# Properties

 Label 273.12 Level 273 Weight 12 Dimension 20884 Nonzero newspaces 30 Sturm bound 64512 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$12$$ Nonzero newspaces: $$30$$ Sturm bound: $$64512$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{12}(\Gamma_1(273))$$.

Total New Old
Modular forms 29856 21100 8756
Cusp forms 29280 20884 8396
Eisenstein series 576 216 360

## Trace form

 $$20884q + 312q^{2} - 504q^{3} + 32492q^{4} - 51852q^{5} + 17472q^{6} - 88548q^{7} - 450924q^{8} + 426804q^{9} + O(q^{10})$$ $$20884q + 312q^{2} - 504q^{3} + 32492q^{4} - 51852q^{5} + 17472q^{6} - 88548q^{7} - 450924q^{8} + 426804q^{9} - 3817104q^{10} - 4703964q^{11} + 7863612q^{12} + 5305938q^{13} - 15033936q^{14} - 21129180q^{15} + 73913196q^{16} + 38687748q^{17} + 53735880q^{18} - 187327948q^{19} + 180289368q^{20} + 40088352q^{21} - 27369120q^{22} - 145071360q^{23} - 107489112q^{24} + 335592400q^{25} + 760747902q^{26} - 501342924q^{27} + 480968164q^{28} - 776498964q^{29} + 1069946748q^{30} - 499698828q^{31} + 2245036716q^{32} + 530769636q^{33} - 608988504q^{34} + 564563172q^{35} + 617055036q^{36} - 3864745700q^{37} - 5726106348q^{38} - 4170226074q^{39} + 15940758576q^{40} - 3932529444q^{41} - 756502968q^{42} + 13228987464q^{43} + 5695718136q^{44} - 15921316152q^{45} - 17783913672q^{46} - 4627231404q^{47} + 11462090184q^{48} - 1220351176q^{49} - 3138789132q^{50} + 23098259700q^{51} + 30480054048q^{52} - 18526135464q^{53} - 36413527692q^{54} - 7823234952q^{55} + 96670542960q^{56} + 43814256792q^{57} - 6547660992q^{58} - 53732439840q^{59} - 56022895548q^{60} + 41776857504q^{61} + 73372108176q^{62} - 8911889844q^{63} - 134618514220q^{64} + 158896994646q^{65} + 213756253140q^{66} - 182861127332q^{67} - 71771846784q^{68} - 167652691884q^{69} + 175520953416q^{70} - 76013831496q^{71} + 216575696616q^{72} + 230778467840q^{73} - 179407216140q^{74} - 106374859260q^{75} + 372348683840q^{76} + 569214299904q^{77} - 544617775632q^{78} + 46195646324q^{79} - 567807727536q^{80} + 276421273896q^{81} - 1253771931552q^{82} - 429773948520q^{83} + 321450371844q^{84} + 879463709340q^{85} + 2650289392212q^{86} + 197817291288q^{87} - 678791940672q^{88} - 2001400378128q^{89} - 524085856560q^{90} - 1282906149920q^{91} - 1332216326736q^{92} + 737139607404q^{93} + 3238313612544q^{94} + 1079913483372q^{95} + 1263466327788q^{96} - 337625636448q^{97} + 74970760800q^{98} + 458966924928q^{99} + O(q^{100})$$

## Decomposition of $$S_{12}^{\mathrm{new}}(\Gamma_1(273))$$

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
273.12.a $$\chi_{273}(1, \cdot)$$ 273.12.a.a 13 1
273.12.a.b 15
273.12.a.c 16
273.12.a.d 17
273.12.a.e 17
273.12.a.f 18
273.12.a.g 18
273.12.a.h 18
273.12.c $$\chi_{273}(64, \cdot)$$ n/a 152 1
273.12.e $$\chi_{273}(209, \cdot)$$ n/a 352 1
273.12.g $$\chi_{273}(272, \cdot)$$ n/a 408 1
273.12.i $$\chi_{273}(79, \cdot)$$ n/a 352 2
273.12.j $$\chi_{273}(100, \cdot)$$ n/a 410 2
273.12.k $$\chi_{273}(22, \cdot)$$ n/a 312 2
273.12.l $$\chi_{273}(16, \cdot)$$ n/a 410 2
273.12.n $$\chi_{273}(8, \cdot)$$ n/a 616 2
273.12.p $$\chi_{273}(34, \cdot)$$ n/a 408 2
273.12.r $$\chi_{273}(68, \cdot)$$ n/a 814 2
273.12.t $$\chi_{273}(4, \cdot)$$ n/a 410 2
273.12.u $$\chi_{273}(62, \cdot)$$ n/a 812 2
273.12.y $$\chi_{273}(101, \cdot)$$ n/a 814 2
273.12.ba $$\chi_{273}(38, \cdot)$$ n/a 812 2
273.12.bd $$\chi_{273}(43, \cdot)$$ n/a 304 2
273.12.bf $$\chi_{273}(152, \cdot)$$ n/a 814 2
273.12.bh $$\chi_{273}(131, \cdot)$$ n/a 704 2
273.12.bj $$\chi_{273}(25, \cdot)$$ n/a 412 2
273.12.bl $$\chi_{273}(88, \cdot)$$ n/a 410 2
273.12.bn $$\chi_{273}(146, \cdot)$$ n/a 812 2
273.12.br $$\chi_{273}(17, \cdot)$$ n/a 814 2
273.12.bt $$\chi_{273}(136, \cdot)$$ n/a 820 4
273.12.bv $$\chi_{273}(2, \cdot)$$ n/a 1628 4
273.12.bw $$\chi_{273}(11, \cdot)$$ n/a 1628 4
273.12.by $$\chi_{273}(76, \cdot)$$ n/a 824 4
273.12.bz $$\chi_{273}(31, \cdot)$$ n/a 824 4
273.12.cc $$\chi_{273}(50, \cdot)$$ n/a 1232 4
273.12.cd $$\chi_{273}(44, \cdot)$$ n/a 1624 4
273.12.cg $$\chi_{273}(19, \cdot)$$ n/a 820 4

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

## Decomposition of $$S_{12}^{\mathrm{old}}(\Gamma_1(273))$$ into lower level spaces

$$S_{12}^{\mathrm{old}}(\Gamma_1(273)) \cong$$ $$S_{12}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 2}$$$$\oplus$$$$S_{12}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 2}$$