# Properties

 Label 966.2.be.a 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.

 $$\operatorname{Tr}(f)(q) =$$ $$320q - 16q^{2} + 16q^{4} + 32q^{8} - 16q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$320q - 16q^{2} + 16q^{4} + 32q^{8} - 16q^{9} - 22q^{14} + 16q^{16} + 66q^{17} + 16q^{18} + 40q^{23} - 48q^{25} + 12q^{26} + 44q^{28} - 24q^{29} + 24q^{31} - 16q^{32} + 98q^{35} + 32q^{36} - 22q^{37} - 66q^{38} - 8q^{39} - 88q^{43} + 4q^{46} - 144q^{47} - 24q^{49} + 80q^{50} - 22q^{51} + 12q^{52} + 44q^{53} + 44q^{57} + 10q^{58} + 12q^{59} - 32q^{64} + 108q^{70} - 16q^{71} + 16q^{72} - 180q^{73} - 22q^{74} - 12q^{75} + 18q^{77} - 16q^{78} + 44q^{79} + 16q^{81} + 36q^{82} + 22q^{84} + 68q^{85} - 22q^{86} + 48q^{87} + 22q^{88} + 8q^{92} + 8q^{93} - 12q^{94} + 66q^{95} - 90q^{98} + O(q^{100})$$

## 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 −3.45344 + 1.78037i −0.755750 + 0.654861i −2.24314 + 1.40298i 0.959493 + 0.281733i −0.0475819 0.998867i −3.60703 + 1.44404i
19.2 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −2.25010 + 1.16001i −0.755750 + 0.654861i 1.37319 2.26149i 0.959493 + 0.281733i −0.0475819 0.998867i −2.35018 + 0.940871i
19.3 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −1.41181 + 0.727837i −0.755750 + 0.654861i 1.71541 + 2.01429i 0.959493 + 0.281733i −0.0475819 0.998867i −1.47460 + 0.590341i
19.4 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i −0.290919 + 0.149979i −0.755750 + 0.654861i −0.738752 2.54052i 0.959493 + 0.281733i −0.0475819 0.998867i −0.303858 + 0.121646i
19.5 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 0.631353 0.325485i −0.755750 + 0.654861i 2.64138 0.152057i 0.959493 + 0.281733i −0.0475819 0.998867i 0.659433 0.263997i
19.6 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 1.05593 0.544372i −0.755750 + 0.654861i −2.51151 + 0.832044i 0.959493 + 0.281733i −0.0475819 0.998867i 1.10290 0.441534i
19.7 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 3.01447 1.55407i −0.755750 + 0.654861i 1.02282 2.44005i 0.959493 + 0.281733i −0.0475819 0.998867i 3.14854 1.26049i
19.8 0.995472 + 0.0950560i −0.690079 + 0.723734i 0.981929 + 0.189251i 3.18053 1.63968i −0.755750 + 0.654861i 1.02341 + 2.43980i 0.959493 + 0.281733i −0.0475819 0.998867i 3.32199 1.32992i
19.9 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −3.73421 + 1.92512i 0.755750 0.654861i −0.120285 2.64302i 0.959493 + 0.281733i −0.0475819 0.998867i −3.90030 + 1.56144i
19.10 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −3.26423 + 1.68283i 0.755750 0.654861i 2.33879 + 1.23696i 0.959493 + 0.281733i −0.0475819 0.998867i −3.40941 + 1.36492i
19.11 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −1.59513 + 0.822347i 0.755750 0.654861i −1.53650 + 2.15387i 0.959493 + 0.281733i −0.0475819 0.998867i −1.66608 + 0.666996i
19.12 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i −0.867285 + 0.447116i 0.755750 0.654861i 2.46361 0.964688i 0.959493 + 0.281733i −0.0475819 0.998867i −0.905859 + 0.362651i
19.13 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 0.525481 0.270904i 0.755750 0.654861i −0.753581 2.53616i 0.959493 + 0.281733i −0.0475819 0.998867i 0.548853 0.219728i
19.14 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 1.83046 0.943666i 0.755750 0.654861i −2.58469 0.565134i 0.959493 + 0.281733i −0.0475819 0.998867i 1.91187 0.765397i
19.15 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 2.34527 1.20907i 0.755750 0.654861i 2.38412 1.14715i 0.959493 + 0.281733i −0.0475819 0.998867i 2.44958 0.980664i
19.16 0.995472 + 0.0950560i 0.690079 0.723734i 0.981929 + 0.189251i 2.54871 1.31395i 0.755750 0.654861i −0.0690376 + 2.64485i 0.959493 + 0.281733i −0.0475819 0.998867i 2.66207 1.06573i
61.1 0.786053 + 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −2.60993 + 0.503023i −0.281733 0.959493i −0.258273 2.63312i −0.415415 + 0.909632i 0.327068 + 0.945001i −2.36249 1.21795i
61.2 0.786053 + 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −2.19052 + 0.422188i −0.281733 0.959493i 1.40168 + 2.24395i −0.415415 + 0.909632i 0.327068 + 0.945001i −1.98285 1.02223i
61.3 0.786053 + 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −1.06718 + 0.205682i −0.281733 0.959493i −1.24125 + 2.33651i −0.415415 + 0.909632i 0.327068 + 0.945001i −0.966005 0.498010i
61.4 0.786053 + 0.618159i −0.814576 0.580057i 0.235759 + 0.971812i −0.436006 + 0.0840333i −0.281733 0.959493i −2.27972 1.34272i −0.415415 + 0.909632i 0.327068 + 0.945001i −0.394670 0.203466i
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.a 320
7.d odd 6 1 inner 966.2.be.a 320
23.d odd 22 1 inner 966.2.be.a 320
161.o even 66 1 inner 966.2.be.a 320

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

## Hecke kernels

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