# Properties

 Label 230.3.k.a Level $230$ Weight $3$ Character orbit 230.k Analytic conductor $6.267$ Analytic rank $0$ Dimension $240$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 230.k (of order $$44$$, degree $$20$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.26704608029$$ Analytic rank: $$0$$ Dimension: $$240$$ Relative dimension: $$12$$ over $$\Q(\zeta_{44})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$240q - 24q^{2} - 4q^{5} - 74q^{7} + 48q^{8} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$240q - 24q^{2} - 4q^{5} - 74q^{7} + 48q^{8} - 16q^{10} + 8q^{11} + 44q^{12} + 24q^{13} + 24q^{15} + 96q^{16} + 12q^{17} + 88q^{18} - 24q^{20} + 24q^{21} + 8q^{22} - 44q^{23} - 128q^{25} + 48q^{26} - 60q^{27} - 116q^{28} + 120q^{30} - 12q^{31} + 96q^{32} - 334q^{33} - 224q^{35} - 176q^{36} + 188q^{37} + 76q^{38} - 16q^{40} - 116q^{41} + 24q^{42} + 120q^{43} + 204q^{45} + 396q^{46} - 144q^{47} - 88q^{48} + 170q^{50} - 176q^{51} + 48q^{52} + 192q^{53} - 312q^{55} + 296q^{56} + 88q^{57} - 28q^{58} - 72q^{60} - 552q^{61} - 12q^{62} - 122q^{63} - 392q^{65} - 8q^{66} - 72q^{67} - 24q^{68} + 100q^{70} + 424q^{71} - 176q^{72} + 452q^{73} + 604q^{75} - 112q^{76} + 356q^{77} + 32q^{78} + 16q^{80} - 704q^{81} + 148q^{82} - 360q^{83} + 428q^{85} - 376q^{86} - 462q^{87} - 104q^{88} - 510q^{90} + 432q^{91} - 192q^{93} - 166q^{95} - 1042q^{97} - 88q^{98} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
3.1 −1.13214 0.847507i −5.47365 + 2.04157i 0.563465 + 1.91899i 1.48407 + 4.77468i 7.92716 + 2.32763i −2.01723 + 9.27304i 0.988434 2.65009i 18.9911 16.4559i 2.36640 6.66334i
3.2 −1.13214 0.847507i −4.48436 + 1.67258i 0.563465 + 1.91899i −1.64232 4.72258i 6.49443 + 1.90694i 1.22526 5.63243i 0.988434 2.65009i 10.5102 9.10714i −2.14308 + 6.73849i
3.3 −1.13214 0.847507i −2.51818 + 0.939231i 0.563465 + 1.91899i 2.35609 4.41008i 3.64692 + 1.07083i −1.24199 + 5.70935i 0.988434 2.65009i −1.34269 + 1.16345i −6.40499 + 2.99601i
3.4 −1.13214 0.847507i −2.44177 + 0.910732i 0.563465 + 1.91899i −4.63287 + 1.88057i 3.53626 + 1.03834i 0.738198 3.39344i 0.988434 2.65009i −1.66895 + 1.44616i 6.83883 + 1.79732i
3.5 −1.13214 0.847507i −1.89358 + 0.706270i 0.563465 + 1.91899i 3.30772 + 3.74953i 2.74236 + 0.805231i 1.94574 8.94444i 0.988434 2.65009i −3.71490 + 3.21898i −0.567036 7.04830i
