# Properties

 Label 25.36 Level 25 Weight 36 Dimension 798 Nonzero newspaces 4 Sturm bound 1800 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$25 = 5^{2}$$ Weight: $$k$$ = $$36$$ Nonzero newspaces: $$4$$ Sturm bound: $$1800$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{36}(\Gamma_1(25))$$.

Total New Old
Modular forms 889 819 70
Cusp forms 861 798 63
Eisenstein series 28 21 7

## Trace form

 $$798q + 401794q^{2} + 261337858q^{3} - 68237952962q^{4} - 786209818295q^{5} + 158049617713966q^{6} + 499562169965934q^{7} + 8447984419519910q^{8} + 223935448630334907q^{9} + O(q^{10})$$ $$798q + 401794q^{2} + 261337858q^{3} - 68237952962q^{4} - 786209818295q^{5} + 158049617713966q^{6} + 499562169965934q^{7} + 8447984419519910q^{8} + 223935448630334907q^{9} - 1113716106029496720q^{10} + 3412481942856731906q^{11} + 42175928538930643254q^{12} + 35853327402027235068q^{13} - 1225457999804471347834q^{14} - 1376749953535241537430q^{15} - 22118972490829324263282q^{16} - 6086741091784412799406q^{17} - 18247113839397898717742q^{18} - 141886078886750147179010q^{19} - 376421776977652424628550q^{20} - 430898242801307058298974q^{21} + 958922388306253176700518q^{22} - 626985616120492625810582q^{23} - 12113247442187069283441620q^{24} - 7600943270678668759924765q^{25} + 3934933011954275183424876q^{26} - 114840610700056710332238440q^{27} + 316679000156274810323072022q^{28} - 64772510093981015543540800q^{29} + 310278060625930856074270630q^{30} + 455703923882980303718369306q^{31} + 49304188018351970941685174q^{32} - 282826997625340074991472934q^{33} + 5171605099522750693401284686q^{34} - 6284566752712269901018975980q^{35} - 24062587707297691474720287882q^{36} - 5300039640156488250458918611q^{37} + 36279720889988539010150041180q^{38} + 3326024852860044982584732054q^{39} - 77495013057886880434499350260q^{40} - 12638775463654014284027936244q^{41} + 166963947191786500056113212858q^{42} + 59317478243565426276556603378q^{43} - 368808388530760987154982001784q^{44} - 39956457109400646994649691235q^{45} - 841085096831639234936615589494q^{46} - 377283071816757803988110481826q^{47} - 2396632749200381435697473851692q^{48} + 1978839645548890553693233459778q^{49} - 5350734708427254274549041061950q^{50} + 2454379505927287786032505105536q^{51} + 4546482766078735308809277949924q^{52} + 208662252246487852563034536373q^{53} - 6517648450732344770674384258720q^{54} + 3440112539483276906181405033930q^{55} - 46022417506007476430956972805870q^{56} + 17915075389169078567450512749590q^{57} + 57691314657244048086841126347300q^{58} - 73853103897028580639815678268000q^{59} - 75875269726663269734698863494110q^{60} - 21490359328263723558921006349844q^{61} - 118758313066019569944705339059072q^{62} + 448198557726103555661748989784068q^{63} - 199500308676616488880233679922792q^{64} - 3946757600758637104231109469785q^{65} + 139849577592426905589813907098542q^{66} - 558793053635867340197151645503366q^{67} + 1467276982683272497090225432289382q^{68} + 608042399936275338916090009050004q^{69} - 1598879775674700009027368696701250q^{70} + 1604684010214888922898946941840606q^{71} - 2043529929508996817216469965732520q^{72} - 2110376318156840858455345250606792q^{73} + 6168287097484013342254298609012116q^{74} - 2488130108605992451408207948849790q^{75} + 1500803541898985353673980433886660q^{76} + 12465649125734213565002103075352518q^{77} - 13895546472258566788903257451308664q^{78} + 2135132741245937850329884447000830q^{79} + 12674810209870926254607998626216390q^{80} - 10113943316229750931481426872557717q^{81} - 17198624378243859774144621682736842q^{82} + 35161654240766055599109576621652508q^{83} + 36964134524838477475307922628167206q^{84} - 20989664200795794344266635757605185q^{85} + 16793354997252445625309627029165946q^{86} + 100318460376555393322906181726862620q^{87} - 158072372215518312042702370146888770q^{88} + 33970153974656639303092985936644905q^{89} - 35391043184789312995991620856998290q^{90} - 86555126912046284737733412224954454q^{91} + 95672093091352115605214613287113634q^{92} + 322172980758211233471761960102679136q^{93} - 739053759943210645714939052674632314q^{94} + 366696388686156110859494483692616010q^{95} - 164632776732033131644009015300676374q^{96} - 537095158424624372247329841696458476q^{97} + 242376978548206651363104076106681262q^{98} + 405633675828896256775643280919031544q^{99} + O(q^{100})$$

## Decomposition of $$S_{36}^{\mathrm{new}}(\Gamma_1(25))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
25.36.a $$\chi_{25}(1, \cdot)$$ 25.36.a.a 3 1
25.36.a.b 5
25.36.a.c 6
25.36.a.d 12
25.36.a.e 12
25.36.a.f 16
25.36.b $$\chi_{25}(24, \cdot)$$ 25.36.b.a 6 1
25.36.b.b 10
25.36.b.c 12
25.36.b.d 24
25.36.d $$\chi_{25}(6, \cdot)$$ n/a 348 4
25.36.e $$\chi_{25}(4, \cdot)$$ n/a 344 4

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{36}^{\mathrm{old}}(\Gamma_1(25))$$ into lower level spaces

$$S_{36}^{\mathrm{old}}(\Gamma_1(25)) \cong$$ $$S_{36}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 3}$$$$\oplus$$$$S_{36}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$