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Properties

Label 3900.2
Level 3900
Weight 2
Dimension 159746
Nonzero newspaces 80
Sturm bound 1612800
Trace bound 24

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Defining parameters

Level: \( N \) = \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(1612800\)
Trace bound: \(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3900))\).

Total New Old
Modular forms 409920 161546 248374
Cusp forms 396481 159746 236735
Eisenstein series 13439 1800 11639

Trace form

\( 159746 q + 8 q^{3} - 148 q^{4} + 4 q^{5} - 122 q^{6} - 12 q^{7} - 48 q^{8} - 154 q^{9} + O(q^{10}) \) \( 159746 q + 8 q^{3} - 148 q^{4} + 4 q^{5} - 122 q^{6} - 12 q^{7} - 48 q^{8} - 154 q^{9} - 192 q^{10} - 20 q^{11} - 80 q^{12} - 296 q^{13} - 28 q^{15} - 180 q^{16} - 114 q^{17} - 12 q^{18} - 88 q^{19} + 40 q^{20} - 290 q^{21} - 144 q^{22} - 104 q^{23} + 10 q^{24} - 452 q^{25} - 28 q^{26} + 20 q^{27} - 80 q^{28} - 62 q^{29} - 4 q^{30} - 8 q^{31} + 20 q^{32} - 150 q^{33} - 68 q^{34} - 8 q^{35} - 44 q^{36} - 218 q^{37} + 184 q^{38} + 12 q^{39} - 112 q^{40} - 2 q^{41} + 192 q^{42} + 80 q^{43} + 340 q^{44} + 4 q^{45} + 84 q^{46} + 136 q^{47} + 170 q^{48} - 196 q^{49} + 328 q^{50} - 48 q^{51} + 72 q^{52} - 44 q^{53} - 34 q^{54} + 92 q^{56} - 162 q^{57} + 36 q^{58} - 148 q^{59} - 4 q^{60} - 682 q^{61} + 36 q^{62} - 62 q^{63} - 64 q^{64} - 162 q^{65} - 292 q^{66} - 360 q^{67} - 64 q^{68} - 106 q^{69} - 168 q^{70} - 168 q^{71} + 68 q^{72} - 288 q^{73} + 44 q^{75} - 380 q^{76} - 24 q^{77} + 108 q^{78} - 24 q^{79} + 8 q^{80} - 30 q^{81} - 52 q^{82} + 116 q^{83} + 132 q^{84} + 108 q^{85} + 64 q^{86} + 344 q^{87} - 120 q^{88} + 692 q^{89} - 76 q^{90} + 180 q^{91} - 104 q^{92} + 326 q^{93} - 244 q^{94} + 160 q^{95} + 92 q^{96} + 604 q^{97} - 356 q^{98} + 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3900))\)

