Properties

Label 2128.2
Level 2128
Weight 2
Dimension 73340
Nonzero newspaces 64
Sturm bound 552960
Trace bound 53

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Defining parameters

Level: \( N \) = \( 2128 = 2^{4} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(552960\)
Trace bound: \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2128))\).

Total New Old
Modular forms 141264 74872 66392
Cusp forms 135217 73340 61877
Eisenstein series 6047 1532 4515

Trace form

\( 73340 q - 128 q^{2} - 98 q^{3} - 120 q^{4} - 158 q^{5} - 104 q^{6} - 117 q^{7} - 296 q^{8} - 30 q^{9} + O(q^{10}) \) \( 73340 q - 128 q^{2} - 98 q^{3} - 120 q^{4} - 158 q^{5} - 104 q^{6} - 117 q^{7} - 296 q^{8} - 30 q^{9} - 120 q^{10} - 82 q^{11} - 136 q^{12} - 152 q^{13} - 164 q^{14} - 218 q^{15} - 152 q^{16} - 286 q^{17} - 112 q^{18} - 81 q^{19} - 248 q^{20} - 163 q^{21} - 312 q^{22} - 54 q^{23} - 120 q^{24} + 18 q^{25} - 104 q^{26} - 80 q^{27} - 140 q^{28} - 342 q^{29} - 136 q^{30} - 106 q^{31} - 88 q^{32} - 238 q^{33} - 104 q^{34} - 89 q^{35} - 328 q^{36} - 84 q^{37} - 156 q^{38} - 204 q^{39} - 152 q^{40} - 24 q^{41} - 300 q^{42} - 206 q^{43} - 232 q^{44} - 220 q^{45} - 192 q^{46} - 62 q^{47} - 328 q^{48} - 407 q^{49} - 504 q^{50} - 134 q^{51} - 352 q^{52} - 286 q^{53} - 456 q^{54} - 168 q^{55} - 340 q^{56} - 180 q^{57} - 480 q^{58} - 162 q^{59} - 456 q^{60} - 246 q^{61} - 272 q^{62} - 97 q^{63} - 480 q^{64} - 176 q^{65} - 344 q^{66} + 62 q^{67} - 240 q^{68} - 96 q^{69} - 236 q^{70} - 66 q^{71} - 296 q^{72} + 234 q^{73} - 120 q^{74} + 246 q^{75} - 108 q^{76} - 208 q^{77} - 328 q^{78} + 246 q^{79} - 88 q^{80} + 100 q^{81} - 120 q^{82} + 112 q^{83} - 172 q^{84} - 134 q^{85} - 120 q^{86} + 216 q^{87} - 88 q^{88} + 210 q^{89} + 8 q^{90} - 163 q^{91} - 384 q^{92} + 58 q^{93} - 40 q^{94} - 159 q^{95} - 88 q^{96} - 232 q^{97} - 28 q^{98} - 470 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)