3.6 −1.13214 0.847507i −1.16785 + 0.435585i 0.563465 + 1.91899i −0.970697 + 4.90487i 1.69133 + 0.496618i −1.47212 + 6.76723i 0.988434 2.65009i −5.62761 + 4.87635i 5.25587 4.73031i
3.7 −1.13214 0.847507i −0.0190211 + 0.00709452i 0.563465 + 1.91899i 4.84193 1.24727i 0.0275472 + 0.00808858i −1.98672 + 9.13280i 0.988434 2.65009i −6.80143 + 5.89348i −6.53880 2.69149i
3.8 −1.13214 0.847507i 1.09130 0.407033i 0.563465 + 1.91899i −4.93104 0.827554i −1.58046 0.464066i 0.600939 2.76247i 0.988434 2.65009i −5.77649 + 5.00536i 4.88125 + 5.11599i
3.9 −1.13214 0.847507i 1.90726 0.711370i 0.563465 + 1.91899i 1.62652 4.72805i −2.76216 0.811045i 2.04047 9.37989i 0.988434 2.65009i −3.67017 + 3.18022i −5.84849 + 3.97431i
3.10 −1.13214 0.847507i 3.55876 1.32735i 0.563465 + 1.91899i −2.88474 + 4.08390i −5.15393 1.51333i −1.27831 + 5.87629i 0.988434 2.65009i 4.10115 3.55367i 6.72706 2.17869i
3.11 −1.13214 0.847507i 4.17989 1.55902i 0.563465 + 1.91899i 4.74689 + 1.57069i −6.05348 1.77746i 0.338789 1.55739i 0.988434 2.65009i 8.23916 7.13928i −4.04295 5.80125i
3.12 −1.13214 0.847507i 4.65466 1.73610i 0.563465 + 1.91899i −3.20030 3.84162i −6.74107 1.97936i −1.76266 + 8.10282i 0.988434 2.65009i 11.8501 10.2682i 0.367373 + 7.06152i
13.1 −1.41061 0.100889i −1.09457 5.03168i 1.97964 + 0.284630i 3.91427 + 3.11103i 1.03638 + 7.20817i −4.48066 + 2.44662i −2.76379 0.601225i −15.9330 + 7.27636i −5.20764 4.78336i
13.2 −1.41061 0.100889i −1.02391 4.70683i 1.97964 + 0.284630i −0.635666 4.95943i 0.969469 + 6.74281i −8.25197 + 4.50592i −2.76379 0.601225i −12.9192 + 5.90000i 0.396327 + 7.05995i
13.3 −1.41061 0.100889i −0.745890 3.42880i 1.97964 + 0.284630i 1.45154 4.78467i 0.706232 + 4.91195i 10.4743 5.71940i −2.76379 0.601225i −3.01364 + 1.37628i −2.53027 + 6.60286i
13.4 −1.41061 0.100889i −0.730822 3.35954i 1.97964 + 0.284630i −1.24754 + 4.84186i 0.691966 + 4.81273i 0.518845 0.283311i −2.76379 0.601225i −2.56569 + 1.17171i 2.24828 6.70412i
13.5 −1.41061 0.100889i −0.160640 0.738452i 1.97964 + 0.284630i −4.82720 1.30312i 0.152100 + 1.05788i 3.79539 2.07244i −2.76379 0.601225i 7.66718 3.50148i 6.67783 + 2.32520i
