# Properties

 Label 930.2.bt.a Level $930$ Weight $2$ Character orbit 930.bt Analytic conductor $7.426$ Analytic rank $0$ Dimension $256$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.bt (of order $$60$$, degree $$16$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$256$$ Relative dimension: $$16$$ over $$\Q(\zeta_{60})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$256q + 8q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$256q + 8q^{7} + 4q^{10} - 24q^{14} - 8q^{15} + 64q^{16} + 36q^{17} - 40q^{19} + 12q^{20} - 16q^{21} + 8q^{22} - 32q^{24} + 20q^{25} + 4q^{28} - 16q^{29} - 8q^{31} - 4q^{33} - 24q^{35} + 128q^{36} + 4q^{37} + 4q^{38} + 48q^{41} + 32q^{42} - 24q^{43} + 4q^{44} - 12q^{45} - 20q^{46} - 168q^{47} - 40q^{49} + 48q^{50} - 64q^{53} + 64q^{54} + 64q^{55} + 28q^{57} + 68q^{58} - 24q^{59} + 4q^{62} + 4q^{63} - 60q^{65} + 12q^{66} - 76q^{67} - 4q^{68} + 12q^{69} - 16q^{70} - 48q^{71} + 52q^{73} + 68q^{74} + 48q^{75} + 48q^{76} + 84q^{77} - 56q^{79} - 32q^{81} - 32q^{82} + 136q^{83} + 68q^{85} + 24q^{86} + 20q^{87} + 56q^{88} - 224q^{89} + 40q^{91} - 48q^{93} - 4q^{95} + 8q^{97} + 64q^{98} + 4q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
13.1 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.68012 1.47553i 0.866025 + 0.500000i −1.74433 0.0914165i 0.453990 0.891007i −0.743145 0.669131i 1.72019 1.42861i
13.2 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.65687 + 1.50160i 0.866025 + 0.500000i −2.43455 0.127590i 0.453990 0.891007i −0.743145 0.669131i −1.22392 1.87137i
13.3 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.65366 + 1.50512i 0.866025 + 0.500000i 0.140670 + 0.00737222i 0.453990 0.891007i −0.743145 0.669131i −1.22790 1.86876i
13.4 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.12100 1.93477i 0.866025 + 0.500000i 0.00733325 0.000384319i 0.453990 0.891007i −0.743145 0.669131i 2.08632 0.804537i
13.5 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.57500 1.58726i 0.866025 + 0.500000i 4.42218 + 0.231757i 0.453990 0.891007i −0.743145 0.669131i 1.32133 + 1.80391i
13.6 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.66702 + 1.49031i 0.866025 + 0.500000i 2.09913 + 0.110011i 0.453990 0.891007i −0.743145 0.669131i −1.73274 + 1.41336i