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
2128.2.a \(\chi_{2128}(1, \cdot)\) 2128.2.a.a 1 1
2128.2.a.b 2
2128.2.a.c 2
2128.2.a.d 2
2128.2.a.e 2
2128.2.a.f 2
2128.2.a.g 2
2128.2.a.h 2
2128.2.a.i 2
2128.2.a.j 2
2128.2.a.k 2
2128.2.a.l 2
2128.2.a.m 2
2128.2.a.n 2
2128.2.a.o 2
2128.2.a.p 3
2128.2.a.q 3
2128.2.a.r 3
2128.2.a.s 3
2128.2.a.t 4
2128.2.a.u 4
2128.2.a.v 5
2128.2.b \(\chi_{2128}(1065, \cdot)\) None 0 1
2128.2.e \(\chi_{2128}(1975, \cdot)\) None 0 1
2128.2.f \(\chi_{2128}(265, \cdot)\) None 0 1
2128.2.i \(\chi_{2128}(951, \cdot)\) None 0 1
2128.2.j \(\chi_{2128}(2015, \cdot)\) 2128.2.j.a 2 1
2128.2.j.b 2
2128.2.j.c 2
2128.2.j.d 2
2128.2.j.e 12
2128.2.j.f 12
2128.2.j.g 20
2128.2.j.h 20
2128.2.m \(\chi_{2128}(1329, \cdot)\) 2128.2.m.a 2 1
2128.2.m.b 4
2128.2.m.c 4
2128.2.m.d 4
2128.2.m.e 8
2128.2.m.f 16
2128.2.m.g 16
2128.2.m.h 24
2128.2.n \(\chi_{2128}(911, \cdot)\) 2128.2.n.a 4 1
2128.2.n.b 4
2128.2.n.c 4
2128.2.n.d 8
2128.2.n.e 40
2128.2.q \(\chi_{2128}(305, \cdot)\) n/a 144 2
2128.2.r \(\chi_{2128}(1569, \cdot)\) n/a 120 2
2128.2.s \(\chi_{2128}(1185, \cdot)\) n/a 156 2
2128.2.t \(\chi_{2128}(961, \cdot)\) n/a 156 2
2128.2.u \(\chi_{2128}(797, \cdot)\) n/a 632 2
2128.2.v \(\chi_{2128}(419, \cdot)\) n/a 576 2
2128.2.ba \(\chi_{2128}(533, \cdot)\) n/a 432 2
2128.2.bb \(\chi_{2128}(379, \cdot)\) n/a 480 2
2128.2.bc \(\chi_{2128}(311, \cdot)\) None 0 2
2128.2.bf \(\chi_{2128}(297, \cdot)\) None 0 2
2128.2.bg \(\chi_{2128}(487, \cdot)\) None 0 2
2128.2.bj \(\chi_{2128}(1033, \cdot)\) None 0 2
2128.2.bk \(\chi_{2128}(145, \cdot)\) n/a 156 2
2128.2.bn \(\chi_{2128}(159, \cdot)\) n/a 160 2
2128.2.bp \(\chi_{2128}(1247, \cdot)\) n/a 120 2
2128.2.br \(\chi_{2128}(303, \cdot)\) n/a 160 2
2128.2.bv \(\chi_{2128}(1455, \cdot)\) n/a 160 2
2128.2.bx \(\chi_{2128}(1025, \cdot)\) n/a 156 2
2128.2.by \(\chi_{2128}(495, \cdot)\) n/a 144 2
2128.2.ca \(\chi_{2128}(1665, \cdot)\) n/a 156 2
2128.2.ce \(\chi_{2128}(639, \cdot)\) n/a 160 2
2128.2.cf \(\chi_{2128}(711, \cdot)\) None 0 2
2128.2.ci \(\chi_{2128}(121, \cdot)\) None 0 2
2128.2.ck \(\chi_{2128}(601, \cdot)\) None 0 2
2128.2.cm \(\chi_{2128}(647, \cdot)\) None 0 2
2128.2.cn \(\chi_{2128}(873, \cdot)\) None 0 2
2128.2.cp \(\chi_{2128}(391, \cdot)\) None 0 2
2128.2.cs \(\chi_{2128}(505, \cdot)\) None 0 2
2128.2.cu \(\chi_{2128}(151, \cdot)\) None 0 2
2128.2.cv \(\chi_{2128}(457, \cdot)\) None 0 2
2128.2.cx \(\chi_{2128}(183, \cdot)\) None 0 2
2128.2.cz \(\chi_{2128}(87, \cdot)\) None 0 2
2128.2.dc \(\chi_{2128}(521, \cdot)\) None 0 2
2128.2.df \(\chi_{2128}(863, \cdot)\) n/a 160 2
2128.2.dg \(\chi_{2128}(369, \cdot)\) n/a 156 2
