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Properties

Label 1088.2
Level 1088
Weight 2
Dimension 20262
Nonzero newspaces 34
Sturm bound 147456
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 34 \)
Sturm bound: \(147456\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1088))\).

Total New Old
Modular forms 38016 20922 17094
Cusp forms 35713 20262 15451
Eisenstein series 2303 660 1643

Trace form

\( 20262 q - 112 q^{2} - 84 q^{3} - 112 q^{4} - 112 q^{5} - 112 q^{6} - 80 q^{7} - 112 q^{8} - 134 q^{9} + O(q^{10}) \) \( 20262 q - 112 q^{2} - 84 q^{3} - 112 q^{4} - 112 q^{5} - 112 q^{6} - 80 q^{7} - 112 q^{8} - 134 q^{9} - 112 q^{10} - 76 q^{11} - 112 q^{12} - 96 q^{13} - 112 q^{14} - 72 q^{15} - 112 q^{16} - 202 q^{17} - 240 q^{18} - 68 q^{19} - 112 q^{20} - 120 q^{21} - 128 q^{22} - 80 q^{23} - 192 q^{24} - 162 q^{25} - 192 q^{26} - 96 q^{27} - 192 q^{28} - 144 q^{29} - 272 q^{30} - 128 q^{31} - 192 q^{32} - 136 q^{33} - 160 q^{34} - 184 q^{35} - 272 q^{36} - 128 q^{37} - 192 q^{38} - 80 q^{39} - 192 q^{40} - 140 q^{41} - 192 q^{42} - 60 q^{43} - 128 q^{44} - 104 q^{45} - 112 q^{46} - 48 q^{47} - 112 q^{48} - 178 q^{49} - 64 q^{50} - 116 q^{51} - 144 q^{52} - 64 q^{53} + 16 q^{54} - 208 q^{55} - 128 q^{57} + 32 q^{58} - 220 q^{59} + 80 q^{60} - 96 q^{61} - 48 q^{62} - 216 q^{63} + 80 q^{64} - 304 q^{65} + 48 q^{66} - 260 q^{67} - 72 q^{68} - 216 q^{69} + 80 q^{70} - 208 q^{71} + 32 q^{72} - 140 q^{73} - 196 q^{75} + 16 q^{76} - 120 q^{77} - 64 q^{78} - 144 q^{79} - 192 q^{80} - 202 q^{81} - 272 q^{82} - 84 q^{83} - 336 q^{84} - 128 q^{85} - 448 q^{86} - 80 q^{87} - 272 q^{88} - 236 q^{89} - 400 q^{90} - 72 q^{91} - 416 q^{92} - 192 q^{93} - 304 q^{94} - 120 q^{95} - 384 q^{96} - 164 q^{97} - 384 q^{98} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1088))\)