13.7 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i 2.05562 + 0.880016i 0.866025 + 0.500000i −0.216795 0.0113618i 0.453990 0.891007i −0.743145 0.669131i −1.19075 + 1.89265i
13.8 −0.156434 + 0.987688i 0.358368 0.933580i −0.951057 0.309017i 2.21938 + 0.272664i 0.866025 + 0.500000i −4.57122 0.239568i 0.453990 0.891007i −0.743145 0.669131i −0.616494 + 2.14940i
13.9 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −2.21293 0.320863i 0.866025 + 0.500000i −2.17593 0.114036i −0.453990 + 0.891007i −0.743145 0.669131i −0.663091 + 2.13549i
13.10 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.90371 + 1.17298i 0.866025 + 0.500000i 1.91384 + 0.100300i −0.453990 + 0.891007i −0.743145 0.669131i 0.860728 + 2.06377i
13.11 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.16716 1.90728i 0.866025 + 0.500000i 2.78313 + 0.145858i −0.453990 + 0.891007i −0.743145 0.669131i −2.06639 + 0.854429i
13.12 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −0.443582 + 2.19163i 0.866025 + 0.500000i −2.50424 0.131242i −0.453990 + 0.891007i −0.743145 0.669131i 2.09525 + 0.780967i
13.13 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 0.904456 2.04498i 0.866025 + 0.500000i −2.34346 0.122815i −0.453990 + 0.891007i −0.743145 0.669131i −1.87832 1.21323i
13.14 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 1.00881 + 1.99557i 0.866025 + 0.500000i 4.83852 + 0.253576i −0.453990 + 0.891007i −0.743145 0.669131i 2.12882 0.684211i
13.15 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 1.45393 1.69884i 0.866025 + 0.500000i 3.84003 + 0.201247i −0.453990 + 0.891007i −0.743145 0.669131i −1.45048 1.70179i
13.16 0.156434 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 1.76830 + 1.36862i 0.866025 + 0.500000i −0.704223 0.0369068i −0.453990 + 0.891007i −0.743145 0.669131i 1.62840 1.53243i
43.1 −0.987688 + 0.156434i 0.933580 0.358368i 0.951057 0.309017i −1.95765 + 1.08055i −0.866025 + 0.500000i −0.179844 3.43163i −0.891007 + 0.453990i 0.743145 0.669131i 1.76452 1.37349i
43.2 −0.987688 + 0.156434i 0.933580 0.358368i 0.951057 0.309017i −1.92766 + 1.13319i −0.866025 + 0.500000i 0.0854612 + 1.63070i −0.891007 + 0.453990i 0.743145 0.669131i 1.72666 1.42079i
43.3 −0.987688 + 0.156434i 0.933580 0.358368i 0.951057 0.309017i −1.71760 1.43173i −0.866025 + 0.500000i 0.0366609 + 0.699531i −0.891007 + 0.453990i 0.743145 0.669131i 1.92043 + 1.14541i