13.6 −1.41061 0.100889i −0.0934166 0.429429i 1.97964 + 0.284630i 4.81942 1.33161i 0.0884498 + 0.615182i −0.371231 + 0.202708i −2.76379 0.601225i 8.01101 3.65850i −6.93267 + 1.39216i
13.7 −1.41061 0.100889i 0.203005 + 0.933200i 1.97964 + 0.284630i −4.34220 2.47897i −0.192212 1.33686i −8.01935 + 4.37890i −2.76379 0.601225i 7.35704 3.35985i 5.87505 + 3.93494i
13.8 −1.41061 0.100889i 0.313117 + 1.43938i 1.97964 + 0.284630i 0.477701 + 4.97713i −0.296470 2.06199i 7.52566 4.10932i −2.76379 0.601225i 6.21292 2.83735i −0.171714 7.06898i
See next 80 embeddings (of 240 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 223.12 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
23.c even 11 1 inner
115.k odd 44 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 230.3.k.a 240
5.c odd 4 1 inner 230.3.k.a 240
23.c even 11 1 inner 230.3.k.a 240
115.k odd 44 1 inner 230.3.k.a 240

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.3.k.a 240 1.a even 1 1 trivial
230.3.k.a 240 5.c odd 4 1 inner
230.3.k.a 240 23.c even 11 1 inner
230.3.k.a 240 115.k odd 44 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$20\!\cdots\!64$$$$T_{3}^{224} +$$$$45\!\cdots\!10$$$$T_{3}^{223} -$$$$82\!\cdots\!28$$$$T_{3}^{222} +$$$$23\!\cdots\!90$$$$T_{3}^{221} -$$$$15\!\cdots\!15$$$$T_{3}^{220} -$$$$45\!\cdots\!72$$$$T_{3}^{219} +$$$$38\!\cdots\!70$$$$T_{3}^{218} -$$$$21\!\cdots\!72$$$$T_{3}^{217} +$$$$87\!\cdots\!27$$$$T_{3}^{216} +$$$$42\!\cdots\!02$$$$T_{3}^{215} -$$$$46\!\cdots\!86$$$$T_{3}^{214} +$$$$13\!\cdots\!22$$$$T_{3}^{213} -$$$$31\!\cdots\!77$$$$T_{3}^{212} -$$$$26\!\cdots\!56$$$$T_{3}^{211} +$$$$60\!\cdots\!88$$$$T_{3}^{210} -$$$$99\!\cdots\!28$$$$T_{3}^{209} +$$$$19\!\cdots\!09$$$$T_{3}^{208} +$$$$22\!\cdots\!22$$$$T_{3}^{207} -$$$$43\!\cdots\!30$$$$T_{3}^{206} +$$$$74\!\cdots\!40$$$$T_{3}^{205} -$$$$15\!\cdots\!37$$$$T_{3}^{204} -$$$$13\!\cdots\!20$$$$T_{3}^{203} +$$$$26\!\cdots\!72$$$$T_{3}^{202} -$$$$38\!\cdots\!66$$$$T_{3}^{201} +$$$$18\!\cdots\!03$$$$T_{3}^{200} +$$$$85\!\cdots\!58$$$$T_{3}^{199} -$$$$16\!\cdots\!66$$$$T_{3}^{198} +$$$$23\!\cdots\!62$$$$T_{3}^{197} -$$$$83\!\cdots\!58$$$$T_{3}^{196} -$$$$46\!\cdots\!18$$$$T_{3}^{195} +$$$$10\!\cdots\!94$$$$T_{3}^{194} -$$$$13\!\cdots\!72$$$$T_{3}^{193} +$$$$56\!