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
1088.2.a \(\chi_{1088}(1, \cdot)\) 1088.2.a.a 1 1
1088.2.a.b 1
1088.2.a.c 1
1088.2.a.d 1
1088.2.a.e 1
1088.2.a.f 1
1088.2.a.g 1
1088.2.a.h 1
1088.2.a.i 1
1088.2.a.j 1
1088.2.a.k 1
1088.2.a.l 1
1088.2.a.m 1
1088.2.a.n 1
1088.2.a.o 2
1088.2.a.p 2
1088.2.a.q 2
1088.2.a.r 2
1088.2.a.s 2
1088.2.a.t 2
1088.2.a.u 3
1088.2.a.v 3
1088.2.b \(\chi_{1088}(577, \cdot)\) 1088.2.b.a 2 1
1088.2.b.b 2
1088.2.b.c 2
1088.2.b.d 2
1088.2.b.e 2
1088.2.b.f 2
1088.2.b.g 2
1088.2.b.h 2
1088.2.b.i 2
1088.2.b.j 4
1088.2.b.k 4
1088.2.b.l 4
1088.2.b.m 4
1088.2.c \(\chi_{1088}(545, \cdot)\) 1088.2.c.a 2 1
1088.2.c.b 2
1088.2.c.c 4
1088.2.c.d 12
1088.2.c.e 12
1088.2.h \(\chi_{1088}(33, \cdot)\) 1088.2.h.a 4 1
1088.2.h.b 8
1088.2.h.c 24
1088.2.j \(\chi_{1088}(81, \cdot)\) 1088.2.j.a 68 2
1088.2.l \(\chi_{1088}(273, \cdot)\) 1088.2.l.a 2 2
1088.2.l.b 30
1088.2.l.c 32
1088.2.m \(\chi_{1088}(225, \cdot)\) 1088.2.m.a 2 2
1088.2.m.b 2
1088.2.m.c 2
1088.2.m.d 2
1088.2.m.e 4
1088.2.m.f 4
1088.2.m.g 4
1088.2.m.h 4
1088.2.m.i 24
1088.2.m.j 24
1088.2.o \(\chi_{1088}(769, \cdot)\) 1088.2.o.a 2 2
1088.2.o.b 2
1088.2.o.c 2
1088.2.o.d 2
1088.2.o.e 2
1088.2.o.f 2
1088.2.o.g 2
1088.2.o.h 2
1088.2.o.i 2
1088.2.o.j 2
1088.2.o.k 2
1088.2.o.l 2
1088.2.o.m 2
1088.2.o.n 2
1088.2.o.o 2
1088.2.o.p 2
1088.2.o.q 2
1088.2.o.r 2
1088.2.o.s 4
1088.2.o.t 4
1088.2.o.u 6
1088.2.o.v 6
1088.2.o.w 12
1088.2.r \(\chi_{1088}(305, \cdot)\) 1088.2.r.a 68 2
1088.2.s \(\chi_{1088}(625, \cdot)\) 1088.2.s.a 68 2
1088.2.v \(\chi_{1088}(281, \cdot)\) None 0 4
1088.2.x \(\chi_{1088}(185, \cdot)\) None 0 4
1088.2.z \(\chi_{1088}(89, \cdot)\) None 0 4
1088.2.bb \(\chi_{1088}(257, \cdot)\) n/a 136 4
1088.2.bc \(\chi_{1088}(169, \cdot)\) None 0 4
1088.2.bd \(\chi_{1088}(137, \cdot)\) None 0 4
1088.2.be \(\chi_{1088}(433, \cdot)\) n/a 136 4
1088.2.bg \(\chi_{1088}(49, \cdot)\) n/a 136 4
1088.2.bk \(\chi_{1088}(161, \cdot)\) n/a 144 4
1088.2.bn \(\chi_{1088}(217, \cdot)\) None 0 4
1088.2.bp \(\chi_{1088}(9, \cdot)\) None 0 4
1088.2.bq \(\chi_{1088}(25, \cdot)\) None 0 4
1088.2.bs \(\chi_{1088}(139, \cdot)\) n/a 1136 8
1088.2.bv \(\chi_{1088}(3, \cdot)\) n/a 1136 8
1088.2.bx \(\chi_{1088}(189, \cdot)\) n/a 1136 8
1088.2.by \(\chi_{1088}(147, \cdot)\) n/a 1136 8
1088.2.ca \(\chi_{1088}(107, \cdot)\) n/a 1136 8
1088.2.cd \(\chi_{1088}(79, \cdot)\) n/a 272 8
1088.2.ce \(\chi_{1088}(53, \cdot)\) n/a 1136 8
1088.2.cf \(\chi_{1088}(77, \cdot)\) n/a 1136 8
1088.2.cg \(\chi_{1088}(7, \cdot)\) None 0 8
1088.2.cj \(\chi_{1088}(75, \cdot)\) n/a 1136 8
1088.2.cl \(\chi_{1088}(91, \cdot)\) n/a 1136 8
1088.2.cn \(\chi_{1088}(69, \cdot)\) n/a 1024 8
1088.2.cp \(\chi_{1088}(63, \cdot)\) n/a 272 8
1088.2.cr \(\chi_{1088}(23, \cdot)\) None 0 8
1088.2.cs \(\chi_{1088}(13, \cdot)\) n/a 1136 8
1088.2.cv \(\chi_{1088}(149, \cdot)\) n/a 1136 8
1088.2.cx \(\chi_{1088}(39, \cdot)\) None 0 8
1088.2.cy \(\chi_{1088}(31, \cdot)\) n/a 288 8
1088.2.da \(\chi_{1088}(101, \cdot)\) n/a 1136 8
1088.2.dc \(\chi_{1088}(231, \cdot)\) None 0 8
1088.2.dh \(\chi_{1088}(207, \cdot)\) n/a 272 8
1088.2.dj \(\chi_{1088}(253, \cdot)\) n/a 1136 8
1088.2.dl \(\chi_{1088}(347, \cdot)\) n/a 1136 8
1088.2.dm \(\chi_{1088}(379, \cdot)\) n/a 1136 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1088))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1088)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 2}\)