Properties

Label 1170.2
Level 1170
Weight 2
Dimension 8672
Nonzero newspaces 50
Sturm bound 145152
Trace bound 31

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Defining parameters

Level: \( N \) = \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 50 \)
Sturm bound: \(145152\)
Trace bound: \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1170))\).

Total New Old
Modular forms 37824 8672 29152
Cusp forms 34753 8672 26081
Eisenstein series 3071 0 3071

Trace form

\( 8672q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 32q^{7} + 28q^{9} + O(q^{10}) \) \( 8672q - 6q^{2} - 12q^{3} - 6q^{4} - 10q^{5} + 12q^{6} - 32q^{7} + 28q^{9} + 7q^{10} + 28q^{11} + 16q^{12} - 34q^{13} + 16q^{14} + 48q^{15} - 14q^{16} + 6q^{17} + 8q^{18} - 40q^{19} + 19q^{20} + 72q^{21} + 20q^{22} + 48q^{23} - 12q^{24} + 34q^{25} - 6q^{26} + 48q^{27} + 24q^{28} + 126q^{29} + 48q^{30} + 160q^{31} - 6q^{32} + 124q^{33} + 136q^{34} + 136q^{35} + 76q^{36} + 214q^{37} + 132q^{38} + 128q^{39} + 6q^{40} + 130q^{41} + 16q^{42} + 116q^{43} + 80q^{44} - 40q^{45} + 144q^{46} + 72q^{47} - 20q^{48} + 154q^{49} - 13q^{50} + 36q^{51} + 20q^{52} - 36q^{53} - 60q^{54} + 124q^{55} - 16q^{56} - 52q^{57} - 14q^{58} + 28q^{59} + 16q^{60} - 10q^{61} + 72q^{62} + 176q^{63} + 12q^{64} + 291q^{65} + 96q^{66} + 268q^{67} + 78q^{68} + 272q^{69} + 156q^{70} + 480q^{71} + 12q^{72} + 468q^{73} + 130q^{74} + 108q^{75} + 84q^{76} + 312q^{77} + 28q^{78} + 160q^{79} - q^{80} + 188q^{81} + 26q^{82} + 216q^{83} + 24q^{84} + 129q^{85} + 92q^{86} + 232q^{87} + 20q^{88} + 188q^{89} + 112q^{90} + 104q^{91} + 24q^{92} + 80q^{93} - 64q^{94} + 16q^{96} - 32q^{97} - 138q^{98} - 248q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)