\cdots\!65$$$$T_{3}^{192} +$$$$21\!\cdots\!38$$$$T_{3}^{191} -$$$$62\!\cdots\!82$$$$T_{3}^{190} +$$$$87\!\cdots\!90$$$$T_{3}^{189} -$$$$21\!\cdots\!77$$$$T_{3}^{188} -$$$$10\!\cdots\!18$$$$T_{3}^{187} +$$$$33\!\cdots\!32$$$$T_{3}^{186} -$$$$44\!\cdots\!58$$$$T_{3}^{185} +$$$$12\!\cdots\!88$$$$T_{3}^{184} +$$$$60\!\cdots\!06$$$$T_{3}^{183} -$$$$16\!\cdots\!36$$$$T_{3}^{182} +$$$$21\!\cdots\!64$$$$T_{3}^{181} -$$$$43\!\cdots\!35$$$$T_{3}^{180} -$$$$38\!\cdots\!82$$$$T_{3}^{179} +$$$$84\!\cdots\!22$$$$T_{3}^{178} -$$$$83\!\cdots\!06$$$$T_{3}^{177} +$$$$24\!\cdots\!22$$$$T_{3}^{176} +$$$$16\!\cdots\!36$$$$T_{3}^{175} -$$$$46\!\cdots\!40$$$$T_{3}^{174} +$$$$37\!\cdots\!00$$$$T_{3}^{173} -$$$$12\!\cdots\!08$$$$T_{3}^{172} -$$$$65\!\cdots\!68$$$$T_{3}^{171} +$$$$24\!\cdots\!28$$$$T_{3}^{170} -$$$$19\!\cdots\!14$$$$T_{3}^{169} +$$$$81\!\cdots\!50$$$$T_{3}^{168} +$$$$15\!\cdots\!24$$$$T_{3}^{167} -$$$$83\!\cdots\!58$$$$T_{3}^{166} +$$$$83\!\cdots\!16$$$$T_{3}^{165} -$$$$44\!\cdots\!74$$$$T_{3}^{164} -$$$$67\!\cdots\!20$$$$T_{3}^{163} +$$$$18\!\cdots\!54$$$$T_{3}^{162} -$$$$23\!\cdots\!90$$$$T_{3}^{161} +$$$$14\!\cdots\!98$$$$T_{3}^{160} -$$$$32\!\cdots\!44$$$$T_{3}^{159} -$$$$46\!\cdots\!48$$$$T_{3}^{158} +$$$$58\!\cdots\!00$$$$T_{3}^{157} -$$$$31\!\cdots\!30$$$$T_{3}^{156} -$$$$87\!\cdots\!58$$$$T_{3}^{155} +$$$$16\!\cdots\!94$$$$T_{3}^{154} -$$$$15\!\cdots\!66$$$$T_{3}^{153} +$$$$58\!\cdots\!86$$$$T_{3}^{152} +$$$$69\!\cdots\!62$$$$T_{3}^{151} -$$$$44\!\cdots\!76$$$$T_{3}^{150} +$$$$36\!\cdots\!66$$$$T_{3}^{149} -$$$$95\!\cdots\!22$$$$T_{3}^{148} -$$$$24\!\cdots\!30$$$$T_{3}^{147} +$$$$10\!\cdots\!64$$$$T_{3}^{146} -$$$$66\!\cdots\!06$$$$T_{3}^{145} +$$$$12\!\cdots\!47$$$$T_{3}^{144} +$$$$55\!\cdots\!08$$$$T_{3}^{143} -$$$$20\!\cdots\!84$$$$T_{3}^{142} +$$$$10\!\cdots\!30$$$$T_{3}^{141} -$$$$77\!\cdots\!51$$$$T_{3}^{140} -$$$$11\!\cdots\!86$$$$T_{3}^{139} +$$$$34\!\cdots\!28$$$$T_{3}^{138} -$$$$16\!\cdots\!10$$$$T_{3}^{137} -$$$$17\!\cdots\!44$$$$T_{3}^{136} +$$$$20\!\cdots\!76$$$$T_{3}^{135} -$$$$52\!\cdots\!86$$$$T_{3}^{134} +$$$$20\!\cdots\!26$$$$T_{3}^{133} +$$$$17\!\cdots\!60$$$$T_{3}^{132} -$$$$28\!\cdots\!84$$$$T_{3}^{131} +$$$$64\!\cdots\!30$$$$T_{3}^{130} -$$$$20\!\cdots\!62$$$$T_{3}^{129} -$$$$43\!