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
3900.2.a \(\chi_{3900}(1, \cdot)\) 3900.2.a.a 1 1
3900.2.a.b 1
3900.2.a.c 1
3900.2.a.d 1
3900.2.a.e 1
3900.2.a.f 1
3900.2.a.g 1
3900.2.a.h 1
3900.2.a.i 1
3900.2.a.j 1
3900.2.a.k 1
3900.2.a.l 1
3900.2.a.m 1
3900.2.a.n 1
3900.2.a.o 2
3900.2.a.p 2
3900.2.a.q 2
3900.2.a.r 2
3900.2.a.s 2
3900.2.a.t 2
3900.2.a.u 3
3900.2.a.v 3
3900.2.a.w 3
3900.2.a.x 3
3900.2.c \(\chi_{3900}(3301, \cdot)\) 3900.2.c.a 2 1
3900.2.c.b 2
3900.2.c.c 2
3900.2.c.d 2
3900.2.c.e 4
3900.2.c.f 4
3900.2.c.g 4
3900.2.c.h 6
3900.2.c.i 6
3900.2.c.j 6
3900.2.c.k 6
3900.2.d \(\chi_{3900}(3899, \cdot)\) n/a 496 1
3900.2.g \(\chi_{3900}(3251, \cdot)\) n/a 456 1
3900.2.h \(\chi_{3900}(1249, \cdot)\) 3900.2.h.a 2 1
3900.2.h.b 2
3900.2.h.c 2
3900.2.h.d 2
3900.2.h.e 2
3900.2.h.f 2
3900.2.h.g 2
3900.2.h.h 2
3900.2.h.i 4
3900.2.h.j 4
3900.2.h.k 6
3900.2.h.l 6
3900.2.j \(\chi_{3900}(649, \cdot)\) 3900.2.j.a 2 1
3900.2.j.b 2
3900.2.j.c 2
3900.2.j.d 2
3900.2.j.e 2
3900.2.j.f 2
3900.2.j.g 4
3900.2.j.h 4
3900.2.j.i 4
3900.2.j.j 8
3900.2.j.k 12
3900.2.m \(\chi_{3900}(2651, \cdot)\) n/a 520 1
3900.2.n \(\chi_{3900}(599, \cdot)\) n/a 432 1
3900.2.q \(\chi_{3900}(601, \cdot)\) 3900.2.q.a 2 2
3900.2.q.b 2
3900.2.q.c 2
3900.2.q.d 2
3900.2.q.e 2
3900.2.q.f 2
3900.2.q.g 2
3900.2.q.h 2
3900.2.q.i 2
3900.2.q.j 4
3900.2.q.k 4
3900.2.q.l 4
3900.2.q.m 6
3900.2.q.n 6
3900.2.q.o 8
3900.2.q.p 8
3900.2.q.q 16
3900.2.q.r 16
3900.2.r \(\chi_{3900}(1357, \cdot)\) 3900.2.r.a 16 2
3900.2.r.b 28
3900.2.r.c 40
3900.2.u \(\chi_{3900}(1607, \cdot)\) n/a 992 2
3900.2.v \(\chi_{3900}(1457, \cdot)\) n/a 144 2
3900.2.y \(\chi_{3900}(2107, \cdot)\) n/a 432 2
3900.2.z \(\chi_{3900}(749, \cdot)\) n/a 168 2
3900.2.bc \(\chi_{3900}(151, \cdot)\) n/a 532 2
3900.2.be \(\chi_{3900}(499, \cdot)\) n/a 504 2
3900.2.bf \(\chi_{3900}(2501, \cdot)\) n/a 176 2
3900.2.bh \(\chi_{3900}(1507, \cdot)\) n/a 504 2
3900.2.bk \(\chi_{3900}(857, \cdot)\) n/a 168 2
3900.2.bm \(\chi_{3900}(2257, \cdot)\) 3900.2.bm.a 16 2
3900.2.bm.b 28
3900.2.bm.c 40
3900.2.bn \(\chi_{3900}(707, \cdot)\) n/a 992 2
3900.2.bp \(\chi_{3900}(781, \cdot)\) n/a 240 4
3900.2.bs \(\chi_{3900}(1199, \cdot)\) n/a 992 2
3900.2.bt \(\chi_{3900}(251, \cdot)\) n/a 1040 2
3900.2.bw \(\chi_{3900}(49, \cdot)\) 3900.2.bw.a 4 2
3900.2.bw.b 4
3900.2.bw.c 4
3900.2.bw.d 4
3900.2.bw.e 4
3900.2.bw.f 4
3900.2.bw.g 8
3900.2.bw.h 8
3900.2.bw.i 8
3900.2.bw.j 8
3900.2.bw.k 8
3900.2.bw.l 8
3900.2.bw.m 16
3900.2.by \(\chi_{3900}(1849, \cdot)\) 3900.2.by.a 4 2
3900.2.by.b 4
3900.2.by.c 4
3900.2.by.d 4
3900.2.by.e 4
3900.2.by.f 4
3900.2.by.g 8
3900.2.by.h 8
3900.2.by.i 12
3900.2.by.j 12
3900.2.by.k 16
3900.2.bz \(\chi_{3900}(1751, \cdot)\) n/a 1040 2
3900.2.cc \(\chi_{3900}(1499, \cdot)\) n/a 992 2
3900.2.cd \(\chi_{3900}(901, \cdot)\) 3900.2.cd.a 2 2
3900.2.cd.b 2
