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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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