Properties

Label 1800.2
Level 1800
Weight 2
Dimension 35092
Nonzero newspaces 36
Sturm bound 345600
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(345600\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1800))\).

Total New Old
Modular forms 89088 35830 53258
Cusp forms 83713 35092 48621
Eisenstein series 5375 738 4637

Trace form

\( 35092q - 38q^{2} - 51q^{3} - 38q^{4} + q^{5} - 88q^{6} - 30q^{7} - 50q^{8} - 105q^{9} + O(q^{10}) \) \( 35092q - 38q^{2} - 51q^{3} - 38q^{4} + q^{5} - 88q^{6} - 30q^{7} - 50q^{8} - 105q^{9} - 144q^{10} - 69q^{11} - 62q^{12} + 2q^{13} - 74q^{14} - 64q^{15} - 102q^{16} - 96q^{17} - 48q^{18} - 162q^{19} - 68q^{20} - 28q^{21} - 62q^{22} - 126q^{23} - 24q^{24} - 123q^{25} - 124q^{26} - 96q^{27} - 92q^{28} - 78q^{29} - 64q^{30} - 156q^{31} + 42q^{32} - 151q^{33} + 14q^{34} - 108q^{35} - 30q^{36} - 75q^{37} + 106q^{38} - 44q^{39} - 8q^{40} - 173q^{41} + 50q^{42} - 99q^{43} + 158q^{44} - 52q^{46} + 6q^{47} + 84q^{48} - 103q^{49} + 92q^{50} - 55q^{51} + 210q^{52} + 25q^{53} + 148q^{54} - 120q^{55} + 244q^{56} - 29q^{57} + 242q^{58} + 197q^{59} + 56q^{60} + 16q^{61} + 260q^{62} + 128q^{63} + 184q^{64} - 27q^{65} + 40q^{66} + 163q^{67} + 248q^{68} + 70q^{69} + 108q^{70} + 172q^{71} + 10q^{72} - 228q^{73} + 110q^{74} + 8q^{75} - 42q^{76} + 108q^{77} - 58q^{78} + 32q^{79} + 52q^{80} - 21q^{81} + 56q^{82} + 248q^{83} - 48q^{84} + 17q^{85} - 22q^{86} + 178q^{87} + 210q^{88} + 17q^{89} - 64q^{90} - 84q^{91} + 114q^{92} + 182q^{93} + 236q^{94} + 200q^{95} - 32q^{96} - 61q^{97} + 84q^{98} + 286q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)

