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Properties

Label 1092.2
Level 1092
Weight 2
Dimension 13140
Nonzero newspaces 60
Sturm bound 129024
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(129024\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1092))\).

Total New Old
Modular forms 33696 13588 20108
Cusp forms 30817 13140 17677
Eisenstein series 2879 448 2431

Trace form

\( 13140 q - 2 q^{3} - 36 q^{4} - 12 q^{5} - 12 q^{6} - 20 q^{7} + 12 q^{8} - 30 q^{9} + O(q^{10}) \) \( 13140 q - 2 q^{3} - 36 q^{4} - 12 q^{5} - 12 q^{6} - 20 q^{7} + 12 q^{8} - 30 q^{9} - 12 q^{11} + 24 q^{12} - 110 q^{13} + 48 q^{14} + 12 q^{15} + 12 q^{16} + 12 q^{17} + 48 q^{18} + 48 q^{19} + 96 q^{20} + 32 q^{21} - 24 q^{22} + 72 q^{23} + 60 q^{24} + 96 q^{25} + 90 q^{26} + 76 q^{27} - 84 q^{28} + 132 q^{29} + 12 q^{30} + 56 q^{31} + 60 q^{32} + 30 q^{33} + 12 q^{35} - 84 q^{36} - 56 q^{37} - 36 q^{38} + 18 q^{39} - 240 q^{40} + 84 q^{41} - 144 q^{42} - 16 q^{43} - 168 q^{44} - 30 q^{45} - 336 q^{46} + 12 q^{47} - 228 q^{48} - 4 q^{49} - 300 q^{50} + 6 q^{51} - 288 q^{52} + 48 q^{53} - 96 q^{54} + 24 q^{55} - 144 q^{56} - 8 q^{57} - 240 q^{58} - 228 q^{60} + 116 q^{61} - 120 q^{62} - 28 q^{63} - 156 q^{64} + 42 q^{65} - 180 q^{66} + 40 q^{67} + 72 q^{68} - 180 q^{69} + 24 q^{70} - 48 q^{71} - 120 q^{72} - 36 q^{73} + 132 q^{74} - 144 q^{75} + 120 q^{76} + 144 q^{77} - 168 q^{78} + 168 q^{79} + 144 q^{80} - 306 q^{81} + 120 q^{82} + 168 q^{83} + 72 q^{84} + 108 q^{85} + 36 q^{86} + 24 q^{87} + 72 q^{88} + 120 q^{89} - 120 q^{90} + 240 q^{91} + 24 q^{92} - 74 q^{93} - 192 q^{94} + 228 q^{95} - 144 q^{96} + 56 q^{97} - 24 q^{98} + 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1092))\)