43.4 −0.987688 + 0.156434i 0.933580 0.358368i 0.951057 0.309017i −0.387188 + 2.20229i −0.866025 + 0.500000i −0.0918879 1.75333i −0.891007 + 0.453990i 0.743145 0.669131i 0.0379066 2.23575i
See next 80 embeddings (of 256 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 823.16 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
155.x even 60 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 930.2.bt.a 256
5.c odd 4 1 930.2.bt.b yes 256
31.h odd 30 1 930.2.bt.b yes 256
155.x even 60 1 inner 930.2.bt.a 256

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.bt.a 256 1.a even 1 1 trivial
930.2.bt.a 256 155.x even 60 1 inner
930.2.bt.b yes 256 5.c odd 4 1
930.2.bt.b yes 256 31.h odd 30 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$16\!\cdots\!70$$$$T_{7}^{240} -$$$$80\!\cdots\!96$$$$T_{7}^{239} +$$$$33\!\cdots\!60$$$$T_{7}^{238} -$$$$10\!\cdots\!40$$$$T_{7}^{237} +$$$$33\!\cdots\!14$$$$T_{7}^{236} -$$$$13\!\cdots\!36$$$$T_{7}^{235} +$$$$36\!\cdots\!40$$$$T_{7}^{234} +$$$$55\!\cdots\!12$$$$T_{7}^{233} -$$$$10\!\cdots\!17$$$$T_{7}^{232} +$$$$71\!\cdots\!36$$$$T_{7}^{231} -$$$$42\!\cdots\!14$$$$T_{7}^{230} +$$$$25\!\cdots\!08$$$$T_{7}^{229} -$$$$14\!\cdots\!89$$$$T_{7}^{228} +$$$$73\!\cdots\!96$$$$T_{7}^{227} -$$$$35\!\cdots\!70$$$$T_{7}^{226} +$$$$16\!\cdots\!72$$$$T_{7}^{225} -$$$$74\!\cdots\!54$$$$T_{7}^{224} +$$$$33\!\cdots\!24$$$$T_{7}^{223} -$$$$14\!\cdots\!42$$$$T_{7}^{222} +$$$$55\!\cdots\!32$$$$T_{7}^{221} -$$$$21\!\cdots\!87$$$$T_{7}^{220} +$$$$80\!\cdots\!68$$$$T_{7}^{219} -$$$$27\!\cdots\!94$$$$T_{7}^{218} +$$$$71\!\cdots\!16$$$$T_{7}^{217} -$$$$96\!\cdots\!09$$$$T_{7}^{216} -$$$$46\!\cdots\!04$$$$T_{7}^{215} +$$$$60\!\cdots\!38$$$$T_{7}^{214} -$$$$44\!\cdots\!00$$$$T_{7}^{213} +$$$$27\!\cdots\!45$$$$T_{7}^{212} -$$$$15\!\cdots\!40$$$$T_{7}^{211} +$$$$77\!\cdots\!26$$$$T_{7}^{210} -$$$$38\!\cdots\!40$$$$T_{7}^{209} +$$$$18\!\cdots\!52$$$$T_{7}^{208} -$$$$86\!\cdots\!84$$$$T_{7}^{207} +$$$$39\!\cdots\!86$$$$T_{7}^{206} -$$$$17\!\cdots\!60$$$$T_{7}^{205} +$$$$76\!\cdots\!95$$$$T_{7}^{204} -$$$$32\!\cdots\!08$$$$T_{7}^{203} +$$$$13\!\cdots\!76$$$$T_{7}^{202} -$$$$57\!\cdots\!56$$$$T_{7}^{201} +$$$$23\!\cdots\!89$$$$T_{7}^{200} -$$$$95\!\cdots\!84$$$$T_{7}^{199} +$$$$37\!\cdots\!58$$$$T_{7}^{198} -$$$$14\!