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
1800.2.a \(\chi_{1800}(1, \cdot)\) 1800.2.a.a 1 1
1800.2.a.b 1
1800.2.a.c 1
1800.2.a.d 1
1800.2.a.e 1
1800.2.a.f 1
1800.2.a.g 1
1800.2.a.h 1
1800.2.a.i 1
1800.2.a.j 1
1800.2.a.k 1
1800.2.a.l 1
1800.2.a.m 1
1800.2.a.n 1
1800.2.a.o 1
1800.2.a.p 1
1800.2.a.q 1
1800.2.a.r 1
1800.2.a.s 1
1800.2.a.t 1
1800.2.a.u 1
1800.2.a.v 1
1800.2.a.w 1
1800.2.a.x 1
1800.2.b \(\chi_{1800}(251, \cdot)\) 1800.2.b.a 2 1
1800.2.b.b 2
1800.2.b.c 4
1800.2.b.d 6
1800.2.b.e 6
1800.2.b.f 8
1800.2.b.g 16
1800.2.b.h 16
1800.2.b.i 16
1800.2.d \(\chi_{1800}(1549, \cdot)\) 1800.2.d.a 2 1
1800.2.d.b 2
1800.2.d.c 2
1800.2.d.d 2
1800.2.d.e 2
1800.2.d.f 2
1800.2.d.g 2
1800.2.d.h 2
1800.2.d.i 2
1800.2.d.j 2
1800.2.d.k 4
1800.2.d.l 4
1800.2.d.m 4
1800.2.d.n 4
1800.2.d.o 4
1800.2.d.p 4
1800.2.d.q 6
1800.2.d.r 6
1800.2.d.s 8
1800.2.d.t 8
1800.2.d.u 16
1800.2.f \(\chi_{1800}(649, \cdot)\) 1800.2.f.a 2 1
1800.2.f.b 2
1800.2.f.c 2
1800.2.f.d 2
1800.2.f.e 2
1800.2.f.f 2
1800.2.f.g 2
1800.2.f.h 2
1800.2.f.i 2
1800.2.f.j 2
1800.2.f.k 2
1800.2.h \(\chi_{1800}(1151, \cdot)\) None 0 1
1800.2.k \(\chi_{1800}(901, \cdot)\) 1800.2.k.a 2 1
1800.2.k.b 2
1800.2.k.c 2
1800.2.k.d 2
1800.2.k.e 2
1800.2.k.f 2
1800.2.k.g 2
1800.2.k.h 2
1800.2.k.i 2
1800.2.k.j 4
1800.2.k.k 4
1800.2.k.l 4
1800.2.k.m 4
1800.2.k.n 4
1800.2.k.o 4
1800.2.k.p 6
1800.2.k.q 8
1800.2.k.r 8
1800.2.k.s 8
1800.2.k.t 8
1800.2.k.u 12
1800.2.m \(\chi_{1800}(899, \cdot)\) 1800.2.m.a 4 1
1800.2.m.b 4
1800.2.m.c 8
1800.2.m.d 12
1800.2.m.e 12
1800.2.m.f 32
1800.2.o \(\chi_{1800}(1799, \cdot)\) None 0 1
1800.2.q \(\chi_{1800}(601, \cdot)\) n/a 114 2
1800.2.s \(\chi_{1800}(593, \cdot)\) 1800.2.s.a 4 2
1800.2.s.b 4
1800.2.s.c 4
1800.2.s.d 8
1800.2.s.e 8
1800.2.s.f 8
1800.2.t \(\chi_{1800}(343, \cdot)\) None 0 2
1800.2.w \(\chi_{1800}(307, \cdot)\) n/a 176 2
1800.2.x \(\chi_{1800}(557, \cdot)\) n/a 144 2
1800.2.z \(\chi_{1800}(361, \cdot)\) n/a 148 4
1800.2.bc \(\chi_{1800}(599, \cdot)\) None 0 2
1800.2.be \(\chi_{1800}(299, \cdot)\) n/a 424 2
1800.2.bg \(\chi_{1800}(301, \cdot)\) n/a 444 2
1800.2.bh \(\chi_{1800}(551, \cdot)\) None 0 2
1800.2.bj \(\chi_{1800}(49, \cdot)\) n/a 108 2
1800.2.bl \(\chi_{1800}(349, \cdot)\) n/a 424 2
1800.2.bn \(\chi_{1800}(851, \cdot)\) n/a 444 2
1800.2.bq \(\chi_{1800}(71, \cdot)\) None 0 4
1800.2.bs \(\chi_{1800}(289, \cdot)\) n/a 152 4
1800.2.bu \(\chi_{1800}(109, \cdot)\) n/a 592 4
1800.2.bw \(\chi_{1800}(611, \cdot)\) n/a 480 4
1800.2.by \(\chi_{1800}(359, \cdot)\) None 0 4
1800.2.ca \(\chi_{1800}(179, \cdot)\) n/a 480 4
1800.2.cc \(\chi_{1800}(181, \cdot)\) n/a 592 4
1800.2.ce \(\chi_{1800}(43, \cdot)\) n/a 848 4
1800.2.ch \(\chi_{1800}(293, \cdot)\) n/a 848 4
1800.2.ci \(\chi_{1800}(257, \cdot)\) n/a 216 4
1800.2.cl \(\chi_{1800}(7, \cdot)\) None 0 4
1800.2.cm \(\chi_{1800}(121, \cdot)\) n/a 720 8
1800.2.co \(\chi_{1800}(53, \cdot)\) n/a 960 8
1800.2.cp \(\chi_{1800}(163, \cdot)\) n/a 1184 8
1800.2.cs \(\chi_{1800}(127, \cdot)\) None 0 8
1800.2.ct \(\chi_{1800}(17, \cdot)\) n/a 240 8
1800.2.cv \(\chi_{1800}(61, \cdot)\) n/a 2848 8
1800.2.cx \(\chi_{1800}(59, \cdot)\) n/a 2848 8
1800.2.cz \(\chi_{1800}(119, \cdot)\) None 0 8
1800.2.dd \(\chi_{1800}(11, \cdot)\) n/a 2848 8
1800.2.df \(\chi_{1800}(229, \cdot)\) n/a 2848 8
1800.2.dh \(\chi_{1800}(169, \cdot)\) n/a 720 8
1800.2.dj \(\chi_{1800}(191, \cdot)\) None 0 8
1800.2.dk \(\chi_{1800}(103, \cdot)\) None 0 16
1800.2.dn \(\chi_{1800}(113, \cdot)\) n/a 1440 16
1800.2.do \(\chi_{1800}(77, \cdot)\) n/a 5696 16
1800.2.dr \(\chi_{1800}(67, \cdot)\) n/a 5696 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1800))\) into lower level spaces

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