Properties

Label 1200.2
Level 1200
Weight 2
Dimension 14747
Nonzero newspaces 28
Sturm bound 153600
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(153600\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1200))\).

Total New Old
Modular forms 39968 15115 24853
Cusp forms 36833 14747 22086
Eisenstein series 3135 368 2767

Trace form

\(14747q \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut -\mathstrut 56q^{4} \) \(\mathstrut -\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14747q \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut -\mathstrut 56q^{4} \) \(\mathstrut -\mathstrut 48q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 64q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 24q^{12} \) \(\mathstrut -\mathstrut 86q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 36q^{15} \) \(\mathstrut -\mathstrut 64q^{16} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut -\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 92q^{19} \) \(\mathstrut -\mathstrut 78q^{21} \) \(\mathstrut -\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 40q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut -\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 160q^{32} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 200q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 66q^{37} \) \(\mathstrut +\mathstrut 216q^{38} \) \(\mathstrut +\mathstrut 52q^{39} \) \(\mathstrut +\mathstrut 96q^{40} \) \(\mathstrut +\mathstrut 122q^{41} \) \(\mathstrut +\mathstrut 92q^{42} \) \(\mathstrut +\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut +\mathstrut 128q^{46} \) \(\mathstrut +\mathstrut 48q^{47} \) \(\mathstrut +\mathstrut 40q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut +\mathstrut 80q^{50} \) \(\mathstrut +\mathstrut 38q^{51} \) \(\mathstrut +\mathstrut 48q^{52} \) \(\mathstrut +\mathstrut 46q^{53} \) \(\mathstrut -\mathstrut 72q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 38q^{57} \) \(\mathstrut -\mathstrut 32q^{58} \) \(\mathstrut +\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 64q^{60} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 202q^{63} \) \(\mathstrut -\mathstrut 80q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 116q^{66} \) \(\mathstrut +\mathstrut 220q^{67} \) \(\mathstrut -\mathstrut 192q^{68} \) \(\mathstrut +\mathstrut 90q^{69} \) \(\mathstrut -\mathstrut 208q^{70} \) \(\mathstrut +\mathstrut 312q^{71} \) \(\mathstrut -\mathstrut 228q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 300q^{74} \) \(\mathstrut +\mathstrut 128q^{75} \) \(\mathstrut -\mathstrut 352q^{76} \) \(\mathstrut +\mathstrut 112q^{77} \) \(\mathstrut -\mathstrut 312q^{78} \) \(\mathstrut +\mathstrut 324q^{79} \) \(\mathstrut -\mathstrut 160q^{80} \) \(\mathstrut -\mathstrut 51q^{81} \) \(\mathstrut -\mathstrut 280q^{82} \) \(\mathstrut +\mathstrut 436q^{83} \) \(\mathstrut -\mathstrut 336q^{84} \) \(\mathstrut +\mathstrut 128q^{85} \) \(\mathstrut -\mathstrut 272q^{86} \) \(\mathstrut +\mathstrut 268q^{87} \) \(\mathstrut -\mathstrut 432q^{88} \) \(\mathstrut +\mathstrut 74q^{89} \) \(\mathstrut -\mathstrut 152q^{90} \) \(\mathstrut +\mathstrut 244q^{91} \) \(\mathstrut -\mathstrut 304q^{92} \) \(\mathstrut +\mathstrut 110q^{93} \) \(\mathstrut -\mathstrut 312q^{94} \) \(\mathstrut +\mathstrut 312q^{95} \) \(\mathstrut -\mathstrut 224q^{96} \) \(\mathstrut +\mathstrut 66q^{97} \) \(\mathstrut -\mathstrut 136q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)