\cdots\!20$$$$T_{7}^{197} +$$$$57\!\cdots\!37$$$$T_{7}^{196} -$$$$21\!\cdots\!04$$$$T_{7}^{195} +$$$$81\!\cdots\!00$$$$T_{7}^{194} -$$$$30\!\cdots\!52$$$$T_{7}^{193} +$$$$11\!\cdots\!90$$$$T_{7}^{192} -$$$$39\!\cdots\!08$$$$T_{7}^{191} +$$$$13\!\cdots\!16$$$$T_{7}^{190} -$$$$48\!\cdots\!20$$$$T_{7}^{189} +$$$$16\!\cdots\!16$$$$T_{7}^{188} -$$$$55\!\cdots\!04$$$$T_{7}^{187} +$$$$17\!\cdots\!80$$$$T_{7}^{186} -$$$$57\!\cdots\!56$$$$T_{7}^{185} +$$$$17\!\cdots\!33$$$$T_{7}^{184} -$$$$52\!\cdots\!24$$$$T_{7}^{183} +$$$$15\!\cdots\!58$$$$T_{7}^{182} -$$$$41\!\cdots\!32$$$$T_{7}^{181} +$$$$10\!\cdots\!47$$$$T_{7}^{180} -$$$$23\!\cdots\!76$$$$T_{7}^{179} +$$$$45\!\cdots\!40$$$$T_{7}^{178} -$$$$43\!\cdots\!16$$$$T_{7}^{177} -$$$$13\!\cdots\!93$$$$T_{7}^{176} +$$$$11\!\cdots\!04$$$$T_{7}^{175} -$$$$56\!\cdots\!98$$$$T_{7}^{174} +$$$$22\!\cdots\!12$$$$T_{7}^{173} -$$$$72\!\cdots\!89$$$$T_{7}^{172} +$$$$23\!\cdots\!68$$$$T_{7}^{171} -$$$$66\!\cdots\!92$$$$T_{7}^{170} +$$$$17\!\cdots\!40$$$$T_{7}^{169} -$$$$39\!\cdots\!57$$$$T_{7}^{168} +$$$$85\!\cdots\!68$$$$T_{7}^{167} -$$$$12\!\cdots\!32$$$$T_{7}^{166} -$$$$17\!\cdots\!36$$$$T_{7}^{165} +$$$$95\!\cdots\!92$$$$T_{7}^{164} -$$$$44\!\cdots\!32$$$$T_{7}^{163} +$$$$18\!\cdots\!32$$$$T_{7}^{162} -$$$$58\!\cdots\!80$$$$T_{7}^{161} +$$$$15\!\cdots\!75$$$$T_{7}^{160} -$$$$39\!\cdots\!56$$$$T_{7}^{159} +$$$$91\!\cdots\!22$$$$T_{7}^{158} -$$$$13\!\cdots\!68$$$$T_{7}^{157} +$$$$85\!\cdots\!85$$$$T_{7}^{156} -$$$$57\!\cdots\!20$$$$T_{7}^{155} -$$$$18\!\cdots\!34$$$$T_{7}^{154} +$$$$10\!\cdots\!00$$$$T_{7}^{153} -$$$$30\!\cdots\!63$$$$T_{7}^{152} +$$$$53\!\cdots\!84$$$$T_{7}^{151} -$$$$13\!\cdots\!98$$$$T_{7}^{150} +$$$$18\!\cdots\!28$$$$T_{7}^{149} -$$$$30\!\cdots\!19$$$$T_{7}^{148} -$$$$34\!\cdots\!12$$$$T_{7}^{147} +$$$$10\!\cdots\!30$$$$T_{7}^{146} -$$$$14\!\cdots\!12$$$$T_{7}^{145} +$$$$40\!\cdots\!58$$$$T_{7}^{144} +$$$$27\!\cdots\!52$$$$T_{7}^{143} -$$$$35\!\cdots\!30$$$$T_{7}^{142} +$$$$62\!\cdots\!32$$$$T_{7}^{141} -$$$$35\!\cdots\!87$$$$T_{7}^{140} +$$$$32\!\cdots\!40$$$$T_{7}^{139} -$$$$47\!\cdots\!84$$$$T_{7}^{138} -$$$$11\!\cdots\!24$$$$T_{7}^{137} +$$$$79\!\cdots\!00$$$$T_{7}^{136} -$$$$14\!\cdots\!48$$$$T_{7}^{135} +$$$$82\!\cdots\!10$$$$T_{7}^{134} -$$$$15\!\cdots\!04$$$$T_{7}^{133} +$$$$12\!\cdots\!81$$$$T_{7}^{132} +$$$$24\!