Properties

 Label 18.5 Level 18 Weight 5 Dimension 8 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 90 Trace bound 0

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Defining parameters

 Level: $$N$$ = $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$90$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(18))$$.

Total New Old
Modular forms 44 8 36
Cusp forms 28 8 20
Eisenstein series 16 0 16

Trace form

 $$8q + 6q^{3} + 32q^{4} + 18q^{5} + 48q^{6} - 26q^{7} - 78q^{9} + O(q^{10})$$ $$8q + 6q^{3} + 32q^{4} + 18q^{5} + 48q^{6} - 26q^{7} - 78q^{9} - 720q^{11} - 144q^{12} + 10q^{13} + 288q^{14} + 1134q^{15} - 256q^{16} - 384q^{18} + 100q^{19} + 144q^{20} + 438q^{21} + 336q^{22} + 1278q^{23} + 384q^{24} + 794q^{25} - 1296q^{27} - 416q^{28} - 1854q^{29} - 3456q^{30} - 1478q^{31} - 3384q^{33} - 96q^{34} + 1056q^{36} - 32q^{37} + 6768q^{38} + 5274q^{39} - 36q^{41} + 2592q^{42} - 68q^{43} + 3402q^{45} + 2112q^{46} + 2214q^{47} - 1536q^{48} + 2442q^{49} - 15552q^{50} - 12006q^{51} - 80q^{52} + 7056q^{54} - 3996q^{55} + 2304q^{56} + 10902q^{57} - 2400q^{58} + 9108q^{59} + 6480q^{60} - 4478q^{61} - 6654q^{63} - 4096q^{64} - 22554q^{65} - 19872q^{66} + 7504q^{67} - 11088q^{68} - 5994q^{69} + 6048q^{70} + 5376q^{72} + 20716q^{73} + 15264q^{74} + 16590q^{75} + 400q^{76} + 34434q^{77} + 24096q^{78} - 6050q^{79} - 21150q^{81} + 1152q^{82} - 3834q^{83} - 9600q^{84} - 16092q^{85} - 12528q^{86} + 10170q^{87} - 2688q^{88} + 2592q^{90} - 45868q^{91} + 10224q^{92} - 10926q^{93} + 672q^{94} + 20880q^{95} + 31336q^{97} - 22338q^{99} + O(q^{100})$$

Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(18))$$

We only show spaces with odd 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
18.5.b $$\chi_{18}(17, \cdot)$$ None 0 1
18.5.d $$\chi_{18}(5, \cdot)$$ 18.5.d.a 8 2

Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(18))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(18)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 - 8 T^{2} + 64 T^{4} )^{2}$$
$3$ $$1 - 6 T + 57 T^{2} + 162 T^{3} + 4212 T^{4} + 13122 T^{5} + 373977 T^{6} - 3188646 T^{7} + 43046721 T^{8}$$
$5$ $$1 - 18 T + 1015 T^{2} - 16326 T^{3} + 558925 T^{4} - 5405940 T^{5} - 314464142 T^{6} + 3511352520 T^{7} - 306662326214 T^{8} + 2194595325000 T^{9} - 122837555468750 T^{10} - 1319809570312500 T^{11} + 85285186767578125 T^{12} - 1556968688964843750 T^{13} + 60498714447021484375 T^{14} -$$$$67\!\cdots\!50$$$$T^{15} +$$$$23\!\cdots\!25$$$$T^{16}$$
$7$ $$1 + 26 T - 5685 T^{2} + 19510 T^{3} + 19835513 T^{4} - 334899084 T^{5} - 45037679042 T^{6} + 451520935736 T^{7} + 90278690161986 T^{8} + 1084101766702136 T^{9} - 259633257179000642 T^{10} - 4635434404995823884 T^{11} +$$$$65\!\cdots\!13$$$$T^{12} +$$$$15\!\cdots\!10$$$$T^{13} -$$$$10\!\cdots\!85$$$$T^{14} +$$$$11\!\cdots\!26$$$$T^{15} +$$$$11\!\cdots\!01$$$$T^{16}$$
$11$ $$1 + 720 T + 274582 T^{2} + 73283040 T^{3} + 15179596969 T^{4} + 2592718024176 T^{5} + 383108185780198 T^{6} + 51080491982360160 T^{7} + 6354846385614434932 T^{8} +$$$$74\!\cdots\!60$$$$T^{9} +$$$$82\!\cdots\!38$$$$T^{10} +$$$$81\!\cdots\!96$$$$T^{11} +$$$$69\!\cdots\!09$$$$T^{12} +$$$$49\!\cdots\!40$$$$T^{13} +$$$$27\!\cdots\!62$$$$T^{14} +$$$$10\!\cdots\!20$$$$T^{15} +$$$$21\!\cdots\!21$$$$T^{16}$$
$13$ $$1 - 10 T - 34545 T^{2} - 8013734 T^{3} + 152683301 T^{4} + 264027759132 T^{5} + 34691703939994 T^{6} - 3939272844487792 T^{7} - 880372532161082934 T^{8} -$$$$11\!\cdots\!12$$$$T^{9} +$$$$28\!\cdots\!74$$$$T^{10} +$$$$61\!\cdots\!92$$$$T^{11} +$$$$10\!\cdots\!41$$$$T^{12} -$$$$15\!\cdots\!34$$$$T^{13} -$$$$18\!\cdots\!45$$$$T^{14} -$$$$15\!\cdots\!10$$$$T^{15} +$$$$44\!\cdots\!81$$$$T^{16}$$
$17$ $$1 - 249218 T^{2} + 30482460289 T^{4} - 3595961342423810 T^{6} +$$$$36\!\cdots\!56$$$$T^{8} -$$$$25\!\cdots\!10$$$$T^{10} +$$$$14\!\cdots\!09$$$$T^{12} -$$$$84\!\cdots\!78$$$$T^{14} +$$$$23\!\cdots\!61$$$$T^{16}$$
$19$ $$( 1 - 50 T + 226153 T^{2} - 12428354 T^{3} + 33132078964 T^{4} - 1619675521634 T^{5} + 3840883732411273 T^{6} - 110665745953308050 T^{7} +$$$$28\!\cdots\!81$$$$T^{8} )^{2}$$
$23$ $$1 - 1278 T + 1655467 T^{2} - 1419907842 T^{3} + 1186049018761 T^{4} - 817434220578732 T^{5} + 550327618738318606 T^{6} -$$$$32\!\cdots\!56$$$$T^{7} +$$$$18\!\cdots\!30$$$$T^{8} -$$$$89\!\cdots\!96$$$$T^{9} +$$$$43\!\cdots\!86$$$$T^{10} -$$$$17\!\cdots\!72$$$$T^{11} +$$$$72\!\cdots\!21$$$$T^{12} -$$$$24\!\cdots\!42$$$$T^{13} +$$$$79\!\cdots\!47$$$$T^{14} -$$$$17\!\cdots\!18$$$$T^{15} +$$$$37\!\cdots\!21$$$$T^{16}$$