2128.2.dj \(\chi_{2128}(1375, \cdot)\) n/a 160 2
2128.2.dk \(\chi_{2128}(225, \cdot)\) n/a 360 6
2128.2.dl \(\chi_{2128}(81, \cdot)\) n/a 468 6
2128.2.dm \(\chi_{2128}(625, \cdot)\) n/a 468 6
2128.2.dp \(\chi_{2128}(429, \cdot)\) n/a 1264 4
2128.2.dq \(\chi_{2128}(331, \cdot)\) n/a 1264 4
2128.2.dr \(\chi_{2128}(829, \cdot)\) n/a 1264 4
2128.2.ds \(\chi_{2128}(467, \cdot)\) n/a 1264 4
2128.2.dx \(\chi_{2128}(115, \cdot)\) n/a 1152 4
2128.2.dy \(\chi_{2128}(341, \cdot)\) n/a 1264 4
2128.2.dz \(\chi_{2128}(107, \cdot)\) n/a 1264 4
2128.2.ea \(\chi_{2128}(715, \cdot)\) n/a 960 4
2128.2.eb \(\chi_{2128}(277, \cdot)\) n/a 1264 4
2128.2.ec \(\chi_{2128}(197, \cdot)\) n/a 960 4
2128.2.el \(\chi_{2128}(619, \cdot)\) n/a 1264 4
2128.2.em \(\chi_{2128}(83, \cdot)\) n/a 1264 4
2128.2.en \(\chi_{2128}(677, \cdot)\) n/a 1264 4
2128.2.eo \(\chi_{2128}(69, \cdot)\) n/a 1264 4
2128.2.ep \(\chi_{2128}(683, \cdot)\) n/a 1264 4
2128.2.eq \(\chi_{2128}(837, \cdot)\) n/a 1152 4
2128.2.et \(\chi_{2128}(271, \cdot)\) n/a 480 6
2128.2.eu \(\chi_{2128}(79, \cdot)\) n/a 480 6
2128.2.ex \(\chi_{2128}(409, \cdot)\) None 0 6
2128.2.ey \(\chi_{2128}(25, \cdot)\) None 0 6
2128.2.fd \(\chi_{2128}(97, \cdot)\) n/a 468 6
2128.2.fg \(\chi_{2128}(257, \cdot)\) n/a 468 6
2128.2.fj \(\chi_{2128}(55, \cdot)\) None 0 6
2128.2.fk \(\chi_{2128}(71, \cdot)\) None 0 6
2128.2.fn \(\chi_{2128}(375, \cdot)\) None 0 6
2128.2.fo \(\chi_{2128}(215, \cdot)\) None 0 6
2128.2.fr \(\chi_{2128}(15, \cdot)\) n/a 360 6
2128.2.fs \(\chi_{2128}(111, \cdot)\) n/a 480 6
2128.2.fv \(\chi_{2128}(47, \cdot)\) n/a 480 6
2128.2.fw \(\chi_{2128}(751, \cdot)\) n/a 480 6
2128.2.fz \(\chi_{2128}(169, \cdot)\) None 0 6
2128.2.ga \(\chi_{2128}(41, \cdot)\) None 0 6
2128.2.gd \(\chi_{2128}(89, \cdot)\) None 0 6
2128.2.ge \(\chi_{2128}(9, \cdot)\) None 0 6
2128.2.gf \(\chi_{2128}(33, \cdot)\) n/a 468 6
2128.2.gi \(\chi_{2128}(135, \cdot)\) None 0 6
2128.2.gj \(\chi_{2128}(199, \cdot)\) None 0 6
2128.2.gq \(\chi_{2128}(85, \cdot)\) n/a 2880 12
2128.2.gr \(\chi_{2128}(13, \cdot)\) n/a 3792 12
2128.2.gs \(\chi_{2128}(131, \cdot)\) n/a 3792 12
2128.2.gt \(\chi_{2128}(67, \cdot)\) n/a 3792 12
2128.2.gu \(\chi_{2128}(93, \cdot)\) n/a 3792 12
2128.2.gv \(\chi_{2128}(117, \cdot)\) n/a 3792 12
2128.2.gw \(\chi_{2128}(139, \cdot)\) n/a 3792 12
2128.2.gx \(\chi_{2128}(155, \cdot)\) n/a 2880 12
2128.2.hg \(\chi_{2128}(51, \cdot)\) n/a 3792 12
2128.2.hh \(\chi_{2128}(283, \cdot)\) n/a 3792 12
2128.2.hi \(\chi_{2128}(269, \cdot)\) n/a 3792 12
2128.2.hj \(\chi_{2128}(541, \cdot)\) n/a 3792 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)\(^{\oplus 1}\)