\cdots\!05$$$$T_{3}^{128} +$$$$30\!\cdots\!60$$$$T_{3}^{127} -$$$$54\!\cdots\!54$$$$T_{3}^{126} +$$$$14\!\cdots\!30$$$$T_{3}^{125} +$$$$63\!\cdots\!44$$$$T_{3}^{124} -$$$$26\!\cdots\!46$$$$T_{3}^{123} +$$$$29\!\cdots\!20$$$$T_{3}^{122} -$$$$57\!\cdots\!24$$$$T_{3}^{121} -$$$$62\!\cdots\!37$$$$T_{3}^{120} +$$$$18\!\cdots\!36$$$$T_{3}^{119} -$$$$64\!\cdots\!18$$$$T_{3}^{118} +$$$$21\!\cdots\!90$$$$T_{3}^{117} +$$$$49\!\cdots\!52$$$$T_{3}^{116} -$$$$85\!\cdots\!54$$$$T_{3}^{115} +$$$$69\!\cdots\!26$$$$T_{3}^{114} -$$$$69\!\cdots\!96$$$$T_{3}^{113} -$$$$35\!\cdots\!54$$$$T_{3}^{112} +$$$$27\!\cdots\!98$$$$T_{3}^{111} -$$$$34\!\cdots\!66$$$$T_{3}^{110} -$$$$20\!\cdots\!92$$$$T_{3}^{109} +$$$$21\!\cdots\!17$$$$T_{3}^{108} -$$$$73\!\cdots\!66$$$$T_{3}^{107} +$$$$14\!\cdots\!54$$$$T_{3}^{106} +$$$$26\!\cdots\!24$$$$T_{3}^{105} -$$$$84\!\cdots\!45$$$$T_{3}^{104} -$$$$21\!\cdots\!86$$$$T_{3}^{103} +$$$$25\!\cdots\!00$$$$T_{3}^{102} -$$$$91\!\cdots\!90$$$$T_{3}^{101} +$$$$21\!\cdots\!21$$$$T_{3}^{100} +$$$$26\!\cdots\!10$$$$T_{3}^{99} -$$$$50\!\cdots\!62$$$$T_{3}^{98} +$$$$82\!\cdots\!02$$$$T_{3}^{97} -$$$$86\!\cdots\!97$$$$T_{3}^{96} +$$$$85\!\cdots\!30$$$$T_{3}^{95} -$$$$27\!\cdots\!58$$$$T_{3}^{94} +$$$$13\!\cdots\!54$$$$T_{3}^{93} +$$$$58\!\cdots\!36$$$$T_{3}^{92} -$$$$76\!\cdots\!02$$$$T_{3}^{91} +$$$$66\!\cdots\!04$$$$T_{3}^{90} +$$$$14\!\cdots\!48$$$$T_{3}^{89} -$$$$20\!\cdots\!30$$$$T_{3}^{88} +$$$$20\!\cdots\!76$$$$T_{3}^{87} -$$$$74\!\cdots\!46$$$$T_{3}^{86} -$$$$16\!\cdots\!92$$$$T_{3}^{85} +$$$$49\!\cdots\!48$$$$T_{3}^{84} -$$$$39\!\cdots\!32$$$$T_{3}^{83} +$$$$11\!\cdots\!80$$$$T_{3}^{82} -$$$$72\!\cdots\!02$$$$T_{3}^{81} -$$$$89\!\cdots\!15$$$$T_{3}^{80} +$$$$83\!\cdots\!38$$$$T_{3}^{79} +$$$$56\!\cdots\!38$$$$T_{3}^{78} +$$$$20\!\cdots\!86$$$$T_{3}^{77} +$$$$15\!\cdots\!41$$$$T_{3}^{76} +$$$$35\!\cdots\!04$$$$T_{3}^{75} -$$$$52\!\cdots\!30$$$$T_{3}^{74} -$$$$74\!\cdots\!48$$$$T_{3}^{73} -$$$$17\!\cdots\!55$$$$T_{3}^{72} -$$$$17\!\cdots\!38$$$$T_{3}^{71} +$$$$13\!\cdots\!40$$$$T_{3}^{70} +$$$$84\!\cdots\!52$$$$T_{3}^{69} +$$$$26\!\cdots\!46$$$$T_{3}^{68} +$$$$17\!\cdots\!20$$$$T_{3}^{67} -$$$$82\!\cdots\!74$$$$T_{3}^{66} -$$$$90\!\cdots\!76$$$$T_{3}^{65} -$$$$19\!\cdots\!99$$$$T_{3}^{64} -$$$$15\!