\cdots\!84$$$$T_{7}^{131} +$$$$76\!\cdots\!48$$$$T_{7}^{130} +$$$$46\!\cdots\!04$$$$T_{7}^{129} -$$$$20\!\cdots\!85$$$$T_{7}^{128} +$$$$25\!\cdots\!96$$$$T_{7}^{127} -$$$$18\!\cdots\!60$$$$T_{7}^{126} +$$$$12\!\cdots\!00$$$$T_{7}^{125} -$$$$34\!\cdots\!00$$$$T_{7}^{124} -$$$$36\!\cdots\!24$$$$T_{7}^{123} +$$$$25\!\cdots\!78$$$$T_{7}^{122} -$$$$87\!\cdots\!88$$$$T_{7}^{121} +$$$$12\!\cdots\!23$$$$T_{7}^{120} +$$$$33\!\cdots\!76$$$$T_{7}^{119} -$$$$59\!\cdots\!26$$$$T_{7}^{118} +$$$$56\!\cdots\!40$$$$T_{7}^{117} -$$$$76\!\cdots\!89$$$$T_{7}^{116} +$$$$80\!\cdots\!16$$$$T_{7}^{115} -$$$$17\!\cdots\!92$$$$T_{7}^{114} -$$$$20\!\cdots\!52$$$$T_{7}^{113} +$$$$17\!\cdots\!85$$$$T_{7}^{112} -$$$$26\!\cdots\!52$$$$T_{7}^{111} +$$$$30\!\cdots\!56$$$$T_{7}^{110} +$$$$70\!\cdots\!72$$$$T_{7}^{109} -$$$$19\!\cdots\!64$$$$T_{7}^{108} +$$$$47\!\cdots\!60$$$$T_{7}^{107} -$$$$47\!\cdots\!70$$$$T_{7}^{106} -$$$$13\!\cdots\!32$$$$T_{7}^{105} +$$$$53\!\cdots\!87$$$$T_{7}^{104} -$$$$67\!\cdots\!56$$$$T_{7}^{103} -$$$$62\!\cdots\!58$$$$T_{7}^{102} +$$$$38\!\cdots\!04$$$$T_{7}^{101} -$$$$71\!\cdots\!21$$$$T_{7}^{100} +$$$$29\!\cdots\!96$$$$T_{7}^{99} +$$$$17\!\cdots\!20$$$$T_{7}^{98} -$$$$49\!\cdots\!44$$$$T_{7}^{97} +$$$$54\!\cdots\!08$$$$T_{7}^{96} +$$$$25\!\cdots\!12$$$$T_{7}^{95} -$$$$21\!\cdots\!20$$$$T_{7}^{94} +$$$$42\!\cdots\!72$$$$T_{7}^{93} -$$$$30\!\cdots\!52$$$$T_{7}^{92} -$$$$73\!\cdots\!32$$$$T_{7}^{91} +$$$$28\!\cdots\!94$$$$T_{7}^{90} -$$$$38\!\cdots\!48$$$$T_{7}^{89} +$$$$33\!\cdots\!29$$$$T_{7}^{88} +$$$$75\!\cdots\!84$$$$T_{7}^{87} -$$$$10\!\cdots\!42$$$$T_{7}^{86} -$$$$13\!\cdots\!48$$$$T_{7}^{85} +$$$$32\!\cdots\!91$$$$T_{7}^{84} -$$$$56\!\cdots\!36$$$$T_{7}^{83} +$$$$36\!\cdots\!74$$$$T_{7}^{82} +$$$$34\!\cdots\!92$$$$T_{7}^{81} -$$$$13\!\cdots\!24$$$$T_{7}^{80} +$$$$34\!\cdots\!48$$$$T_{7}^{79} -$$$$81\!\cdots\!76$$$$T_{7}^{78} +$$$$14\!\cdots\!20$$$$T_{7}^{77} -$$$$20\!\cdots\!04$$$$T_{7}^{76} +$$$$25\!\cdots\!92$$$$T_{7}^{75} -$$$$30\!\cdots\!16$$$$T_{7}^{74} +$$$$32\!\cdots\!92$$$$T_{7}^{73} -$$$$18\!\cdots\!43$$$$T_{7}^{72} -$$$$23\!\cdots\!92$$$$T_{7}^{71} +$$$$12\!\cdots\!12$$$$T_{7}^{70} -$$$$33\!\cdots\!32$$$$T_{7}^{69} +$$$$75\!\cdots\!68$$$$T_{7}^{68} -$$$$14\!\cdots\!60$$$$T_{7}^{67} +$$$$25\!\cdots\!86$$$$T_{7}^{66} -$$$$38\!