$29$ $$1 + 1854 T + 3116071 T^{2} + 3652934346 T^{3} + 3878113467181 T^{4} + 4083633101435148 T^{5} + 4044828167734324498 T^{6} +$$$$39\!\cdots\!28$$$$T^{7} +$$$$34\!\cdots\!30$$$$T^{8} +$$$$28\!\cdots\!68$$$$T^{9} +$$$$20\!\cdots\!78$$$$T^{10} +$$$$14\!\cdots\!68$$$$T^{11} +$$$$97\!\cdots\!01$$$$T^{12} +$$$$64\!\cdots\!46$$$$T^{13} +$$$$39\!\cdots\!51$$$$T^{14} +$$$$16\!\cdots\!94$$$$T^{15} +$$$$62\!\cdots\!41$$$$T^{16}$$
$31$ $$1 + 1478 T - 273609 T^{2} - 14717462 T^{3} + 1239820588133 T^{4} - 59691395608740 T^{5} - 148444619433025670 T^{6} -$$$$17\!\cdots\!40$$$$T^{7} -$$$$10\!\cdots\!22$$$$T^{8} -$$$$16\!\cdots\!40$$$$T^{9} -$$$$12\!\cdots\!70$$$$T^{10} -$$$$47\!\cdots\!40$$$$T^{11} +$$$$90\!\cdots\!73$$$$T^{12} -$$$$98\!\cdots\!62$$$$T^{13} -$$$$16\!\cdots\!89$$$$T^{14} +$$$$84\!\cdots\!98$$$$T^{15} +$$$$52\!\cdots\!61$$$$T^{16}$$
$37$ $$( 1 + 16 T + 5152060 T^{2} + 1816976752 T^{3} + 11981316770374 T^{4} + 3405306966505072 T^{5} + 18096504895368227260 T^{6} +$$$$10\!\cdots\!96$$$$T^{7} +$$$$12\!\cdots\!41$$$$T^{8} )^{2}$$
$41$ $$1 + 36 T + 10981366 T^{2} + 395313624 T^{3} + 74491912981249 T^{4} + 2021455678408920 T^{5} +$$$$33\!\cdots\!50$$$$T^{6} +$$$$74\!\cdots\!60$$$$T^{7} +$$$$10\!\cdots\!68$$$$T^{8} +$$$$21\!\cdots\!60$$$$T^{9} +$$$$26\!\cdots\!50$$$$T^{10} +$$$$45\!\cdots\!20$$$$T^{11} +$$$$47\!\cdots\!09$$$$T^{12} +$$$$71\!\cdots\!24$$$$T^{13} +$$$$55\!\cdots\!26$$$$T^{14} +$$$$51\!\cdots\!56$$$$T^{15} +$$$$40\!\cdots\!81$$$$T^{16}$$
$43$ $$1 + 68 T - 10748538 T^{2} + 2055805384 T^{3} + 65375958867329 T^{4} - 16226764390392264 T^{5} -$$$$28\!\cdots\!82$$$$T^{6} +$$$$26\!\cdots\!32$$$$T^{7} +$$$$10\!\cdots\!76$$$$T^{8} +$$$$91\!\cdots\!32$$$$T^{9} -$$$$33\!\cdots\!82$$$$T^{10} -$$$$64\!\cdots\!64$$$$T^{11} +$$$$89\!\cdots\!29$$$$T^{12} +$$$$96\!\cdots\!84$$$$T^{13} -$$$$17\!\cdots\!38$$$$T^{14} +$$$$37\!\cdots\!68$$$$T^{15} +$$$$18\!\cdots\!01$$$$T^{16}$$
$47$ $$1 - 2214 T + 16322779 T^{2} - 32521107258 T^{3} + 136095840713065 T^{4} - 267869759907619980 T^{5} +$$$$91\!\cdots\!74$$$$T^{6} -$$$$16\!\cdots\!08$$$$T^{7} +$$$$50\!\cdots\!62$$$$T^{8} -$$$$82\!\cdots\!48$$$$T^{9} +$$$$21\!\cdots\!14$$$$T^{10} -$$$$31\!\cdots\!80$$$$T^{11} +$$$$77\!\cdots\!65$$$$T^{12} -$$$$89\!\cdots\!58$$$$T^{13} +$$$$22\!\cdots\!99$$$$T^{14} -$$$$14\!\cdots\!54$$$$T^{15} +$$$$32\!\cdots\!41$$$$T^{16}$$
$53$ $$1 - 47149064 T^{2} + 1030375014657436 T^{4} -$$$$13\!\cdots\!20$$$$T^{6} +$$$$12\!\cdots\!10$$$$T^{8} -$$$$86\!\cdots\!20$$$$T^{10} +$$$$39\!\cdots\!56$$$$T^{12} -$$$$11\!\cdots\!84$$$$T^{14} +$$$$15\!\cdots\!41$$$$T^{16}$$
$59$ $$1 - 9108 T + 65431078 T^{2} - 344092862520 T^{3} + 1463362600081057 T^{4} - 4890955357569963960 T^{5} +$$$$14\!\cdots\!50$$$$T^{6} -$$$$36\!\cdots\!52$$$$T^{7} +$$$$11\!\cdots\!92$$$$T^{8} -$$$$44\!\cdots\!72$$$$T^{9} +$$$$21\!\cdots\!50$$$$T^{10} -$$$$87\!\cdots\!60$$$$T^{11} +$$$$31\!\cdots\!37$$$$T^{12} -$$$$89\!\cdots\!20$$$$T^{13} +$$$$20\!\cdots\!58$$$$T^{14} -$$$$34\!\cdots\!68$$$$T^{15} +$$$$46\!\cdots\!81$$$$T^{16}$$
