# Properties

 Label 273.2 Level 273 Weight 2 Dimension 1803 Nonzero newspaces 30 Newform subspaces 86 Sturm bound 10752 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Newform subspaces: $$86$$ Sturm bound: $$10752$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(273))$$.

Total New Old
Modular forms 2976 2019 957
Cusp forms 2401 1803 598
Eisenstein series 575 216 359

## Trace form

 $$1803 q + 9 q^{2} - 17 q^{3} - 31 q^{4} + 6 q^{5} - 27 q^{6} - 53 q^{7} - 27 q^{8} - 33 q^{9} + O(q^{10})$$ $$1803 q + 9 q^{2} - 17 q^{3} - 31 q^{4} + 6 q^{5} - 27 q^{6} - 53 q^{7} - 27 q^{8} - 33 q^{9} - 102 q^{10} - 24 q^{11} - 75 q^{12} - 83 q^{13} - 27 q^{14} - 66 q^{15} - 95 q^{16} - 6 q^{17} - 63 q^{18} - 96 q^{19} - 78 q^{20} - 49 q^{21} - 180 q^{22} - 24 q^{23} - 87 q^{24} - 111 q^{25} - 81 q^{26} - 125 q^{27} - 171 q^{28} - 42 q^{29} - 66 q^{30} - 76 q^{31} - 63 q^{32} - 36 q^{33} - 102 q^{34} - 18 q^{35} + 25 q^{36} - 26 q^{37} + 72 q^{38} + 21 q^{39} - 90 q^{40} - 6 q^{41} - 27 q^{42} - 196 q^{43} - 36 q^{44} + 6 q^{45} - 216 q^{46} - 60 q^{47} - 47 q^{48} - 145 q^{49} - 129 q^{50} - 102 q^{51} - 251 q^{52} - 126 q^{53} - 111 q^{54} - 240 q^{55} - 159 q^{56} - 236 q^{57} - 246 q^{58} - 156 q^{59} - 198 q^{60} - 214 q^{61} - 240 q^{62} - 85 q^{63} - 355 q^{64} - 108 q^{65} - 36 q^{66} - 104 q^{67} - 66 q^{68} - 12 q^{69} - 138 q^{70} + 48 q^{71} - 3 q^{72} + 30 q^{73} + 126 q^{74} + 117 q^{75} + 252 q^{76} + 180 q^{77} + 225 q^{78} + 132 q^{79} + 498 q^{80} + 75 q^{81} + 414 q^{82} + 228 q^{83} + 269 q^{84} + 216 q^{85} + 240 q^{86} + 186 q^{87} + 564 q^{88} + 198 q^{89} + 126 q^{90} + 111 q^{91} + 408 q^{92} + 88 q^{93} + 360 q^{94} + 84 q^{95} + 237 q^{96} + 206 q^{97} + 129 q^{98} - 204 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$

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
273.2.a $$\chi_{273}(1, \cdot)$$ 273.2.a.a 1 1
273.2.a.b 1
273.2.a.c 2
273.2.a.d 3
273.2.a.e 4
273.2.c $$\chi_{273}(64, \cdot)$$ 273.2.c.a 2 1
273.2.c.b 6
273.2.c.c 8
273.2.e $$\chi_{273}(209, \cdot)$$ 273.2.e.a 32 1
273.2.g $$\chi_{273}(272, \cdot)$$ 273.2.g.a 32 1
273.2.i $$\chi_{273}(79, \cdot)$$ 273.2.i.a 2 2
273.2.i.b 6
273.2.i.c 6
273.2.i.d 8
273.2.i.e 10
273.2.j $$\chi_{273}(100, \cdot)$$ 273.2.j.a 2 2
273.2.j.b 16
273.2.j.c 20
273.2.k $$\chi_{273}(22, \cdot)$$ 273.2.k.a 6 2
273.2.k.b 6
273.2.k.c 6
273.2.k.d 6
273.2.l $$\chi_{273}(16, \cdot)$$ 273.2.l.a 2 2
273.2.l.b 16
273.2.l.c 20
273.2.n $$\chi_{273}(8, \cdot)$$ 273.2.n.a 4 2
273.2.n.b 4
273.2.n.c 48
273.2.p $$\chi_{273}(34, \cdot)$$ 273.2.p.a 4 2
273.2.p.b 4
273.2.p.c 4
273.2.p.d 4
273.2.p.e 12
273.2.p.f 12
273.2.r $$\chi_{273}(68, \cdot)$$ 273.2.r.a 2 2
273.2.r.b 64
273.2.t $$\chi_{273}(4, \cdot)$$ 273.2.t.a 2 2
273.2.t.b 4
273.2.t.c 12
273.2.t.d 20
273.2.u $$\chi_{273}(62, \cdot)$$ 273.2.u.a 2 2
273.2.u.b 2
273.2.u.c 64
273.2.y $$\chi_{273}(101, \cdot)$$ 273.2.y.a 2 2
273.2.y.b 64
273.2.ba $$\chi_{273}(38, \cdot)$$ 273.2.ba.a 2 2
273.2.ba.b 2
273.2.ba.c 64
273.2.bd $$\chi_{273}(43, \cdot)$$ 273.2.bd.a 16 2
273.2.bd.b 16
273.2.bf $$\chi_{273}(152, \cdot)$$ 273.2.bf.a 2 2
273.2.bf.b 64
273.2.bh $$\chi_{273}(131, \cdot)$$ 273.2.bh.a 64 2
273.2.bj $$\chi_{273}(25, \cdot)$$ 273.2.bj.a 2 2
273.2.bj.b 2
273.2.bj.c 16
273.2.bj.d 16
273.2.bl $$\chi_{273}(88, \cdot)$$ 273.2.bl.a 2 2
273.2.bl.b 4
273.2.bl.c 12
273.2.bl.d 20
273.2.bn $$\chi_{273}(146, \cdot)$$ 273.2.bn.a 2 2
273.2.bn.b 2
273.2.bn.c 64
273.2.br $$\chi_{273}(17, \cdot)$$ 273.2.br.a 2 2
273.2.br.b 64
273.2.bt $$\chi_{273}(136, \cdot)$$ 273.2.bt.a 36 4
273.2.bt.b 40
273.2.bv $$\chi_{273}(2, \cdot)$$ 273.2.bv.a 4 4
273.2.bv.b 128
273.2.bw $$\chi_{273}(11, \cdot)$$ 273.2.bw.a 4 4
273.2.bw.b 128
273.2.by $$\chi_{273}(76, \cdot)$$ 273.2.by.a 4 4
273.2.by.b 4
273.2.by.c 32
273.2.by.d 32
273.2.bz $$\chi_{273}(31, \cdot)$$ 273.2.bz.a 36 4
273.2.bz.b 36
273.2.cc $$\chi_{273}(50, \cdot)$$ 273.2.cc.a 112 4
273.2.cd $$\chi_{273}(44, \cdot)$$ 273.2.cd.a 4 4
273.2.cd.b 4
273.2.cd.c 8
273.2.cd.d 8
273.2.cd.e 112
273.2.cg $$\chi_{273}(19, \cdot)$$ 273.2.cg.a 36 4
273.2.cg.b 40

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(273))$$ into lower level spaces

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