Properties

Label 1120.3
Level 1120
Weight 3
Dimension 36132
Nonzero newspaces 40
Sturm bound 221184
Trace bound 21

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Defining parameters

Level: \( N \) = \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(221184\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1120))\).

Total New Old
Modular forms 75264 36732 38532
Cusp forms 72192 36132 36060
Eisenstein series 3072 600 2472

Trace form

\( 36132 q - 32 q^{2} - 20 q^{3} - 32 q^{4} - 40 q^{5} - 96 q^{6} - 32 q^{7} - 80 q^{8} - 116 q^{9} + O(q^{10}) \) \( 36132 q - 32 q^{2} - 20 q^{3} - 32 q^{4} - 40 q^{5} - 96 q^{6} - 32 q^{7} - 80 q^{8} - 116 q^{9} - 128 q^{10} - 132 q^{11} - 224 q^{12} - 144 q^{13} - 72 q^{14} - 100 q^{15} - 16 q^{16} + 144 q^{17} + 208 q^{18} + 100 q^{19} + 112 q^{20} + 8 q^{21} + 512 q^{22} - 284 q^{23} + 816 q^{24} - 152 q^{25} + 304 q^{26} - 608 q^{27} + 80 q^{28} - 352 q^{29} - 316 q^{31} - 112 q^{32} - 440 q^{33} - 208 q^{34} - 46 q^{35} - 1568 q^{36} - 432 q^{37} - 1600 q^{38} + 640 q^{39} - 856 q^{40} - 304 q^{41} - 880 q^{42} + 232 q^{43} - 768 q^{44} - 176 q^{45} - 224 q^{46} - 236 q^{47} + 176 q^{48} + 60 q^{49} + 504 q^{50} + 756 q^{51} + 1664 q^{52} - 112 q^{53} + 2352 q^{54} + 680 q^{55} + 992 q^{56} + 1072 q^{57} + 2096 q^{58} + 1188 q^{59} + 1352 q^{60} + 880 q^{61} + 848 q^{62} + 1168 q^{63} + 448 q^{64} + 1148 q^{65} + 928 q^{66} + 524 q^{67} + 976 q^{68} + 2720 q^{69} + 576 q^{70} - 312 q^{71} + 352 q^{72} + 688 q^{73} - 384 q^{74} - 158 q^{75} - 1376 q^{76} + 472 q^{77} - 400 q^{78} - 2052 q^{79} + 264 q^{80} - 1140 q^{81} + 1568 q^{82} - 2912 q^{83} + 432 q^{84} - 928 q^{85} + 880 q^{86} - 2680 q^{87} - 496 q^{88} - 976 q^{89} - 2712 q^{90} - 272 q^{91} - 432 q^{92} + 176 q^{93} + 1680 q^{94} - 422 q^{95} + 2256 q^{96} + 976 q^{97} + 2768 q^{98} + 1232 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1120))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1120.3.c \(\chi_{1120}(209, \cdot)\) 1120.3.c.a 1 1
1120.3.c.b 1
1120.3.c.c 1
1120.3.c.d 1
1120.3.c.e 4
1120.3.c.f 4
1120.3.c.g 80
1120.3.d \(\chi_{1120}(351, \cdot)\) 1120.3.d.a 24 1
1120.3.d.b 24
1120.3.f \(\chi_{1120}(321, \cdot)\) 1120.3.f.a 32 1
1120.3.f.b 32
1120.3.i \(\chi_{1120}(239, \cdot)\) 1120.3.i.a 72 1
1120.3.j \(\chi_{1120}(799, \cdot)\) 1120.3.j.a 36 1
1120.3.j.b 36
1120.3.m \(\chi_{1120}(881, \cdot)\) 1120.3.m.a 64 1
1120.3.o \(\chi_{1120}(911, \cdot)\) 1120.3.o.a 48 1
1120.3.p \(\chi_{1120}(769, \cdot)\) 1120.3.p.a 8 1
