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Properties

Label 3762.2
Level 3762
Weight 2
Dimension 100328
Nonzero newspaces 64
Sturm bound 1555200
Trace bound 22

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Defining parameters

Level: \( N \) = \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1555200\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3762))\).

Total New Old
Modular forms 394560 100328 294232
Cusp forms 383041 100328 282713
Eisenstein series 11519 0 11519

Trace form

\( 100328 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10}) \) \( 100328 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 28 q^{7} + 8 q^{8} + 12 q^{9} - 20 q^{10} - 14 q^{11} - 76 q^{13} - 64 q^{14} - 4 q^{16} - 100 q^{17} - 24 q^{18} - 103 q^{19} - 36 q^{20} + 24 q^{21} - 21 q^{22} + 28 q^{23} + 8 q^{24} + 28 q^{25} + 100 q^{26} + 120 q^{27} + 64 q^{28} + 100 q^{29} + 120 q^{30} + 80 q^{31} + 26 q^{32} + 182 q^{33} + 132 q^{34} + 208 q^{35} + 32 q^{36} + 52 q^{37} + 92 q^{38} + 120 q^{39} + 60 q^{40} + 88 q^{41} + 80 q^{42} + 28 q^{43} + 25 q^{44} + 256 q^{45} + 128 q^{46} + 232 q^{47} + 48 q^{48} + 108 q^{49} + 412 q^{50} + 416 q^{51} - 12 q^{52} + 588 q^{53} + 252 q^{54} + 236 q^{55} + 208 q^{56} + 446 q^{57} + 112 q^{58} + 678 q^{59} + 144 q^{60} + 408 q^{61} + 232 q^{62} + 400 q^{63} + 44 q^{64} + 624 q^{65} + 144 q^{66} + 300 q^{67} + 26 q^{68} + 376 q^{69} + 136 q^{70} + 352 q^{71} + 48 q^{72} + 110 q^{73} - 24 q^{74} + 80 q^{75} - 8 q^{76} + 136 q^{77} - 24 q^{78} - 80 q^{79} - 20 q^{80} - 116 q^{81} + 50 q^{82} - 402 q^{83} - 184 q^{84} - 204 q^{85} - 338 q^{86} - 328 q^{87} - 14 q^{88} - 456 q^{89} - 400 q^{90} + 120 q^{91} - 228 q^{92} - 400 q^{93} - 80 q^{94} - 162 q^{95} + 58 q^{97} - 438 q^{98} - 478 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3762))\)

