# Properties

 Label 43.5.b Level 43 Weight 5 Character orbit b Rep. character $$\chi_{43}(42,\cdot)$$ Character field $$\Q$$ Dimension 13 Newform subspaces 2 Sturm bound 18 Trace bound 1

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## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 43.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$43$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(43, [\chi])$$.

Total New Old
Modular forms 15 15 0
Cusp forms 13 13 0
Eisenstein series 2 2 0

## Trace form

 $$13q - 76q^{4} + 126q^{6} - 381q^{9} + O(q^{10})$$ $$13q - 76q^{4} + 126q^{6} - 381q^{9} + 182q^{10} + 19q^{11} - 265q^{13} + 732q^{14} - 92q^{15} + 1332q^{16} + 181q^{17} - 2392q^{21} + 517q^{23} - 4234q^{24} + 451q^{25} + 4149q^{31} + 936q^{35} + 5506q^{36} + 1242q^{38} - 2618q^{40} + 3037q^{41} + 741q^{43} - 11984q^{44} - 3860q^{47} - 6143q^{49} + 23300q^{52} - 437q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 9970q^{59} + 15848q^{60} - 11484q^{64} + 29808q^{66} - 1785q^{67} + 7234q^{68} - 7674q^{74} - 67708q^{78} + 12016q^{79} - 17099q^{81} - 5681q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 31570q^{92} + 606q^{95} + 50546q^{96} + 12589q^{97} - 9805q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(43, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
43.5.b.a $$1$$ $$4.445$$ $$\Q$$ $$\Q(\sqrt{-43})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots$$
43.5.b.b $$12$$ $$4.445$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 4 T )( 1 + 4 T )$$)($$1 - 50 T^{2} + 1349 T^{4} - 26056 T^{6} + 463232 T^{8} - 8751936 T^{10} + 150915312 T^{12} - 2240495616 T^{14} + 30358372352 T^{16} - 437147140096 T^{18} + 5793910882304 T^{20} - 54975581388800 T^{22} + 281474976710656 T^{24}$$)
$3$ ($$( 1 - 9 T )( 1 + 9 T )$$)($$1 - 255 T^{2} + 47783 T^{4} - 6646421 T^{6} + 799989903 T^{8} - 79711532676 T^{10} + 6990833564658 T^{12} - 522987365887236 T^{14} + 34436942157258063 T^{16} - 1877145602287584501 T^{18} + 88542863683907518503 T^{20} -$$$$31\!\cdots\!55$$$$T^{22} +$$$$79\!\cdots\!61$$$$T^{24}$$)
$5$ ($$( 1 - 25 T )( 1 + 25 T )$$)($$1 - 3663 T^{2} + 6511015 T^{4} - 7365160765 T^{6} + 5973224140031 T^{8} - 3902236317085676 T^{10} + 2399998678381934162 T^{12} -$$$$15\!\cdots\!00$$$$T^{14} +$$$$91\!\cdots\!75$$$$T^{16} -$$$$43\!\cdots\!25$$$$T^{18} +$$$$15\!\cdots\!75$$$$T^{20} -$$$$33\!\cdots\!75$$$$T^{22} +$$$$35\!\cdots\!25$$$$T^{24}$$)
$7$ ($$( 1 - 49 T )( 1 + 49 T )$$)($$1 - 10134 T^{2} + 60060006 T^{4} - 249160434566 T^{6} + 812915964019071 T^{8} - 2246049549704995236 T^{10} +$$$$56\!\cdots\!48$$$$T^{12} -$$$$12\!\cdots\!36$$$$T^{14} +$$$$27\!\cdots\!71$$$$T^{16} -$$$$47\!\cdots\!66$$$$T^{18} +$$$$66\!\cdots\!06$$$$T^{20} -$$$$64\!\cdots\!34$$$$T^{22} +$$$$36\!\cdots\!01$$$$T^{24}$$)
