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Properties

Label 273.3
Level 273
Weight 3
Dimension 3708
Nonzero newspaces 30
Newform subspaces 62
Sturm bound 16128
Trace bound 7

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Defining parameters

Level: \( N \) = \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 62 \)
Sturm bound: \(16128\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(273))\).

Total New Old
Modular forms 5664 3932 1732
Cusp forms 5088 3708 1380
Eisenstein series 576 224 352

Trace form

\( 3708 q - 12 q^{3} - 4 q^{4} + 12 q^{5} - 12 q^{6} - 44 q^{7} + 156 q^{8} + 36 q^{9} + O(q^{10}) \) \( 3708 q - 12 q^{3} - 4 q^{4} + 12 q^{5} - 12 q^{6} - 44 q^{7} + 156 q^{8} + 36 q^{9} + 96 q^{10} + 12 q^{11} - 48 q^{12} - 98 q^{13} - 96 q^{14} - 228 q^{15} - 548 q^{16} - 120 q^{17} - 36 q^{18} + 12 q^{19} + 192 q^{20} + 96 q^{21} + 456 q^{22} + 288 q^{23} + 324 q^{24} + 240 q^{25} + 6 q^{26} + 72 q^{27} - 84 q^{28} - 216 q^{29} - 936 q^{30} - 508 q^{31} - 996 q^{32} - 960 q^{33} - 1392 q^{34} - 660 q^{35} - 1044 q^{36} - 512 q^{37} - 348 q^{38} + 150 q^{39} + 768 q^{40} + 840 q^{41} + 528 q^{42} + 1280 q^{43} + 1176 q^{44} + 1008 q^{45} + 1560 q^{46} + 828 q^{47} + 1596 q^{48} + 356 q^{49} + 612 q^{50} + 948 q^{51} + 592 q^{52} + 264 q^{53} + 816 q^{54} - 480 q^{55} - 384 q^{57} - 744 q^{58} - 576 q^{59} - 1020 q^{60} - 1780 q^{61} - 1032 q^{62} - 576 q^{63} - 1900 q^{64} - 1290 q^{65} - 2208 q^{66} - 1052 q^{67} - 792 q^{68} - 1596 q^{69} - 672 q^{70} - 576 q^{71} - 2304 q^{72} - 768 q^{73} - 2796 q^{74} - 2016 q^{75} - 4872 q^{76} - 2952 q^{77} - 2016 q^{78} - 3252 q^{79} - 5280 q^{80} - 120 q^{81} - 3552 q^{82} - 1008 q^{83} - 1248 q^{84} - 576 q^{85} + 444 q^{86} + 1632 q^{87} + 648 q^{88} + 1944 q^{89} + 4272 q^{90} + 1500 q^{91} + 2520 q^{92} + 3408 q^{93} + 4248 q^{94} + 3756 q^{95} + 3936 q^{96} + 3128 q^{97} + 3000 q^{98} + 960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(273))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
273.3.b \(\chi_{273}(92, \cdot)\) 273.3.b.a 48 1
273.3.d \(\chi_{273}(181, \cdot)\) 273.3.d.a 36 1
273.3.f \(\chi_{273}(118, \cdot)\) 273.3.f.a 32 1
273.3.h \(\chi_{273}(155, \cdot)\) 273.3.h.a 56 1
273.3.m \(\chi_{273}(148, \cdot)\) 273.3.m.a 56 2
273.3.o \(\chi_{273}(83, \cdot)\) 273.3.o.a 144 2
273.3.q \(\chi_{273}(166, \cdot)\) 273.3.q.a 36 2
273.3.q.b 38
273.3.s \(\chi_{273}(74, \cdot)\) 273.3.s.a 2 2
273.3.s.b 140
273.3.v \(\chi_{273}(55, \cdot)\) 273.3.v.a 2 2
273.3.v.b 2
273.3.v.c 36
273.3.v.d 36
273.3.w \(\chi_{273}(116, \cdot)\) 273.3.w.a 2 2
273.3.w.b 2
273.3.w.c 16
273.3.w.d 120
273.3.x \(\chi_{273}(179, \cdot)\) 273.3.x.a 2 2
273.3.x.b 140
273.3.z \(\chi_{273}(61, \cdot)\) 273.3.z.a 2 2
273.3.z.b 34
273.3.z.c 38
273.3.bb \(\chi_{273}(40, \cdot)\) 273.3.bb.a 4 2
273.3.bb.b 28
273.3.bb.c 32
273.3.bc \(\chi_{273}(134, \cdot)\) 273.3.bc.a 112 2
273.3.be \(\chi_{273}(29, \cdot)\) 273.3.be.a 112 2
273.3.bg \(\chi_{273}(10, \cdot)\) 273.3.bg.a 36 2
273.3.bg.b 38
273.3.bi \(\chi_{273}(103, \cdot)\) 273.3.bi.a 36 2
273.3.bi.b 40
273.3.bk \(\chi_{273}(53, \cdot)\) 273.3.bk.a 128 2
273.3.bm \(\chi_{273}(191, \cdot)\) 273.3.bm.a 2 2
273.3.bm.b 140
273.3.bo \(\chi_{273}(160, \cdot)\) 273.3.bo.a 2 2
273.3.bo.b 2
273.3.bo.c 36
273.3.bo.d 36
273.3.bp \(\chi_{273}(23, \cdot)\) 273.3.bp.a 2 2
273.3.bp.b 140
273.3.bq \(\chi_{273}(178, \cdot)\) 273.3.bq.a 2 2
273.3.bq.b 34
273.3.bq.c 38
273.3.bs \(\chi_{273}(59, \cdot)\) 273.3.bs.a 4 4
273.3.bs.b 280
273.3.bu \(\chi_{273}(37, \cdot)\) 273.3.bu.a 72 4
273.3.bu.b 76
273.3.bx \(\chi_{273}(58, \cdot)\) 273.3.bx.a 72 4
273.3.bx.b 76
273.3.ca \(\chi_{273}(20, \cdot)\) 273.3.ca.a 4 4
273.3.ca.b 4
273.3.ca.c 272
273.3.cb \(\chi_{273}(5, \cdot)\) 273.3.cb.a 4 4
273.3.cb.b 4
273.3.cb.c 272
273.3.ce \(\chi_{273}(85, \cdot)\) 273.3.ce.a 56 4
273.3.ce.b 56
273.3.cf \(\chi_{273}(109, \cdot)\) 273.3.cf.a 76 4
273.3.cf.b 76
273.3.ch \(\chi_{273}(80, \cdot)\) 273.3.ch.a 4 4
273.3.ch.b 280

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(273))\) into lower level spaces

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