\cdots\!54$$$$T_{3}^{63} +$$$$78\!\cdots\!50$$$$T_{3}^{62} +$$$$51\!\cdots\!42$$$$T_{3}^{61} +$$$$97\!\cdots\!02$$$$T_{3}^{60} +$$$$73\!\cdots\!08$$$$T_{3}^{59} -$$$$28\!\cdots\!84$$$$T_{3}^{58} -$$$$19\!\cdots\!78$$$$T_{3}^{57} -$$$$31\!\cdots\!47$$$$T_{3}^{56} -$$$$17\!\cdots\!02$$$$T_{3}^{55} +$$$$89\!\cdots\!66$$$$T_{3}^{54} +$$$$42\!\cdots\!34$$$$T_{3}^{53} +$$$$62\!\cdots\!96$$$$T_{3}^{52} +$$$$27\!\cdots\!74$$$$T_{3}^{51} -$$$$29\!\cdots\!72$$$$T_{3}^{50} -$$$$73\!\cdots\!18$$$$T_{3}^{49} -$$$$67\!\cdots\!98$$$$T_{3}^{48} +$$$$14\!\cdots\!82$$$$T_{3}^{47} +$$$$77\!\cdots\!50$$$$T_{3}^{46} +$$$$10\!\cdots\!14$$$$T_{3}^{45} +$$$$45\!\cdots\!41$$$$T_{3}^{44} -$$$$81\!\cdots\!44$$$$T_{3}^{43} -$$$$10\!\cdots\!00$$$$T_{3}^{42} -$$$$43\!\cdots\!26$$$$T_{3}^{41} +$$$$12\!\cdots\!93$$$$T_{3}^{40} +$$$$16\!\cdots\!98$$$$T_{3}^{39} +$$$$12\!\cdots\!94$$$$T_{3}^{38} +$$$$67\!\cdots\!58$$$$T_{3}^{37} -$$$$20\!\cdots\!55$$$$T_{3}^{36} -$$$$82\!\cdots\!24$$$$T_{3}^{35} -$$$$59\!\cdots\!66$$$$T_{3}^{34} -$$$$21\!\cdots\!00$$$$T_{3}^{33} -$$$$11\!\cdots\!58$$$$T_{3}^{32} -$$$$41\!\cdots\!04$$$$T_{3}^{31} +$$$$15\!\cdots\!90$$$$T_{3}^{30} +$$$$37\!\cdots\!64$$$$T_{3}^{29} +$$$$45\!\cdots\!97$$$$T_{3}^{28} +$$$$32\!\cdots\!58$$$$T_{3}^{27} +$$$$18\!\cdots\!14$$$$T_{3}^{26} +$$$$12\!\cdots\!58$$$$T_{3}^{25} +$$$$10\!\cdots\!78$$$$T_{3}^{24} +$$$$64\!\cdots\!48$$$$T_{3}^{23} +$$$$28\!\cdots\!50$$$$T_{3}^{22} +$$$$11\!\cdots\!68$$$$T_{3}^{21} +$$$$63\!\cdots\!22$$$$T_{3}^{20} +$$$$39\!\cdots\!64$$$$T_{3}^{19} +$$$$16\!\cdots\!84$$$$T_{3}^{18} +$$$$27\!\cdots\!20$$$$T_{3}^{17} -$$$$20\!\cdots\!15$$$$T_{3}^{16} -$$$$16\!\cdots\!84$$$$T_{3}^{15} -$$$$60\!\cdots\!86$$$$T_{3}^{14} -$$$$10\!\cdots\!58$$$$T_{3}^{13} +$$$$14\!\cdots\!74$$$$T_{3}^{12} +$$$$14\!\cdots\!80$$$$T_{3}^{11} +$$$$45\!\cdots\!64$$$$T_{3}^{10} +$$$$72\!\cdots\!26$$$$T_{3}^{9} +$$$$53\!\cdots\!51$$$$T_{3}^{8} -$$$$14\!\cdots\!66$$$$T_{3}^{7} +$$$$14\!\cdots\!60$$$$T_{3}^{6} +$$$$54\!\cdots\!30$$$$T_{3}^{5} +$$$$78\!\cdots\!06$$$$T_{3}^{4} +$$$$17\!\cdots\!24$$$$T_{3}^{3} +$$$$24\!\cdots\!18$$$$T_{3}^{2} +$$$$73\!\cdots\!46$$$$T_{3} +$$$$11\!\cdots\!81$$">$$T_{3}^{240} + \cdots$$ acting on $$S_{3}^{\mathrm{new}}(230, [\chi])$$.