$11$ ($$1 - 199 T + 14641 T^{2}$$)($$( 1 + 90 T + 69626 T^{2} + 4275732 T^{3} + 2084651350 T^{4} + 90865763142 T^{5} + 37469241503078 T^{6} + 1330365638162022 T^{7} + 446863530661139350 T^{8} + 13419078640054034772 T^{9} +$$$$31\!\cdots\!86$$$$T^{10} +$$$$60\!\cdots\!90$$$$T^{11} +$$$$98\!\cdots\!41$$$$T^{12} )^{2}$$)
$13$ ($$1 + 49 T + 28561 T^{2}$$)($$( 1 + 108 T + 78130 T^{2} + 14124934 T^{3} + 3639591614 T^{4} + 705010114760 T^{5} + 121575713991590 T^{6} + 20135793887660360 T^{7} + 2968926691433773694 T^{8} +$$$$32\!\cdots\!54$$$$T^{9} +$$$$51\!\cdots\!30$$$$T^{10} +$$$$20\!\cdots\!08$$$$T^{11} +$$$$54\!\cdots\!61$$$$T^{12} )^{2}$$)
$17$ ($$1 + 497 T + 83521 T^{2}$$)($$( 1 - 339 T + 345843 T^{2} - 103717833 T^{3} + 57770879546 T^{4} - 15179725016055 T^{5} + 6016834256618483 T^{6} - 1267825813065929655 T^{7} +$$$$40\!\cdots\!86$$$$T^{8} -$$$$60\!\cdots\!13$$$$T^{9} +$$$$16\!\cdots\!83$$$$T^{10} -$$$$13\!\cdots\!39$$$$T^{11} +$$$$33\!\cdots\!21$$$$T^{12} )^{2}$$)
$19$ ($$( 1 - 361 T )( 1 + 361 T )$$)($$1 - 1175657 T^{2} + 671010023409 T^{4} - 244979577528319381 T^{6} +$$$$63\!\cdots\!63$$$$T^{8} -$$$$12\!\cdots\!10$$$$T^{10} +$$$$18\!\cdots\!98$$$$T^{12} -$$$$20\!\cdots\!10$$$$T^{14} +$$$$18\!\cdots\!03$$$$T^{16} -$$$$12\!\cdots\!01$$$$T^{18} +$$$$55\!\cdots\!49$$$$T^{20} -$$$$16\!\cdots\!57$$$$T^{22} +$$$$23\!\cdots\!41$$$$T^{24}$$)
$23$ ($$1 + 1049 T + 279841 T^{2}$$)($$( 1 - 783 T + 1163077 T^{2} - 843582057 T^{3} + 713091466102 T^{4} - 397049506101027 T^{5} + 259574077696956889 T^{6} -$$$$11\!\cdots\!07$$$$T^{7} +$$$$55\!\cdots\!62$$$$T^{8} -$$$$18\!\cdots\!97$$$$T^{9} +$$$$71\!\cdots\!97$$$$T^{10} -$$$$13\!\cdots\!83$$$$T^{11} +$$$$48\!\cdots\!41$$$$T^{12} )^{2}$$)
$29$ ($$( 1 - 841 T )( 1 + 841 T )$$)($$1 - 5231219 T^{2} + 13592412986871 T^{4} - 23367533349246758977 T^{6} +$$$$29\!\cdots\!35$$$$T^{8} -$$$$29\!\cdots\!88$$$$T^{10} +$$$$23\!\cdots\!82$$$$T^{12} -$$$$14\!\cdots\!68$$$$T^{14} +$$$$74\!\cdots\!35$$$$T^{16} -$$$$29\!\cdots\!37$$$$T^{18} +$$$$85\!\cdots\!11$$$$T^{20} -$$$$16\!\cdots\!19$$$$T^{22} +$$$$15\!\cdots\!61$$$$T^{24}$$)
$31$ ($$1 + 1561 T + 923521 T^{2}$$)($$( 1 - 2855 T + 6518969 T^{2} - 8600011177 T^{3} + 10228398490358 T^{4} - 8682474860253963 T^{5} + 8850492205571119245 T^{6} -$$$$80\!\cdots\!23$$$$T^{7} +$$$$87\!\cdots\!78$$$$T^{8} -$$$$67\!\cdots\!97$$$$T^{9} +$$$$47\!\cdots\!89$$$$T^{10} -$$$$19\!\cdots\!55$$$$T^{11} +$$$$62\!\cdots\!21$$$$T^{12} )^{2}$$)
