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Properties

Label 990.2
Level 990
Weight 2
Dimension 6164
Nonzero newspaces 24
Newform subspaces 103
Sturm bound 103680
Trace bound 5

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Defining parameters

Level: \( N \) = \( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 103 \)
Sturm bound: \(103680\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(990))\).

Total New Old
Modular forms 27200 6164 21036
Cusp forms 24641 6164 18477
Eisenstein series 2559 0 2559

Trace form

\( 6164 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 44 q^{7} + 6 q^{8} + 28 q^{9} + O(q^{10}) \) \( 6164 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 10 q^{5} + 12 q^{6} - 44 q^{7} + 6 q^{8} + 28 q^{9} + 12 q^{10} + 6 q^{11} + 16 q^{12} + 8 q^{13} + 20 q^{14} + 48 q^{15} - 6 q^{16} - 4 q^{17} + 8 q^{18} - 14 q^{19} + 22 q^{20} + 72 q^{21} + 10 q^{22} + 112 q^{23} + 8 q^{24} + 74 q^{25} + 108 q^{26} + 168 q^{27} + 60 q^{28} + 172 q^{29} + 60 q^{30} + 116 q^{31} + 24 q^{32} + 190 q^{33} + 112 q^{34} + 108 q^{35} + 172 q^{37} + 96 q^{38} - 8 q^{39} + 36 q^{40} + 8 q^{41} - 48 q^{42} + 120 q^{43} + 18 q^{44} - 140 q^{45} + 40 q^{46} - 80 q^{47} - 20 q^{48} + 74 q^{49} - 34 q^{50} - 40 q^{51} + 20 q^{52} + 120 q^{53} - 60 q^{54} + 190 q^{55} - 40 q^{56} + 108 q^{57} + 12 q^{58} + 250 q^{59} + 16 q^{60} + 152 q^{61} + 20 q^{62} + 240 q^{63} + 6 q^{64} + 264 q^{65} + 48 q^{66} + 296 q^{67} + 72 q^{68} + 288 q^{69} + 48 q^{70} + 304 q^{71} + 12 q^{72} + 156 q^{73} + 60 q^{74} + 8 q^{75} + 72 q^{76} + 172 q^{77} + 56 q^{78} + 124 q^{79} - 20 q^{80} - 84 q^{81} + 166 q^{82} - 282 q^{83} - 136 q^{84} + 30 q^{85} - 130 q^{86} - 360 q^{87} - 10 q^{88} - 268 q^{89} - 88 q^{90} + 448 q^{91} - 108 q^{92} - 464 q^{93} + 96 q^{94} - 214 q^{95} + 16 q^{96} + 178 q^{97} - 216 q^{98} - 620 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)

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
990.2.a \(\chi_{990}(1, \cdot)\) 990.2.a.a 1 1
990.2.a.b 1
990.2.a.c 1
990.2.a.d 1
990.2.a.e 1
990.2.a.f 1
990.2.a.g 1
990.2.a.h 1
990.2.a.i 1
990.2.a.j 1
990.2.a.k 1
990.2.a.l 1
990.2.a.m 2
990.2.c \(\chi_{990}(199, \cdot)\) 990.2.c.a 2 1
990.2.c.b 2
990.2.c.c 2
990.2.c.d 2
990.2.c.e 2
990.2.c.f 4
990.2.c.g 4
990.2.c.h 4
990.2.c.i 4
990.2.d \(\chi_{990}(791, \cdot)\) 990.2.d.a 8 1
990.2.d.b 8
990.2.f \(\chi_{990}(989, \cdot)\) 990.2.f.a 4 1
990.2.f.b 4
990.2.f.c 16
990.2.i \(\chi_{990}(331, \cdot)\) 990.2.i.a 2 2
990.2.i.b 2
990.2.i.c 6
990.2.i.d 6
990.2.i.e 6
990.2.i.f 6
990.2.i.g 6
990.2.i.h 6
990.2.i.i 12
990.2.i.j 14
990.2.i.k 14
990.2.k \(\chi_{990}(287, \cdot)\) 990.2.k.a 8 2
990.2.k.b 8
990.2.k.c 12
990.2.k.d 12
990.2.m \(\chi_{990}(307, \cdot)\) 990.2.m.a 4 2
990.2.m.b 4
990.2.m.c 4
990.2.m.d 4
990.2.m.e 4
990.2.m.f 8
990.2.m.g 8
990.2.m.h 24
990.2.n \(\chi_{990}(91, \cdot)\) 990.2.n.a 4 4
990.2.n.b 4
990.2.n.c 4
990.2.n.d 4
990.2.n.e 4
990.2.n.f 4
990.2.n.g 4
990.2.n.h 4
990.2.n.i 8
990.2.n.j 8
990.2.n.k 8
990.2.n.l 12
990.2.n.m 12
990.2.o \(\chi_{990}(329, \cdot)\) 990.2.o.a 144 2
990.2.s \(\chi_{990}(529, \cdot)\) 990.2.s.a 4 2
990.2.s.b 8
990.2.s.c 52
990.2.s.d 56
990.2.t \(\chi_{990}(131, \cdot)\) 990.2.t.a 48 2
990.2.t.b 48
990.2.x \(\chi_{990}(359, \cdot)\) 990.2.x.a 96 4
990.2.z \(\chi_{990}(161, \cdot)\) 990.2.z.a 32 4
990.2.z.b 32
990.2.ba \(\chi_{990}(289, \cdot)\) 990.2.ba.a 8 4
990.2.ba.b 8
990.2.ba.c 8
990.2.ba.d 8
990.2.ba.e 8
990.2.ba.f 16
990.2.ba.g 16
990.2.ba.h 16
990.2.ba.i 32
990.2.bc \(\chi_{990}(23, \cdot)\) 990.2.bc.a 120 4
990.2.bc.b 120
990.2.be \(\chi_{990}(43, \cdot)\) 990.2.be.a 8 4
990.2.be.b 8
990.2.be.c 272
990.2.bg \(\chi_{990}(31, \cdot)\) 990.2.bg.a 88 8
990.2.bg.b 88
990.2.bg.c 104
990.2.bg.d 104
990.2.bh \(\chi_{990}(73, \cdot)\) 990.2.bh.a 48 8
990.2.bh.b 48
990.2.bh.c 48
990.2.bh.d 96
990.2.bj \(\chi_{990}(53, \cdot)\) 990.2.bj.a 96 8
990.2.bj.b 96
990.2.bm \(\chi_{990}(41, \cdot)\) 990.2.bm.a 192 8
990.2.bm.b 192
990.2.bn \(\chi_{990}(49, \cdot)\) 990.2.bn.a 576 8
990.2.br \(\chi_{990}(29, \cdot)\) 990.2.br.a 576 8
990.2.bt \(\chi_{990}(7, \cdot)\) 990.2.bt.a 1152 16
990.2.bv \(\chi_{990}(47, \cdot)\) 990.2.bv.a 1152 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(990))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(990)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)