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
3762.2.a \(\chi_{3762}(1, \cdot)\) 3762.2.a.a 1 1
3762.2.a.b 1
3762.2.a.c 1
3762.2.a.d 1
3762.2.a.e 1
3762.2.a.f 1
3762.2.a.g 1
3762.2.a.h 1
3762.2.a.i 1
3762.2.a.j 1
3762.2.a.k 1
3762.2.a.l 1
3762.2.a.m 1
3762.2.a.n 1
3762.2.a.o 1
3762.2.a.p 1
3762.2.a.q 1
3762.2.a.r 1
3762.2.a.s 2
3762.2.a.t 2
3762.2.a.u 2
3762.2.a.v 2
3762.2.a.w 2
3762.2.a.x 2
3762.2.a.y 2
3762.2.a.z 2
3762.2.a.ba 2
3762.2.a.bb 2
3762.2.a.bc 2
3762.2.a.bd 3
3762.2.a.be 3
3762.2.a.bf 3
3762.2.a.bg 3
3762.2.a.bh 4
3762.2.a.bi 5
3762.2.a.bj 5
3762.2.a.bk 5
3762.2.a.bl 5
3762.2.b \(\chi_{3762}(989, \cdot)\) 3762.2.b.a 36 1
3762.2.b.b 36
3762.2.d \(\chi_{3762}(683, \cdot)\) 3762.2.d.a 36 1
3762.2.d.b 36
3762.2.g \(\chi_{3762}(2089, \cdot)\) 3762.2.g.a 2 1
3762.2.g.b 2
3762.2.g.c 2
3762.2.g.d 2
3762.2.g.e 2
3762.2.g.f 2
3762.2.g.g 8
3762.2.g.h 8
3762.2.g.i 16
3762.2.g.j 16
3762.2.g.k 20
3762.2.g.l 20
3762.2.i \(\chi_{3762}(1255, \cdot)\) n/a 360 2
3762.2.j \(\chi_{3762}(1717, \cdot)\) n/a 400 2
3762.2.k \(\chi_{3762}(1189, \cdot)\) n/a 172 2
3762.2.l \(\chi_{3762}(463, \cdot)\) n/a 400 2
3762.2.m \(\chi_{3762}(685, \cdot)\) n/a 360 4
3762.2.o \(\chi_{3762}(221, \cdot)\) n/a 400 2
3762.2.q \(\chi_{3762}(2705, \cdot)\) n/a 480 2
3762.2.r \(\chi_{3762}(901, \cdot)\) n/a 200 2
3762.2.w \(\chi_{3762}(835, \cdot)\) n/a 480 2
3762.2.y \(\chi_{3762}(1627, \cdot)\) n/a 480 2
3762.2.bb \(\chi_{3762}(197, \cdot)\) n/a 160 2
3762.2.bc \(\chi_{3762}(2003, \cdot)\) n/a 400 2
3762.2.be \(\chi_{3762}(1937, \cdot)\) n/a 400 2
3762.2.bg \(\chi_{3762}(923, \cdot)\) n/a 480 2
3762.2.bi \(\chi_{3762}(2243, \cdot)\) n/a 432 2
3762.2.bl \(\chi_{3762}(1475, \cdot)\) n/a 144 2
3762.2.bn \(\chi_{3762}(373, \cdot)\) n/a 480 2
3762.2.bp \(\chi_{3762}(199, \cdot)\) n/a 492 6
3762.2.bq \(\chi_{3762}(1651, \cdot)\) n/a 1200 6
3762.2.br \(\chi_{3762}(529, \cdot)\) n/a 1200 6
3762.2.bt \(\chi_{3762}(721, \cdot)\) n/a 400 4
3762.2.bw \(\chi_{3762}(1367, \cdot)\) n/a 320 4
3762.2.by \(\chi_{3762}(305, \cdot)\) n/a 288 4
3762.2.bz \(\chi_{3762}(619, \cdot)\) n/a 1920 8
3762.2.ca \(\chi_{3762}(163, \cdot)\) n/a 800 8
3762.2.cb \(\chi_{3762}(49, \cdot)\) n/a 1920 8
3762.2.cc \(\chi_{3762}(115, \cdot)\) n/a 1728 8
3762.2.cd \(\chi_{3762}(263, \cdot)\) n/a 1440 6
3762.2.cf \(\chi_{3762}(439, \cdot)\) n/a 1440 6
3762.2.ci \(\chi_{3762}(1211, \cdot)\) n/a 1200 6
3762.2.ck \(\chi_{3762}(89, \cdot)\) n/a 384 6
3762.2.co \(\chi_{3762}(241, \cdot)\) n/a 1440 6
3762.2.cp \(\chi_{3762}(593, \cdot)\) n/a 480 6
3762.2.cr \(\chi_{3762}(109, \cdot)\) n/a 600 6
3762.2.cu \(\chi_{3762}(131, \cdot)\) n/a 1440 6
3762.2.cw \(\chi_{3762}(155, \cdot)\) n/a 1200 6
3762.2.cz \(\chi_{3762}(673, \cdot)\) n/a 1920 8
3762.2.db \(\chi_{3762}(179, \cdot)\) n/a 640 8
3762.2.de \(\chi_{3762}(761, \cdot)\) n/a 1728 8
3762.2.dg \(\chi_{3762}(83, \cdot)\) n/a 1920 8
3762.2.di \(\chi_{3762}(113, \cdot)\) n/a 1920 8
3762.2.dk \(\chi_{3762}(335, \cdot)\) n/a 1920 8
3762.2.dl \(\chi_{3762}(809, \cdot)\) n/a 640 8
3762.2.do \(\chi_{3762}(259, \cdot)\) n/a 1920 8
3762.2.dq \(\chi_{3762}(151, \cdot)\) n/a 1920 8
3762.2.dv \(\chi_{3762}(145, \cdot)\) n/a 800 8
3762.2.dw \(\chi_{3762}(695, \cdot)\) n/a 1920 8
3762.2.dy \(\chi_{3762}(905, \cdot)\) n/a 1920 8
3762.2.ea \(\chi_{3762}(169, \cdot)\) n/a 5760 24
3762.2.eb \(\chi_{3762}(25, \cdot)\) n/a 5760 24
3762.2.ec \(\chi_{3762}(289, \cdot)\) n/a 2400 24
3762.2.ed \(\chi_{3762}(203, \cdot)\) n/a 5760 24
3762.2.eh \(\chi_{3762}(101, \cdot)\) n/a 5760 24
3762.2.ei \(\chi_{3762}(127, \cdot)\) n/a 2400 24
3762.2.ek \(\chi_{3762}(17, \cdot)\) n/a 1920 24
3762.2.en \(\chi_{3762}(193, \cdot)\) n/a 5760 24
3762.2.ep \(\chi_{3762}(53, \cdot)\) n/a 1920 24
3762.2.et \(\chi_{3762}(59, \cdot)\) n/a 5760 24
3762.2.eu \(\chi_{3762}(13, \cdot)\) n/a 5760 24
3762.2.ew \(\chi_{3762}(365, \cdot)\) n/a 5760 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3762))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3762)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1881))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3762))\)\(^{\oplus 1}\)