$37$ ($$( 1 - 1369 T )( 1 + 1369 T )$$)($$1 - 6978249 T^{2} + 25643197308697 T^{4} - 70260487375765593853 T^{6} +$$$$17\!\cdots\!59$$$$T^{8} -$$$$39\!\cdots\!70$$$$T^{10} +$$$$80\!\cdots\!70$$$$T^{12} -$$$$13\!\cdots\!70$$$$T^{14} +$$$$21\!\cdots\!19$$$$T^{16} -$$$$30\!\cdots\!33$$$$T^{18} +$$$$39\!\cdots\!57$$$$T^{20} -$$$$37\!\cdots\!49$$$$T^{22} +$$$$18\!\cdots\!21$$$$T^{24}$$)
$41$ ($$1 + 1841 T + 2825761 T^{2}$$)($$( 1 - 2439 T + 13822603 T^{2} - 19943096547 T^{3} + 69051390319336 T^{4} - 65595635499999207 T^{5} +$$$$21\!\cdots\!21$$$$T^{6} -$$$$18\!\cdots\!27$$$$T^{7} +$$$$55\!\cdots\!56$$$$T^{8} -$$$$44\!\cdots\!07$$$$T^{9} +$$$$88\!\cdots\!23$$$$T^{10} -$$$$43\!\cdots\!39$$$$T^{11} +$$$$50\!\cdots\!61$$$$T^{12} )^{2}$$)
$43$ ($$1 - 1849 T$$)($$1 + 1108 T + 1897246 T^{2} - 4681128092 T^{3} + 681017924063 T^{4} - 846563366867960 T^{5} + 64607141521498794692 T^{6} -$$$$28\!\cdots\!60$$$$T^{7} +$$$$79\!\cdots\!63$$$$T^{8} -$$$$18\!\cdots\!92$$$$T^{9} +$$$$25\!\cdots\!46$$$$T^{10} +$$$$51\!\cdots\!08$$$$T^{11} +$$$$15\!\cdots\!01$$$$T^{12}$$)
$47$ ($$1 - 1666 T + 4879681 T^{2}$$)($$( 1 + 2763 T + 21754149 T^{2} + 55851382377 T^{3} + 234662825346711 T^{4} + 481604898621884868 T^{5} +$$$$14\!\cdots\!34$$$$T^{6} +$$$$23\!\cdots\!08$$$$T^{7} +$$$$55\!\cdots\!71$$$$T^{8} +$$$$64\!\cdots\!57$$$$T^{9} +$$$$12\!\cdots\!29$$$$T^{10} +$$$$76\!\cdots\!63$$$$T^{11} +$$$$13\!\cdots\!81$$$$T^{12} )^{2}$$)
$53$ ($$1 + 1649 T + 7890481 T^{2}$$)($$( 1 - 606 T + 25718024 T^{2} - 24674633094 T^{3} + 346581142619392 T^{4} - 336085601563787574 T^{5} +$$$$32\!\cdots\!82$$$$T^{6} -$$$$26\!\cdots\!94$$$$T^{7} +$$$$21\!\cdots\!12$$$$T^{8} -$$$$12\!\cdots\!54$$$$T^{9} +$$$$99\!\cdots\!04$$$$T^{10} -$$$$18\!\cdots\!06$$$$T^{11} +$$$$24\!\cdots\!81$$$$T^{12} )^{2}$$)
$59$ ($$1 + 4046 T + 12117361 T^{2}$$)($$( 1 - 7008 T + 80137258 T^{2} - 394451068512 T^{3} + 2532059909380847 T^{4} - 9247600606403540352 T^{5} +$$$$41\!\cdots\!80$$$$T^{6} -$$$$11\!\cdots\!72$$$$T^{7} +$$$$37\!\cdots\!87$$$$T^{8} -$$$$70\!\cdots\!72$$$$T^{9} +$$$$17\!\cdots\!78$$$$T^{10} -$$$$18\!\cdots\!08$$$$T^{11} +$$$$31\!\cdots\!61$$$$T^{12} )^{2}$$)
$61$ ($$( 1 - 3721 T )( 1 + 3721 T )$$)($$1 - 32665486 T^{2} + 1118892201421590 T^{4} -$$$$24\!\cdots\!14$$$$T^{6} +$$$$52\!\cdots\!07$$$$T^{8} -$$$$83\!\cdots\!88$$$$T^{10} +$$$$13\!\cdots\!08$$$$T^{12} -$$$$16\!\cdots\!28$$$$T^{14} +$$$$19\!\cdots\!27$$$$T^{16} -$$$$17\!\cdots\!74$$$$T^{18} +$$$$15\!\cdots\!90$$$$T^{20} -$$$$84\!\cdots\!86$$$$T^{22} +$$$$49\!\cdots\!81$$$$T^{24}$$)