3900.2.cd.c 2
3900.2.cd.d 4
3900.2.cd.e 4
3900.2.cd.f 4
3900.2.cd.g 4
3900.2.cd.h 4
3900.2.cd.i 4
3900.2.cd.j 8
3900.2.cd.k 8
3900.2.cd.l 8
3900.2.cd.m 8
3900.2.cd.n 12
3900.2.cd.o 12
3900.2.cg \(\chi_{3900}(469, \cdot)\) n/a 240 4
3900.2.ch \(\chi_{3900}(131, \cdot)\) n/a 2880 4
3900.2.ck \(\chi_{3900}(779, \cdot)\) n/a 3328 4
3900.2.cl \(\chi_{3900}(181, \cdot)\) n/a 288 4
3900.2.cp \(\chi_{3900}(1379, \cdot)\) n/a 2880 4
3900.2.cq \(\chi_{3900}(311, \cdot)\) n/a 3328 4
3900.2.ct \(\chi_{3900}(1429, \cdot)\) n/a 272 4
3900.2.cv \(\chi_{3900}(1007, \cdot)\) n/a 1984 4
3900.2.cw \(\chi_{3900}(1393, \cdot)\) n/a 168 4
3900.2.cy \(\chi_{3900}(257, \cdot)\) n/a 336 4
3900.2.db \(\chi_{3900}(43, \cdot)\) n/a 1008 4
3900.2.dd \(\chi_{3900}(401, \cdot)\) n/a 356 4
3900.2.de \(\chi_{3900}(799, \cdot)\) n/a 1008 4
3900.2.dg \(\chi_{3900}(1051, \cdot)\) n/a 1064 4
3900.2.dj \(\chi_{3900}(149, \cdot)\) n/a 336 4
3900.2.dk \(\chi_{3900}(607, \cdot)\) n/a 1008 4
3900.2.dn \(\chi_{3900}(893, \cdot)\) n/a 336 4
3900.2.do \(\chi_{3900}(743, \cdot)\) n/a 1984 4
3900.2.dr \(\chi_{3900}(193, \cdot)\) n/a 168 4
3900.2.ds \(\chi_{3900}(61, \cdot)\) n/a 544 8
3900.2.dt \(\chi_{3900}(47, \cdot)\) n/a 6656 8
3900.2.dw \(\chi_{3900}(73, \cdot)\) n/a 560 8
3900.2.dx \(\chi_{3900}(77, \cdot)\) n/a 1120 8
3900.2.ea \(\chi_{3900}(103, \cdot)\) n/a 3360 8
3900.2.ec \(\chi_{3900}(161, \cdot)\) n/a 1120 8
3900.2.ed \(\chi_{3900}(619, \cdot)\) n/a 3360 8
3900.2.ef \(\chi_{3900}(31, \cdot)\) n/a 3360 8
3900.2.ei \(\chi_{3900}(629, \cdot)\) n/a 1120 8
3900.2.ej \(\chi_{3900}(547, \cdot)\) n/a 2880 8
3900.2.em \(\chi_{3900}(53, \cdot)\) n/a 960 8
3900.2.eo \(\chi_{3900}(203, \cdot)\) n/a 6656 8
3900.2.ep \(\chi_{3900}(697, \cdot)\) n/a 560 8
3900.2.er \(\chi_{3900}(589, \cdot)\) n/a 544 8
3900.2.eu \(\chi_{3900}(491, \cdot)\) n/a 6656 8
3900.2.ev \(\chi_{3900}(419, \cdot)\) n/a 6656 8
3900.2.ez \(\chi_{3900}(121, \cdot)\) n/a 576 8
3900.2.fa \(\chi_{3900}(179, \cdot)\) n/a 6656 8
3900.2.fd \(\chi_{3900}(191, \cdot)\) n/a 6656 8
3900.2.fe \(\chi_{3900}(289, \cdot)\) n/a 576 8
3900.2.fh \(\chi_{3900}(37, \cdot)\) n/a 1120 16
3900.2.fi \(\chi_{3900}(227, \cdot)\) n/a 13312 16
3900.2.fk \(\chi_{3900}(113, \cdot)\) n/a 2240 16
3900.2.fn \(\chi_{3900}(367, \cdot)\) n/a 6720 16
3900.2.fo \(\chi_{3900}(89, \cdot)\) n/a 2240 16
3900.2.fr \(\chi_{3900}(271, \cdot)\) n/a 6720 16
3900.2.ft \(\chi_{3900}(19, \cdot)\) n/a 6720 16
3900.2.fu \(\chi_{3900}(41, \cdot)\) n/a 2240 16
3900.2.fw \(\chi_{3900}(127, \cdot)\) n/a 6720 16
3900.2.fz \(\chi_{3900}(17, \cdot)\) n/a 2240 16
3900.2.ga \(\chi_{3900}(97, \cdot)\) n/a 1120 16
3900.2.gd \(\chi_{3900}(167, \cdot)\) n/a 13312 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(780))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1950))\)\(^{\oplus 2}\)