$61$ $$1 + 4478 T - 125937 T^{2} - 125289669758 T^{3} - 568176190027387 T^{4} - 742254823045377828 T^{5} +$$$$27\!\cdots\!38$$$$T^{6} +$$$$22\!\cdots\!92$$$$T^{7} +$$$$73\!\cdots\!38$$$$T^{8} +$$$$30\!\cdots\!72$$$$T^{9} +$$$$52\!\cdots\!78$$$$T^{10} -$$$$19\!\cdots\!88$$$$T^{11} -$$$$20\!\cdots\!07$$$$T^{12} -$$$$63\!\cdots\!58$$$$T^{13} -$$$$88\!\cdots\!17$$$$T^{14} +$$$$43\!\cdots\!18$$$$T^{15} +$$$$13\!\cdots\!21$$$$T^{16}$$
$67$ $$1 - 7504 T - 22347594 T^{2} + 226068030400 T^{3} + 738296226968777 T^{4} - 4521766862440091376 T^{5} -$$$$18\!\cdots\!90$$$$T^{6} +$$$$18\!\cdots\!56$$$$T^{7} +$$$$57\!\cdots\!20$$$$T^{8} +$$$$38\!\cdots\!76$$$$T^{9} -$$$$76\!\cdots\!90$$$$T^{10} -$$$$37\!\cdots\!36$$$$T^{11} +$$$$12\!\cdots\!37$$$$T^{12} +$$$$75\!\cdots\!00$$$$T^{13} -$$$$14\!\cdots\!74$$$$T^{14} -$$$$10\!\cdots\!64$$$$T^{15} +$$$$27\!\cdots\!61$$$$T^{16}$$
$71$ $$1 - 125290160 T^{2} + 8106610376011420 T^{4} -$$$$34\!\cdots\!88$$$$T^{6} +$$$$10\!\cdots\!18$$$$T^{8} -$$$$21\!\cdots\!68$$$$T^{10} +$$$$33\!\cdots\!20$$$$T^{12} -$$$$33\!\cdots\!60$$$$T^{14} +$$$$17\!\cdots\!41$$$$T^{16}$$
$73$ $$( 1 - 10358 T + 106803217 T^{2} - 769838088062 T^{3} + 4439859073965124 T^{4} - 21862047555763898942 T^{5} +$$$$86\!\cdots\!77$$$$T^{6} -$$$$23\!\cdots\!18$$$$T^{7} +$$$$65\!\cdots\!61$$$$T^{8} )^{2}$$
$79$ $$1 + 6050 T - 42146805 T^{2} + 267987207070 T^{3} + 3321952223354537 T^{4} - 14945323617952326060 T^{5} +$$$$48\!\cdots\!70$$$$T^{6} +$$$$67\!\cdots\!20$$$$T^{7} -$$$$27\!\cdots\!02$$$$T^{8} +$$$$26\!\cdots\!20$$$$T^{9} +$$$$73\!\cdots\!70$$$$T^{10} -$$$$88\!\cdots\!60$$$$T^{11} +$$$$76\!\cdots\!77$$$$T^{12} +$$$$24\!\cdots\!70$$$$T^{13} -$$$$14\!\cdots\!05$$$$T^{14} +$$$$82\!\cdots\!50$$$$T^{15} +$$$$52\!\cdots\!41$$$$T^{16}$$
$83$ $$1 + 3834 T + 163867483 T^{2} + 609481897254 T^{3} + 15130998622630921 T^{4} + 49888358310056197140 T^{5} +$$$$10\!\cdots\!30$$$$T^{6} +$$$$30\!\cdots\!80$$$$T^{7} +$$$$54\!\cdots\!10$$$$T^{8} +$$$$14\!\cdots\!80$$$$T^{9} +$$$$23\!\cdots\!30$$$$T^{10} +$$$$53\!\cdots\!40$$$$T^{11} +$$$$76\!\cdots\!01$$$$T^{12} +$$$$14\!\cdots\!54$$$$T^{13} +$$$$18\!\cdots\!43$$$$T^{14} +$$$$20\!\cdots\!94$$$$T^{15} +$$$$25\!\cdots\!61$$$$T^{16}$$
$89$ $$1 - 206196488 T^{2} + 19314405141094684 T^{4} -$$$$14\!\cdots\!60$$$$T^{6} +$$$$10\!\cdots\!86$$$$T^{8} -$$$$57\!\cdots\!60$$$$T^{10} +$$$$29\!\cdots\!24$$$$T^{12} -$$$$12\!\cdots\!08$$$$T^{14} +$$$$24\!\cdots\!21$$$$T^{16}$$
$97$ $$1 - 31336 T + 307771782 T^{2} - 2149219106864 T^{3} + 52690258168920329 T^{4} -$$$$68\!\cdots\!16$$$$T^{5} +$$$$38\!\cdots\!30$$$$T^{6} -$$$$46\!\cdots\!00$$$$T^{7} +$$$$68\!\cdots\!04$$$$T^{8} -$$$$40\!\cdots\!00$$$$T^{9} +$$$$30\!\cdots\!30$$$$T^{10} -$$$$47\!\cdots\!56$$$$T^{11} +$$$$32\!\cdots\!09$$$$T^{12} -$$$$11\!\cdots\!64$$$$T^{13} +$$$$14\!\cdots\!42$$$$T^{14} -$$$$13\!\cdots\!96$$$$T^{15} +$$$$37\!\cdots\!41$$$$T^{16}$$
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