Properties

Label 3600.2
Level 3600
Weight 2
Dimension 141014
Nonzero newspaces 56
Sturm bound 1382400
Trace bound 45

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Defining parameters

Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1382400\)
Trace bound: \(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3600))\).

Total New Old
Modular forms 351872 142675 209197
Cusp forms 339329 141014 198315
Eisenstein series 12543 1661 10882

Trace form

\( 141014q - 78q^{2} - 78q^{3} - 76q^{4} - 120q^{5} - 168q^{6} - 53q^{7} - 72q^{8} - 22q^{9} + O(q^{10}) \) \( 141014q - 78q^{2} - 78q^{3} - 76q^{4} - 120q^{5} - 168q^{6} - 53q^{7} - 72q^{8} - 22q^{9} - 288q^{10} - 81q^{11} - 104q^{12} - 81q^{13} - 96q^{14} - 96q^{15} - 148q^{16} - 168q^{17} - 124q^{18} - 152q^{19} - 96q^{20} - 223q^{21} - 124q^{22} - 55q^{23} - 136q^{24} - 16q^{25} - 304q^{26} - 96q^{27} - 336q^{28} - 147q^{29} - 128q^{30} - 123q^{31} - 188q^{32} - 255q^{33} - 216q^{34} - 84q^{35} - 172q^{36} - 364q^{37} - 144q^{38} - 135q^{39} - 176q^{40} - 109q^{41} - 64q^{42} - 149q^{43} - 104q^{44} - 180q^{45} - 444q^{46} - 225q^{47} - 52q^{48} - 308q^{49} - 136q^{50} - 374q^{51} - 80q^{52} - 266q^{53} - 60q^{54} - 298q^{55} - 24q^{56} - 132q^{57} - 40q^{58} - 287q^{59} - 128q^{60} - 277q^{61} + 24q^{62} - 219q^{63} - 256q^{64} - 316q^{65} - 48q^{66} - 311q^{67} + 120q^{68} - 151q^{69} - 24q^{70} - 330q^{71} + 8q^{72} - 162q^{73} + 156q^{74} - 120q^{75} - 152q^{76} - 185q^{77} + 68q^{78} - 201q^{79} - 16q^{80} - 302q^{81} - 96q^{82} - 191q^{83} + 40q^{84} - 224q^{85} + 148q^{86} + 15q^{87} + 172q^{88} - 28q^{89} - 128q^{90} - 384q^{91} + 356q^{92} - 195q^{93} + 132q^{94} - 198q^{95} - 100q^{96} - 291q^{97} + 398q^{98} + 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3600))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3600.2.a \(\chi_{3600}(1, \cdot)\) 3600.2.a.a 1 1
3600.2.a.b 1
3600.2.a.c 1
3600.2.a.d 1
3600.2.a.e 1
3600.2.a.f 1
3600.2.a.g 1
3600.2.a.h 1
3600.2.a.i 1
3600.2.a.j 1
3600.2.a.k 1
3600.2.a.l 1
3600.2.a.m 1
3600.2.a.n 1
3600.2.a.o 1
3600.2.a.p 1
3600.2.a.q 1
3600.2.a.r 1
3600.2.a.s 1
3600.2.a.t 1
3600.2.a.u 1
3600.2.a.v 1
3600.2.a.w 1
3600.2.a.x 1
3600.2.a.y 1
3600.2.a.z 1
3600.2.a.ba 1
3600.2.a.bb 1
3600.2.a.bc 1
3600.2.a.bd 1
3600.2.a.be 1
3600.2.a.bf 1
3600.2.a.bg 1
3600.2.a.bh 1
3600.2.a.bi 1
3600.2.a.bj 1
3600.2.a.bk 1
3600.2.a.bl 1
3600.2.a.bm 1