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
1170.2.a \(\chi_{1170}(1, \cdot)\) 1170.2.a.a 1 1
1170.2.a.b 1
1170.2.a.c 1
1170.2.a.d 1
1170.2.a.e 1
1170.2.a.f 1
1170.2.a.g 1
1170.2.a.h 1
1170.2.a.i 1
1170.2.a.j 1
1170.2.a.k 1
1170.2.a.l 1
1170.2.a.m 1
1170.2.a.n 1
1170.2.a.o 2
1170.2.a.p 2
1170.2.a.q 2
1170.2.b \(\chi_{1170}(181, \cdot)\) 1170.2.b.a 2 1
1170.2.b.b 2
1170.2.b.c 2
1170.2.b.d 4
1170.2.b.e 4
1170.2.b.f 4
1170.2.b.g 8
1170.2.e \(\chi_{1170}(469, \cdot)\) 1170.2.e.a 2 1
1170.2.e.b 2
1170.2.e.c 2
1170.2.e.d 2
1170.2.e.e 4
1170.2.e.f 6
1170.2.e.g 6
1170.2.e.h 6
1170.2.f \(\chi_{1170}(649, \cdot)\) 1170.2.f.a 4 1
1170.2.f.b 4
1170.2.f.c 6
1170.2.f.d 6
1170.2.f.e 8
1170.2.f.f 8
1170.2.i \(\chi_{1170}(451, \cdot)\) 1170.2.i.a 2 2
1170.2.i.b 2
1170.2.i.c 2
1170.2.i.d 2
1170.2.i.e 2
1170.2.i.f 2
1170.2.i.g 2
1170.2.i.h 2
1170.2.i.i 2
1170.2.i.j 2
1170.2.i.k 2
1170.2.i.l 2
1170.2.i.m 4
1170.2.i.n 4
1170.2.i.o 4
1170.2.i.p 4
1170.2.i.q 4
1170.2.j \(\chi_{1170}(391, \cdot)\) 1170.2.j.a 2 2
1170.2.j.b 2
1170.2.j.c 2
1170.2.j.d 2
1170.2.j.e 2
1170.2.j.f 2
1170.2.j.g 4
1170.2.j.h 8
1170.2.j.i 10
1170.2.j.j 10
1170.2.j.k 12
1170.2.j.l 12
1170.2.j.m 12
1170.2.j.n 16
1170.2.k \(\chi_{1170}(601, \cdot)\) n/a 112 2
1170.2.l \(\chi_{1170}(61, \cdot)\) n/a 112 2
1170.2.m \(\chi_{1170}(73, \cdot)\) 1170.2.m.a 2 2
1170.2.m.b 2
1170.2.m.c 2
1170.2.m.d 4
1170.2.m.e 4
1170.2.m.f 12
1170.2.m.g 14
1170.2.m.h 14
1170.2.m.i 16
1170.2.o \(\chi_{1170}(53, \cdot)\) 1170.2.o.a 12 2
1170.2.o.b 12
1170.2.o.c 12
1170.2.o.d 12
1170.2.q \(\chi_{1170}(359, \cdot)\) 1170.2.q.a 4 2
1170.2.q.b 4
1170.2.q.c 24
1170.2.q.d 24
1170.2.s \(\chi_{1170}(161, \cdot)\) 1170.2.s.a 4 2
1170.2.s.b 4
1170.2.s.c 4
1170.2.s.d 4
1170.2.s.e 8
1170.2.s.f 12
1170.2.s.g 12
1170.2.v \(\chi_{1170}(233, \cdot)\) 1170.2.v.a 4 2
1170.2.v.b 4
1170.2.v.c 24
1170.2.v.d 24
1170.2.w \(\chi_{1170}(307, \cdot)\) 1170.2.w.a 2 2
1170.2.w.b 2
1170.2.w.c 2
1170.2.w.d 4
1170.2.w.e 4
1170.2.w.f 12
1170.2.w.g 14
1170.2.w.h 14
1170.2.w.i 16
1170.2.y \(\chi_{1170}(529, \cdot)\) n/a 168 2
1170.2.bb \(\chi_{1170}(511, \cdot)\) n/a 112 2
1170.2.bd \(\chi_{1170}(439, \cdot)\) n/a 168 2
1170.2.bg \(\chi_{1170}(259, \cdot)\) n/a 168 2
1170.2.bj \(\chi_{1170}(199, \cdot)\) 1170.2.bj.a 8 2
1170.2.bj.b 8
1170.2.bj.c 12
1170.2.bj.d 12
1170.2.bj.e 16
1170.2.bj.f 16
1170.2.bm \(\chi_{1170}(121, \cdot)\) n/a 112 2
1170.2.bo \(\chi_{1170}(79, \cdot)\) n/a 144 2
1170.2.bp \(\chi_{1170}(289, \cdot)\) 1170.2.bp.a 4 2
1170.2.bp.b 4
1170.2.bp.c 4
1170.2.bp.d 4
1170.2.bp.e 4
1170.2.bp.f 4
1170.2.bp.g 8
1170.2.bp.h 12
1170.2.bp.i 24
1170.2.bs \(\chi_{1170}(361, \cdot)\) 1170.2.bs.a 4 2
1170.2.bs.b 4
1170.2.bs.c 4
1170.2.bs.d 4
1170.2.bs.e 4
1170.2.bs.f 8
1170.2.bs.g 8
1170.2.bs.h 8
1170.2.bt \(\chi_{1170}(571, \cdot)\) n/a 112 2
1170.2.bv \(\chi_{1170}(139, \cdot)\) n/a 168 2
1170.2.bz \(\chi_{1170}(49, \cdot)\) n/a 168 2
1170.2.cb \(\chi_{1170}(67, \cdot)\) n/a 336 4
1170.2.cc \(\chi_{1170}(223, \cdot)\) n/a 336 4
1170.2.cf \(\chi_{1170}(37, \cdot)\) n/a 140 4
1170.2.cg \(\chi_{1170}(697, \cdot)\) n/a 336 4
1170.2.cj \(\chi_{1170}(113, \cdot)\) n/a 336 4
1170.2.cl \(\chi_{1170}(17, \cdot)\) n/a 112 4
1170.2.cm \(\chi_{1170}(23, \cdot)\) n/a 336 4
1170.2.cp \(\chi_{1170}(77, \cdot)\) n/a 336 4
1170.2.cr \(\chi_{1170}(239, \cdot)\) n/a 336 4
1170.2.cs \(\chi_{1170}(11, \cdot)\) n/a 224 4
1170.2.cu \(\chi_{1170}(71, \cdot)\) 1170.2.cu.a 8 4
1170.2.cu.b 8
1170.2.cu.c 8
1170.2.cu.d 8
1170.2.cu.e 16
1170.2.cu.f 16
1170.2.cx \(\chi_{1170}(41, \cdot)\) n/a 224 4
1170.2.cz \(\chi_{1170}(509, \cdot)\) n/a 336 4
1170.2.da \(\chi_{1170}(59, \cdot)\) n/a 336 4
1170.2.dc \(\chi_{1170}(89, \cdot)\) n/a 112 4
1170.2.df \(\chi_{1170}(281, \cdot)\) n/a 224 4
1170.2.dg \(\chi_{1170}(443, \cdot)\) n/a 288 4
1170.2.dj \(\chi_{1170}(653, \cdot)\) n/a 336 4
1170.2.dk \(\chi_{1170}(107, \cdot)\) n/a 112 4
1170.2.dm \(\chi_{1170}(563, \cdot)\) n/a 336 4
1170.2.do \(\chi_{1170}(457, \cdot)\) n/a 336 4
1170.2.dr \(\chi_{1170}(187, \cdot)\) n/a 336 4
1170.2.ds \(\chi_{1170}(163, \cdot)\) n/a 140 4
1170.2.dv \(\chi_{1170}(7, \cdot)\) n/a 336 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1170))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1170)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 2}\)