$67$ ($$1 + 697 T + 20151121 T^{2}$$)($$( 1 + 544 T + 66684038 T^{2} + 18315837698 T^{3} + 2452178722840730 T^{4} + 587634295199545788 T^{5} +$$$$60\!\cdots\!70$$$$T^{6} +$$$$11\!\cdots\!48$$$$T^{7} +$$$$99\!\cdots\!30$$$$T^{8} +$$$$14\!\cdots\!78$$$$T^{9} +$$$$10\!\cdots\!78$$$$T^{10} +$$$$18\!\cdots\!44$$$$T^{11} +$$$$66\!\cdots\!21$$$$T^{12} )^{2}$$)
$71$ ($$( 1 - 5041 T )( 1 + 5041 T )$$)($$1 - 101562020 T^{2} + 5784818387848562 T^{4} -$$$$20\!\cdots\!64$$$$T^{6} +$$$$47\!\cdots\!67$$$$T^{8} -$$$$75\!\cdots\!84$$$$T^{10} +$$$$13\!\cdots\!88$$$$T^{12} -$$$$48\!\cdots\!24$$$$T^{14} +$$$$20\!\cdots\!07$$$$T^{16} -$$$$54\!\cdots\!84$$$$T^{18} +$$$$10\!\cdots\!42$$$$T^{20} -$$$$11\!\cdots\!20$$$$T^{22} +$$$$72\!\cdots\!61$$$$T^{24}$$)
$73$ ($$( 1 - 5329 T )( 1 + 5329 T )$$)($$1 - 193491698 T^{2} + 19000747654703030 T^{4} -$$$$12\!\cdots\!18$$$$T^{6} +$$$$60\!\cdots\!75$$$$T^{8} -$$$$23\!\cdots\!56$$$$T^{10} +$$$$72\!\cdots\!44$$$$T^{12} -$$$$18\!\cdots\!36$$$$T^{14} +$$$$39\!\cdots\!75$$$$T^{16} -$$$$65\!\cdots\!38$$$$T^{18} +$$$$80\!\cdots\!30$$$$T^{20} -$$$$66\!\cdots\!98$$$$T^{22} +$$$$27\!\cdots\!81$$$$T^{24}$$)
$79$ ($$1 + 12286 T + 38950081 T^{2}$$)($$( 1 - 12151 T + 155715789 T^{2} - 800821687889 T^{3} + 4128429862975343 T^{4} + 5685482156720652576 T^{5} -$$$$30\!\cdots\!42$$$$T^{6} +$$$$22\!\cdots\!56$$$$T^{7} +$$$$62\!\cdots\!23$$$$T^{8} -$$$$47\!\cdots\!49$$$$T^{9} +$$$$35\!\cdots\!69$$$$T^{10} -$$$$10\!\cdots\!51$$$$T^{11} +$$$$34\!\cdots\!81$$$$T^{12} )^{2}$$)
$83$ ($$1 - 1351 T + 47458321 T^{2}$$)($$( 1 + 3516 T + 117162268 T^{2} + 863865543048 T^{3} + 7914887456622244 T^{4} + 75598926847021341108 T^{5} +$$$$40\!\cdots\!22$$$$T^{6} +$$$$35\!\cdots\!68$$$$T^{7} +$$$$17\!\cdots\!04$$$$T^{8} +$$$$92\!\cdots\!28$$$$T^{9} +$$$$59\!\cdots\!08$$$$T^{10} +$$$$84\!\cdots\!16$$$$T^{11} +$$$$11\!\cdots\!21$$$$T^{12} )^{2}$$)
$89$ ($$( 1 - 7921 T )( 1 + 7921 T )$$)($$1 - 474457834 T^{2} + 111655192487117862 T^{4} -$$$$17\!\cdots\!66$$$$T^{6} +$$$$19\!\cdots\!11$$$$T^{8} -$$$$17\!\cdots\!92$$$$T^{10} +$$$$12\!\cdots\!28$$$$T^{12} -$$$$68\!\cdots\!52$$$$T^{14} +$$$$30\!\cdots\!71$$$$T^{16} -$$$$10\!\cdots\!06$$$$T^{18} +$$$$26\!\cdots\!02$$$$T^{20} -$$$$44\!\cdots\!34$$$$T^{22} +$$$$37\!\cdots\!81$$$$T^{24}$$)
$97$ ($$1 - 18431 T + 88529281 T^{2}$$)($$( 1 + 2921 T + 384124299 T^{2} + 837647682043 T^{3} + 69794294829141482 T^{4} +$$$$11\!\cdots\!33$$$$T^{5} +$$$$76\!\cdots\!95$$$$T^{6} +$$$$10\!\cdots\!73$$$$T^{7} +$$$$54\!\cdots\!02$$$$T^{8} +$$$$58\!\cdots\!63$$$$T^{9} +$$$$23\!\cdots\!79$$$$T^{10} +$$$$15\!\cdots\!21$$$$T^{11} +$$$$48\!\cdots\!81$$$$T^{12} )^{2}$$)
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