# Properties

 Label 930.2.bt.b 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.

 $$\operatorname{Tr}(f)(q) =$$ $$256q + 16q^{7} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$256q + 16q^{7} + 4q^{10} + 24q^{14} + 8q^{15} + 64q^{16} - 36q^{17} + 40q^{19} - 12q^{20} - 16q^{21} + 44q^{22} + 32q^{24} - 28q^{25} - 8q^{28} + 16q^{29} - 8q^{31} - 4q^{33} - 24q^{35} + 128q^{36} - 76q^{37} + 28q^{38} + 48q^{41} - 4q^{42} + 120q^{43} - 4q^{44} + 12q^{45} - 20q^{46} + 72q^{47} + 40q^{49} + 48q^{50} - 16q^{53} - 64q^{54} + 36q^{55} - 4q^{57} - 68q^{58} + 24q^{59} - 20q^{62} + 4q^{63} + 156q^{65} + 12q^{66} + 44q^{67} + 4q^{68} - 12q^{69} + 104q^{70} - 48q^{71} - 84q^{73} - 68q^{74} - 48q^{75} + 48q^{76} - 124q^{77} + 56q^{79} - 32q^{81} + 16q^{82} - 112q^{83} + 132q^{85} + 24q^{86} + 32q^{87} + 52q^{88} + 224q^{89} + 40q^{91} + 64q^{93} - 204q^{95} + 8q^{97} - 32q^{98} - 4q^{99} + O(q^{100})$$

## 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 −2.21414 + 0.312392i −0.866025 0.500000i −3.70934 0.194398i 0.453990 0.891007i −0.743145 0.669131i 0.0378215 2.23575i
13.2 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.71365 1.43646i −0.866025 0.500000i 1.75333 + 0.0918879i 0.453990 0.891007i −0.743145 0.669131i 1.68685 1.46784i
13.3 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.61201 + 1.54966i −0.866025 0.500000i 2.94133 + 0.154149i 0.453990 0.891007i −0.743145 0.669131i −1.27840 1.83458i
13.4 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −0.0175372 2.23600i −0.866025 0.500000i −1.63070 0.0854612i 0.453990 0.891007i −0.743145 0.669131i 2.21121 + 0.332466i
13.5 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 0.0430415 2.23565i −0.866025 0.500000i 3.43163 + 0.179844i 0.453990 0.891007i −0.743145 0.669131i 2.20140 + 0.392245i
13.6 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 0.402123 + 2.19961i −0.866025 0.500000i −0.877389 0.0459820i 0.453990 0.891007i −0.743145 0.669131i −2.23544 + 0.0530771i
13.7 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 1.76804 + 1.36895i −0.866025 0.500000i 3.85109 + 0.201827i 0.453990 0.891007i −0.743145 0.669131i −1.62868 + 1.53213i
13.8 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 2.09871 0.771623i −0.866025 0.500000i −0.699531 0.0366609i 0.453990 0.891007i −0.743145 0.669131i 0.433812 + 2.19358i
13.9 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −2.22514 + 0.220752i −0.866025 0.500000i −2.35743 0.123548i −0.453990 + 0.891007i −0.743145 0.669131i −0.130055 + 2.23228i
13.10 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.14184 + 1.92255i −0.866025 0.500000i −0.0309572 0.00162240i −0.453990 + 0.891007i −0.743145 0.669131i 1.72026 + 1.42854i
13.11 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.657500 2.13722i −0.866025 0.500000i −3.81046 0.199698i −0.453990 + 0.891007i −0.743145 0.669131i −2.21376 + 0.315071i
13.12 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.322096 2.21275i −0.866025 0.500000i 3.31662 + 0.173817i −0.453990 + 0.891007i −0.743145 0.669131i −2.23589 0.0280193i
13.13 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.285666 + 2.21775i −0.866025 0.500000i 2.60023 + 0.136272i −0.453990 + 0.891007i −0.743145 0.669131i 2.14575 + 0.629081i
13.14 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.23620 + 1.86328i −0.866025 0.500000i −0.503455 0.0263849i −0.453990 + 0.891007i −0.743145 0.669131i 2.03372 0.929500i
13.15 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.65605 1.50249i −0.866025 0.500000i −3.28823 0.172329i −0.453990 + 0.891007i −0.743145 0.669131i −1.22493 1.87071i
13.16 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 2.17193 0.531716i −0.866025 0.500000i 1.18884 + 0.0623043i −0.453990 + 0.891007i −0.743145 0.669131i −0.185405 2.22837i
43.1 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −2.16210 0.570360i 0.866025 0.500000i −0.231757 4.42218i −0.891007 + 0.453990i 0.743145 0.669131i 2.22471 + 0.225111i
43.2 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −1.11506 + 1.93820i 0.866025 0.500000i −0.000384319 0.00733325i −0.891007 + 0.453990i 0.743145 0.669131i 0.798131 2.08878i
43.3 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −0.873557 2.05837i 0.866025 0.500000i 0.239568 + 4.57122i −0.891007 + 0.453990i 0.743145 0.669131i 1.18480 + 1.89638i
43.4 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −0.437784 + 2.19279i 0.866025 0.500000i 0.0914165 + 1.74433i −0.891007 + 0.453990i 0.743145 0.669131i 0.0893656 2.23428i
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.b yes 256
5.c odd 4 1 930.2.bt.a 256
31.h odd 30 1 930.2.bt.a 256
155.x even 60 1 inner 930.2.bt.b yes 256

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

## Hecke kernels

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