3600.2.a.bn 1
3600.2.a.bo 1
3600.2.a.bp 1
3600.2.a.bq 1
3600.2.a.br 1
3600.2.a.bs 2
3600.2.b \(\chi_{3600}(2951, \cdot)\) None 0 1
3600.2.d \(\chi_{3600}(649, \cdot)\) None 0 1
3600.2.f \(\chi_{3600}(2449, \cdot)\) 3600.2.f.a 2 1
3600.2.f.b 2
3600.2.f.c 2
3600.2.f.d 2
3600.2.f.e 2
3600.2.f.f 2
3600.2.f.g 2
3600.2.f.h 2
3600.2.f.i 2
3600.2.f.j 2
3600.2.f.k 2
3600.2.f.l 2
3600.2.f.m 2
3600.2.f.n 2
3600.2.f.o 2
3600.2.f.p 2
3600.2.f.q 2
3600.2.f.r 2
3600.2.f.s 2
3600.2.f.t 2
3600.2.f.u 2
3600.2.f.v 2
3600.2.h \(\chi_{3600}(1151, \cdot)\) 3600.2.h.a 2 1
3600.2.h.b 2
3600.2.h.c 2
3600.2.h.d 4
3600.2.h.e 4
3600.2.h.f 4
3600.2.h.g 4
3600.2.h.h 4
3600.2.h.i 4
3600.2.h.j 8
3600.2.k \(\chi_{3600}(1801, \cdot)\) None 0 1
3600.2.m \(\chi_{3600}(1799, \cdot)\) None 0 1
3600.2.o \(\chi_{3600}(3599, \cdot)\) 3600.2.o.a 4 1
3600.2.o.b 8
3600.2.o.c 8
3600.2.o.d 8
3600.2.o.e 8
3600.2.q \(\chi_{3600}(1201, \cdot)\) n/a 222 2
3600.2.t \(\chi_{3600}(901, \cdot)\) n/a 374 2
3600.2.u \(\chi_{3600}(899, \cdot)\) n/a 288 2
3600.2.w \(\chi_{3600}(593, \cdot)\) 3600.2.w.a 4 2
3600.2.w.b 4
3600.2.w.c 4
3600.2.w.d 4
3600.2.w.e 4
3600.2.w.f 4
3600.2.w.g 4
3600.2.w.h 4
3600.2.w.i 8
3600.2.w.j 8
3600.2.w.k 8
3600.2.w.l 8
3600.2.w.m 8
3600.2.x \(\chi_{3600}(2143, \cdot)\) 3600.2.x.a 2 2
3600.2.x.b 2
3600.2.x.c 2
3600.2.x.d 4
3600.2.x.e 4
3600.2.x.f 4
3600.2.x.g 8
3600.2.x.h 8
3600.2.x.i 8
3600.2.x.j 8
3600.2.x.k 8
3600.2.x.l 8
3600.2.x.m 8
3600.2.x.n 8
3600.2.x.o 8
3600.2.z \(\chi_{3600}(2107, \cdot)\) n/a 356 2
3600.2.bc \(\chi_{3600}(2357, \cdot)\) n/a 288 2
3600.2.bd \(\chi_{3600}(307, \cdot)\) n/a 356 2
3600.2.bg \(\chi_{3600}(557, \cdot)\) n/a 288 2
3600.2.bi \(\chi_{3600}(343, \cdot)\) None 0 2
3600.2.bj \(\chi_{3600}(2393, \cdot)\) None 0 2
3600.2.bl \(\chi_{3600}(251, \cdot)\) n/a 304 2
3600.2.bm \(\chi_{3600}(1549, \cdot)\) n/a 356 2
3600.2.bp \(\chi_{3600}(721, \cdot)\) n/a 296 4
3600.2.bs \(\chi_{3600}(1199, \cdot)\) n/a 216 2
3600.2.bu \(\chi_{3600}(599, \cdot)\) None 0 2
3600.2.bw \(\chi_{3600}(601, \cdot)\) None 0 2
3600.2.bx \(\chi_{3600}(2351, \cdot)\) n/a 228 2
3600.2.bz \(\chi_{3600}(49, \cdot)\) n/a 212 2
3600.2.cb \(\chi_{3600}(1849, \cdot)\) None 0 2
3600.2.cd \(\chi_{3600}(551, \cdot)\) None 0 2
3600.2.cg \(\chi_{3600}(431, \cdot)\) n/a 240 4
3600.2.ci \(\chi_{3600}(289, \cdot)\) n/a 296 4
3600.2.ck \(\chi_{3600}(1369, \cdot)\) None 0 4
