$$T_{5}^{82} +$$$$94\!\cdots\!14$$$$T_{5}^{81} +$$$$24\!\cdots\!64$$$$T_{5}^{80} -$$$$87\!\cdots\!86$$$$T_{5}^{79} -$$$$10\!\cdots\!84$$$$T_{5}^{78} +$$$$22\!\cdots\!42$$$$T_{5}^{77} +$$$$16\!\cdots\!26$$$$T_{5}^{76} +$$$$16\!\cdots\!88$$$$T_{5}^{75} +$$$$19\!\cdots\!26$$$$T_{5}^{74} -$$$$10\!\cdots\!42$$$$T_{5}^{73} -$$$$74\!\cdots\!86$$$$T_{5}^{72} +$$$$72\!\cdots\!22$$$$T_{5}^{71} +$$$$16\!\cdots\!09$$$$T_{5}^{70} +$$$$10\!\cdots\!56$$$$T_{5}^{69} -$$$$41\!\cdots\!18$$$$T_{5}^{68} -$$$$51\!\cdots\!32$$$$T_{5}^{67} -$$$$10\!\cdots\!38$$$$T_{5}^{66} +$$$$48\!\cdots\!46$$$$T_{5}^{65} +$$$$64\!\cdots\!89$$$$T_{5}^{64} +$$$$40\!\cdots\!28$$$$T_{5}^{63} +$$$$98\!\cdots\!57$$$$T_{5}^{62} -$$$$38\!\cdots\!78$$$$T_{5}^{61} -$$$$29\!\cdots\!32$$$$T_{5}^{60} +$$$$12\!\cdots\!00$$$$T_{5}^{59} +$$$$28\!\cdots\!32$$$$T_{5}^{58} +$$$$18\!\cdots\!62$$$$T_{5}^{57} +$$$$56\!\cdots\!30$$$$T_{5}^{56} -$$$$22\!\cdots\!00$$$$T_{5}^{55} -$$$$73\!\cdots\!65$$$$T_{5}^{54} +$$$$75\!\cdots\!20$$$$T_{5}^{53} +$$$$38\!\cdots\!31$$$$T_{5}^{52} +$$$$24\!\cdots\!98$$$$T_{5}^{51} +$$$$68\!\cdots\!21$$$$T_{5}^{50} +$$$$34\!\cdots\!82$$$$T_{5}^{49} -$$$$61\!\cdots\!37$$$$T_{5}^{48} -$$$$11\!\cdots\!80$$$$T_{5}^{47} +$$$$96\!\cdots\!70$$$$T_{5}^{46} +$$$$95\!\cdots\!10$$$$T_{5}^{45} +$$$$51\!\cdots\!77$$$$T_{5}^{44} +$$$$16\!\cdots\!22$$$$T_{5}^{43} -$$$$83\!\cdots\!58$$$$T_{5}^{42} -$$$$42\!\cdots\!88$$$$T_{5}^{41} -$$$$30\!\cdots\!41$$$$T_{5}^{40} -$$$$15\!\cdots\!78$$$$T_{5}^{39} -$$$$67\!\cdots\!77$$$$T_{5}^{38} -$$$$18\!\cdots\!68$$$$T_{5}^{37} +$$$$60\!\cdots\!38$$$$T_{5}^{36} +$$$$31\!\cdots\!46$$$$T_{5}^{35} +$$$$19\!\cdots\!57$$$$T_{5}^{34} +$$$$76\!\cdots\!14$$$$T_{5}^{33} +$$$$22\!\cdots\!55$$$$T_{5}^{32} +$$$$41\!\cdots\!64$$$$T_{5}^{31} -$$$$17\!\cdots\!94$$$$T_{5}^{30} -$$$$46\!\cdots\!94$$$$T_{5}^{29} -$$$$21\!\cdots\!41$$$$T_{5}^{28} -$$$$70\!\cdots\!36$$$$T_{5}^{27} -$$$$19\!\cdots\!37$$$$T_{5}^{26} -$$$$37\!\cdots\!90$$$$T_{5}^{25} -$$$$12\!\cdots\!47$$$$T_{5}^{24} +$$$$23\!\cdots\!02$$$$T_{5}^{23} +$$$$10\!\cdots\!40$$$$T_{5}^{22} +$$$$26\!\cdots\!78$$$$T_{5}^{21} +$$$$54\!\cdots\!66$$$$T_{5}^{20} +$$$$87\!\cdots\!42$$$$T_{5}^{19} +$$$$85\!\cdots\!67$$$$T_{5}^{18} +$$$$10\!\cdots\!72$$$$T_{5}^{17} +$$$$34\!\cdots\!65$$$$T_{5}^{16} +$$$$84\!\cdots\!38$$$$T_{5}^{15} +$$$$19\!\cdots\!31$$$$T_{5}^{14} +$$$$33\!\cdots\!54$$$$T_{5}^{13} +$$$$53\!\cdots\!27$$$$T_{5}^{12} +$$$$18\!\cdots\!20$$$$T_{5}^{11} +$$$$92\!\cdots\!09$$$$T_{5}^{10} +$$$$50\!\cdots\!52$$$$T_{5}^{9} +$$$$12\!\cdots\!08$$$$T_{5}^{8} +$$$$33\!\cdots\!00$$$$T_{5}^{7} +$$$$59\!\cdots\!32$$$$T_{5}^{6} +$$$$78\!\cdots\!92$$$$T_{5}^{5} +$$$$25\!\cdots\!17$$$$T_{5}^{4} -$$$$24\!\cdots\!00$$$$T_{5}^{3} +$$$$55\!\cdots\!81$$$$T_{5}^{2} -$$$$12\!\cdots\!00$$$$T_{5} +$$$$27\!\cdots\!41$$">$$T_{5}^{320} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(966, [\chi])$$.