Properties

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

Downloads

Learn more

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

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