\cdots\!64$$$$T_{7}^{65} +$$$$54\!\cdots\!10$$$$T_{7}^{64} -$$$$70\!\cdots\!36$$$$T_{7}^{63} +$$$$83\!\cdots\!76$$$$T_{7}^{62} -$$$$91\!\cdots\!56$$$$T_{7}^{61} +$$$$91\!\cdots\!66$$$$T_{7}^{60} -$$$$84\!\cdots\!44$$$$T_{7}^{59} +$$$$72\!\cdots\!76$$$$T_{7}^{58} -$$$$59\!\cdots\!28$$$$T_{7}^{57} +$$$$46\!\cdots\!92$$$$T_{7}^{56} -$$$$34\!\cdots\!48$$$$T_{7}^{55} +$$$$25\!\cdots\!54$$$$T_{7}^{54} -$$$$17\!\cdots\!88$$$$T_{7}^{53} +$$$$11\!\cdots\!11$$$$T_{7}^{52} -$$$$61\!\cdots\!24$$$$T_{7}^{51} -$$$$18\!\cdots\!62$$$$T_{7}^{50} +$$$$56\!\cdots\!80$$$$T_{7}^{49} -$$$$75\!\cdots\!45$$$$T_{7}^{48} +$$$$52\!\cdots\!64$$$$T_{7}^{47} -$$$$83\!\cdots\!02$$$$T_{7}^{46} -$$$$24\!\cdots\!08$$$$T_{7}^{45} +$$$$28\!\cdots\!51$$$$T_{7}^{44} -$$$$13\!\cdots\!32$$$$T_{7}^{43} -$$$$41\!\cdots\!24$$$$T_{7}^{42} +$$$$12\!\cdots\!72$$$$T_{7}^{41} -$$$$12\!\cdots\!44$$$$T_{7}^{40} +$$$$81\!\cdots\!80$$$$T_{7}^{39} -$$$$38\!\cdots\!38$$$$T_{7}^{38} +$$$$10\!\cdots\!64$$$$T_{7}^{37} +$$$$43\!\cdots\!41$$$$T_{7}^{36} -$$$$10\!\cdots\!00$$$$T_{7}^{35} +$$$$95\!\cdots\!66$$$$T_{7}^{34} -$$$$62\!\cdots\!68$$$$T_{7}^{33} +$$$$30\!\cdots\!57$$$$T_{7}^{32} -$$$$10\!\cdots\!16$$$$T_{7}^{31} +$$$$31\!\cdots\!88$$$$T_{7}^{30} -$$$$10\!\cdots\!76$$$$T_{7}^{29} +$$$$48\!\cdots\!28$$$$T_{7}^{28} -$$$$21\!\cdots\!84$$$$T_{7}^{27} +$$$$92\!\cdots\!28$$$$T_{7}^{26} -$$$$70\!\cdots\!48$$$$T_{7}^{25} +$$$$65\!\cdots\!20$$$$T_{7}^{24} -$$$$45\!\cdots\!32$$$$T_{7}^{23} +$$$$21\!\cdots\!32$$$$T_{7}^{22} -$$$$62\!\cdots\!80$$$$T_{7}^{21} +$$$$63\!\cdots\!76$$$$T_{7}^{20} +$$$$30\!\cdots\!16$$$$T_{7}^{19} -$$$$14\!\cdots\!04$$$$T_{7}^{18} +$$$$24\!\cdots\!00$$$$T_{7}^{17} +$$$$12\!\cdots\!80$$$$T_{7}^{16} -$$$$11\!\cdots\!48$$$$T_{7}^{15} +$$$$14\!\cdots\!24$$$$T_{7}^{14} +$$$$20\!\cdots\!36$$$$T_{7}^{13} -$$$$72\!\cdots\!56$$$$T_{7}^{12} +$$$$39\!\cdots\!88$$$$T_{7}^{11} +$$$$14\!\cdots\!08$$$$T_{7}^{10} -$$$$37\!\cdots\!52$$$$T_{7}^{9} +$$$$37\!\cdots\!68$$$$T_{7}^{8} -$$$$21\!\cdots\!32$$$$T_{7}^{7} +$$$$16\!\cdots\!32$$$$T_{7}^{6} -$$$$13\!\cdots\!80$$$$T_{7}^{5} +$$$$66\!\cdots\!72$$$$T_{7}^{4} -$$$$18\!\cdots\!68$$$$T_{7}^{3} +$$$$53\!\cdots\!96$$$$T_{7}^{2} -$$$$56\!\cdots\!64$$$$T_{7} +$$$$18\!\cdots\!36$$">$$T_{7}^{256} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(930, [\chi])$$.