1120.3.p.b 40
1120.3.p.c 48
1120.3.s \(\chi_{1120}(57, \cdot)\) None 0 2
1120.3.u \(\chi_{1120}(167, \cdot)\) None 0 2
1120.3.v \(\chi_{1120}(223, \cdot)\) n/a 192 2
1120.3.y \(\chi_{1120}(113, \cdot)\) n/a 144 2
1120.3.z \(\chi_{1120}(41, \cdot)\) None 0 2
1120.3.ba \(\chi_{1120}(519, \cdot)\) None 0 2
1120.3.bf \(\chi_{1120}(489, \cdot)\) None 0 2
1120.3.bg \(\chi_{1120}(71, \cdot)\) None 0 2
1120.3.bh \(\chi_{1120}(673, \cdot)\) n/a 144 2
1120.3.bk \(\chi_{1120}(783, \cdot)\) n/a 184 2
1120.3.bm \(\chi_{1120}(727, \cdot)\) None 0 2
1120.3.bo \(\chi_{1120}(617, \cdot)\) None 0 2
1120.3.bp \(\chi_{1120}(431, \cdot)\) n/a 128 2
1120.3.br \(\chi_{1120}(129, \cdot)\) n/a 192 2
1120.3.bt \(\chi_{1120}(319, \cdot)\) n/a 192 2
1120.3.bu \(\chi_{1120}(241, \cdot)\) n/a 128 2
1120.3.bx \(\chi_{1120}(481, \cdot)\) n/a 128 2
1120.3.by \(\chi_{1120}(79, \cdot)\) n/a 184 2
1120.3.ca \(\chi_{1120}(369, \cdot)\) n/a 184 2
1120.3.cd \(\chi_{1120}(191, \cdot)\) n/a 128 2
1120.3.ce \(\chi_{1120}(69, \cdot)\) n/a 1520 4
1120.3.cf \(\chi_{1120}(211, \cdot)\) n/a 768 4
1120.3.ck \(\chi_{1120}(197, \cdot)\) n/a 1152 4
1120.3.cl \(\chi_{1120}(307, \cdot)\) n/a 1520 4
1120.3.co \(\chi_{1120}(27, \cdot)\) n/a 1520 4
1120.3.cp \(\chi_{1120}(477, \cdot)\) n/a 1152 4
1120.3.cq \(\chi_{1120}(99, \cdot)\) n/a 1152 4
1120.3.cr \(\chi_{1120}(181, \cdot)\) n/a 1024 4
1120.3.cu \(\chi_{1120}(87, \cdot)\) None 0 4
1120.3.cw \(\chi_{1120}(137, \cdot)\) None 0 4
1120.3.cz \(\chi_{1120}(47, \cdot)\) n/a 368 4
1120.3.da \(\chi_{1120}(193, \cdot)\) n/a 384 4
1120.3.dc \(\chi_{1120}(151, \cdot)\) None 0 4
1120.3.dd \(\chi_{1120}(89, \cdot)\) None 0 4
1120.3.di \(\chi_{1120}(39, \cdot)\) None 0 4
1120.3.dj \(\chi_{1120}(201, \cdot)\) None 0 4
1120.3.dl \(\chi_{1120}(177, \cdot)\) n/a 368 4
1120.3.dm \(\chi_{1120}(383, \cdot)\) n/a 384 4
1120.3.do \(\chi_{1120}(233, \cdot)\) None 0 4
1120.3.dq \(\chi_{1120}(327, \cdot)\) None 0 4
1120.3.du \(\chi_{1120}(61, \cdot)\) n/a 2048 8
1120.3.dv \(\chi_{1120}(179, \cdot)\) n/a 3040 8
1120.3.dw \(\chi_{1120}(3, \cdot)\) n/a 3040 8
1120.3.dx \(\chi_{1120}(53, \cdot)\) n/a 3040 8
1120.3.ea \(\chi_{1120}(37, \cdot)\) n/a 3040 8
1120.3.eb \(\chi_{1120}(227, \cdot)\) n/a 3040 8
1120.3.eg \(\chi_{1120}(11, \cdot)\) n/a 2048 8
1120.3.eh \(\chi_{1120}(229, \cdot)\) n/a 3040 8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1120))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1120)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)