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
1092.2.a \(\chi_{1092}(1, \cdot)\) 1092.2.a.a 1 1
1092.2.a.b 1
1092.2.a.c 1
1092.2.a.d 1
1092.2.a.e 1
1092.2.a.f 2
1092.2.a.g 2
1092.2.a.h 3
1092.2.c \(\chi_{1092}(391, \cdot)\) 1092.2.c.a 48 1
1092.2.c.b 48
1092.2.e \(\chi_{1092}(337, \cdot)\) 1092.2.e.a 2 1
1092.2.e.b 2
1092.2.e.c 2
1092.2.e.d 2
1092.2.e.e 4
1092.2.f \(\chi_{1092}(911, \cdot)\) n/a 144 1
1092.2.h \(\chi_{1092}(545, \cdot)\) 1092.2.h.a 2 1
1092.2.h.b 2
1092.2.h.c 32
1092.2.j \(\chi_{1092}(155, \cdot)\) n/a 168 1
1092.2.l \(\chi_{1092}(209, \cdot)\) 1092.2.l.a 32 1
1092.2.o \(\chi_{1092}(727, \cdot)\) n/a 112 1
1092.2.q \(\chi_{1092}(625, \cdot)\) 1092.2.q.a 4 2
1092.2.q.b 6
1092.2.q.c 6
1092.2.q.d 6
1092.2.q.e 10
1092.2.r \(\chi_{1092}(289, \cdot)\) 1092.2.r.a 2 2
1092.2.r.b 2
1092.2.r.c 2
1092.2.r.d 2
1092.2.r.e 12
1092.2.r.f 18
1092.2.s \(\chi_{1092}(373, \cdot)\) 1092.2.s.a 2 2
1092.2.s.b 2
1092.2.s.c 2
1092.2.s.d 2
1092.2.s.e 12
1092.2.s.f 18
1092.2.t \(\chi_{1092}(757, \cdot)\) 1092.2.t.a 2 2
1092.2.t.b 6
1092.2.t.c 8
1092.2.t.d 8
1092.2.t.e 8
1092.2.u \(\chi_{1092}(83, \cdot)\) n/a 432 2
1092.2.x \(\chi_{1092}(463, \cdot)\) n/a 168 2
1092.2.z \(\chi_{1092}(265, \cdot)\) 1092.2.z.a 20 2
1092.2.z.b 20
1092.2.ba \(\chi_{1092}(281, \cdot)\) 1092.2.ba.a 56 2
1092.2.bd \(\chi_{1092}(797, \cdot)\) 1092.2.bd.a 2 2
1092.2.bd.b 2
1092.2.bd.c 72
1092.2.bf \(\chi_{1092}(575, \cdot)\) n/a 336 2
1092.2.bg \(\chi_{1092}(589, \cdot)\) 1092.2.bg.a 12 2
1092.2.bg.b 12
1092.2.bi \(\chi_{1092}(55, \cdot)\) n/a 224 2
1092.2.bl \(\chi_{1092}(185, \cdot)\) 1092.2.bl.a 2 2
1092.2.bl.b 2
1092.2.bl.c 2
1092.2.bl.d 68
1092.2.bn \(\chi_{1092}(179, \cdot)\) n/a 432 2
1092.2.bo \(\chi_{1092}(199, \cdot)\) n/a 224 2
1092.2.bs \(\chi_{1092}(103, \cdot)\) n/a 224 2
1092.2.bv \(\chi_{1092}(23, \cdot)\) n/a 432 2
1092.2.bw \(\chi_{1092}(521, \cdot)\) 1092.2.bw.a 64 2
1092.2.by \(\chi_{1092}(779, \cdot)\) n/a 432 2
1092.2.cb \(\chi_{1092}(269, \cdot)\) 1092.2.cb.a 2 2
1092.2.cb.b 2
1092.2.cb.c 2
1092.2.cb.d 68
1092.2.cd \(\chi_{1092}(283, \cdot)\) n/a 224 2
1092.2.cf \(\chi_{1092}(121, \cdot)\) 1092.2.cf.a 2 2
1092.2.cf.b 2
1092.2.cf.c 4
1092.2.cf.d 14
1092.2.cf.e 16
1092.2.ch \(\chi_{1092}(367, \cdot)\) n/a 224 2
1092.2.ck \(\chi_{1092}(107, \cdot)\) n/a 432 2
1092.2.cl \(\chi_{1092}(857, \cdot)\) 1092.2.cl.a 2 2
1092.2.cl.b 2
1092.2.cl.c 72
1092.2.cn \(\chi_{1092}(443, \cdot)\) n/a 384 2
1092.2.cq \(\chi_{1092}(17, \cdot)\) 1092.2.cq.a 2 2
1092.2.cq.b 2
1092.2.cq.c 2
1092.2.cq.d 4
1092.2.cq.e 4
1092.2.cq.f 4
1092.2.cq.g 56
1092.2.cr \(\chi_{1092}(451, \cdot)\) n/a 224 2
1092.2.cu \(\chi_{1092}(25, \cdot)\) 1092.2.cu.a 4 2
1092.2.cu.b 12
1092.2.cu.c 20
1092.2.cw \(\chi_{1092}(703, \cdot)\) n/a 192 2
1092.2.cx \(\chi_{1092}(205, \cdot)\) 1092.2.cx.a 2 2
1092.2.cx.b 2
1092.2.cx.c 4
1092.2.cx.d 14
1092.2.cx.e 16
1092.2.da \(\chi_{1092}(101, \cdot)\) 1092.2.da.a 2 2
1092.2.da.b 2
1092.2.da.c 2
1092.2.da.d 4
1092.2.da.e 4
1092.2.da.f 4
1092.2.da.g 56
1092.2.dc \(\chi_{1092}(191, \cdot)\) n/a 432 2
1092.2.de \(\chi_{1092}(979, \cdot)\) n/a 224 2
1092.2.dh \(\chi_{1092}(965, \cdot)\) 1092.2.dh.a 2 2
1092.2.dh.b 2
1092.2.dh.c 72
1092.2.dj \(\chi_{1092}(407, \cdot)\) n/a 336 2
1092.2.dl \(\chi_{1092}(59, \cdot)\) n/a 864 4
1092.2.dm \(\chi_{1092}(319, \cdot)\) n/a 448 4
1092.2.dp \(\chi_{1092}(197, \cdot)\) n/a 112 4
1092.2.dq \(\chi_{1092}(317, \cdot)\) n/a 152 4
1092.2.ds \(\chi_{1092}(149, \cdot)\) n/a 148 4
1092.2.du \(\chi_{1092}(97, \cdot)\) 1092.2.du.a 36 4
1092.2.du.b 36
1092.2.dx \(\chi_{1092}(397, \cdot)\) 1092.2.dx.a 4 4
1092.2.dx.b 4
1092.2.dx.c 4
1092.2.dx.d 28
1092.2.dx.e 36
1092.2.dz \(\chi_{1092}(73, \cdot)\) 1092.2.dz.a 4 4
1092.2.dz.b 4
1092.2.dz.c 32
1092.2.dz.d 32
1092.2.ea \(\chi_{1092}(379, \cdot)\) n/a 336 4
1092.2.ed \(\chi_{1092}(67, \cdot)\) n/a 448 4
1092.2.ef \(\chi_{1092}(151, \cdot)\) n/a 448 4
1092.2.eh \(\chi_{1092}(167, \cdot)\) n/a 864 4
1092.2.ei \(\chi_{1092}(47, \cdot)\) n/a 864 4
1092.2.ek \(\chi_{1092}(215, \cdot)\) n/a 864 4
1092.2.em \(\chi_{1092}(145, \cdot)\) 1092.2.em.a 4 4
1092.2.em.b 4
1092.2.em.c 4
1092.2.em.d 28
1092.2.em.e 36
1092.2.ep \(\chi_{1092}(137, \cdot)\) n/a 148 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1092))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1092)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)