3600.2.cm \(\chi_{3600}(71, \cdot)\) None 0 4
3600.2.co \(\chi_{3600}(719, \cdot)\) n/a 240 4
3600.2.cq \(\chi_{3600}(359, \cdot)\) None 0 4
3600.2.cs \(\chi_{3600}(361, \cdot)\) None 0 4
3600.2.cu \(\chi_{3600}(349, \cdot)\) n/a 1712 4
3600.2.cv \(\chi_{3600}(851, \cdot)\) n/a 1800 4
3600.2.cy \(\chi_{3600}(7, \cdot)\) None 0 4
3600.2.db \(\chi_{3600}(857, \cdot)\) None 0 4
3600.2.dc \(\chi_{3600}(293, \cdot)\) n/a 1712 4
3600.2.df \(\chi_{3600}(43, \cdot)\) n/a 1712 4
3600.2.dg \(\chi_{3600}(893, \cdot)\) n/a 1712 4
3600.2.dj \(\chi_{3600}(643, \cdot)\) n/a 1712 4
3600.2.dk \(\chi_{3600}(257, \cdot)\) n/a 424 4
3600.2.dn \(\chi_{3600}(607, \cdot)\) n/a 432 4
3600.2.dq \(\chi_{3600}(299, \cdot)\) n/a 1712 4
3600.2.dr \(\chi_{3600}(301, \cdot)\) n/a 1800 4
3600.2.ds \(\chi_{3600}(241, \cdot)\) n/a 1424 8
3600.2.dt \(\chi_{3600}(179, \cdot)\) n/a 1920 8
3600.2.du \(\chi_{3600}(181, \cdot)\) n/a 2384 8
3600.2.dy \(\chi_{3600}(233, \cdot)\) None 0 8
3600.2.dz \(\chi_{3600}(487, \cdot)\) None 0 8
3600.2.eb \(\chi_{3600}(53, \cdot)\) n/a 1920 8
3600.2.ee \(\chi_{3600}(523, \cdot)\) n/a 2384 8
3600.2.ef \(\chi_{3600}(197, \cdot)\) n/a 1920 8
3600.2.ei \(\chi_{3600}(163, \cdot)\) n/a 2384 8
3600.2.ek \(\chi_{3600}(127, \cdot)\) n/a 600 8
3600.2.el \(\chi_{3600}(17, \cdot)\) n/a 480 8
3600.2.ep \(\chi_{3600}(109, \cdot)\) n/a 2384 8
3600.2.eq \(\chi_{3600}(611, \cdot)\) n/a 1920 8
3600.2.er \(\chi_{3600}(121, \cdot)\) None 0 8
3600.2.et \(\chi_{3600}(119, \cdot)\) None 0 8
3600.2.ev \(\chi_{3600}(239, \cdot)\) n/a 1440 8
3600.2.ez \(\chi_{3600}(311, \cdot)\) None 0 8
3600.2.fb \(\chi_{3600}(169, \cdot)\) None 0 8
3600.2.fd \(\chi_{3600}(529, \cdot)\) n/a 1424 8
3600.2.ff \(\chi_{3600}(191, \cdot)\) n/a 1440 8
3600.2.fi \(\chi_{3600}(11, \cdot)\) n/a 11456 16
3600.2.fj \(\chi_{3600}(229, \cdot)\) n/a 11456 16
3600.2.fk \(\chi_{3600}(223, \cdot)\) n/a 2880 16
3600.2.fn \(\chi_{3600}(113, \cdot)\) n/a 2848 16
3600.2.fo \(\chi_{3600}(187, \cdot)\) n/a 11456 16
3600.2.fr \(\chi_{3600}(173, \cdot)\) n/a 11456 16
3600.2.fs \(\chi_{3600}(67, \cdot)\) n/a 11456 16
3600.2.fv \(\chi_{3600}(77, \cdot)\) n/a 11456 16
3600.2.fw \(\chi_{3600}(137, \cdot)\) None 0 16
3600.2.fz \(\chi_{3600}(103, \cdot)\) None 0 16
3600.2.ga \(\chi_{3600}(61, \cdot)\) n/a 11456 16
3600.2.gb \(\chi_{3600}(59, \cdot)\) n/a 11456 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 2}\)