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
1200.2.a \(\chi_{1200}(1, \cdot)\) 1200.2.a.a 1 1
1200.2.a.b 1
1200.2.a.c 1
1200.2.a.d 1
1200.2.a.e 1
1200.2.a.f 1
1200.2.a.g 1
1200.2.a.h 1
1200.2.a.i 1
1200.2.a.j 1
1200.2.a.k 1
1200.2.a.l 1
1200.2.a.m 1
1200.2.a.n 1
1200.2.a.o 1
1200.2.a.p 1
1200.2.a.q 1
1200.2.a.r 1
1200.2.a.s 1
1200.2.b \(\chi_{1200}(551, \cdot)\) None 0 1
1200.2.d \(\chi_{1200}(649, \cdot)\) None 0 1
1200.2.f \(\chi_{1200}(49, \cdot)\) 1200.2.f.a 2 1
1200.2.f.b 2
1200.2.f.c 2
1200.2.f.d 2
1200.2.f.e 2
1200.2.f.f 2
1200.2.f.g 2
1200.2.f.h 2
1200.2.f.i 2
1200.2.h \(\chi_{1200}(1151, \cdot)\) 1200.2.h.a 2 1
1200.2.h.b 2
1200.2.h.c 2
1200.2.h.d 2
1200.2.h.e 2
1200.2.h.f 2
1200.2.h.g 2
1200.2.h.h 2
1200.2.h.i 2
1200.2.h.j 4
1200.2.h.k 4
1200.2.h.l 4
1200.2.h.m 4
1200.2.h.n 4
1200.2.k \(\chi_{1200}(601, \cdot)\) None 0 1
1200.2.m \(\chi_{1200}(599, \cdot)\) None 0 1
1200.2.o \(\chi_{1200}(1199, \cdot)\) 1200.2.o.a 4 1
1200.2.o.b 4
1200.2.o.c 4
1200.2.o.d 4
1200.2.o.e 4
1200.2.o.f 4
1200.2.o.g 4
1200.2.o.h 4
1200.2.o.i 4
1200.2.s \(\chi_{1200}(301, \cdot)\) n/a 152 2
1200.2.t \(\chi_{1200}(299, \cdot)\) n/a 280 2
1200.2.v \(\chi_{1200}(257, \cdot)\) 1200.2.v.a 4 2
1200.2.v.b 4
1200.2.v.c 4
1200.2.v.d 4
1200.2.v.e 4
1200.2.v.f 4
1200.2.v.g 4
1200.2.v.h 4
1200.2.v.i 4
1200.2.v.j 4
1200.2.v.k 4
1200.2.v.l 8
1200.2.v.m 16
1200.2.w \(\chi_{1200}(607, \cdot)\) 1200.2.w.a 4 2
1200.2.w.b 8
1200.2.w.c 8
1200.2.w.d 8
1200.2.w.e 8
1200.2.y \(\chi_{1200}(643, \cdot)\) n/a 144 2
1200.2.bb \(\chi_{1200}(893, \cdot)\) n/a 280 2
1200.2.bc \(\chi_{1200}(43, \cdot)\) n/a 144 2
1200.2.bf \(\chi_{1200}(293, \cdot)\) n/a 280 2
1200.2.bh \(\chi_{1200}(7, \cdot)\) None 0 2
1200.2.bi \(\chi_{1200}(857, \cdot)\) None 0 2
1200.2.bk \(\chi_{1200}(251, \cdot)\) n/a 292 2
1200.2.bl \(\chi_{1200}(349, \cdot)\) n/a 144 2
1200.2.bo \(\chi_{1200}(241, \cdot)\) n/a 120 4
1200.2.bq \(\chi_{1200}(191, \cdot)\) n/a 240 4
1200.2.bs \(\chi_{1200}(289, \cdot)\) n/a 120 4
1200.2.bu \(\chi_{1200}(169, \cdot)\) None 0 4
1200.2.bw \(\chi_{1200}(71, \cdot)\) None 0 4
1200.2.by \(\chi_{1200}(239, \cdot)\) n/a 240 4
1200.2.ca \(\chi_{1200}(119, \cdot)\) None 0 4
1200.2.cc \(\chi_{1200}(121, \cdot)\) None 0 4
1200.2.ce \(\chi_{1200}(59, \cdot)\) n/a 1888 8
1200.2.cf \(\chi_{1200}(61, \cdot)\) n/a 960 8
1200.2.cj \(\chi_{1200}(137, \cdot)\) None 0 8
1200.2.ck \(\chi_{1200}(103, \cdot)\) None 0 8
1200.2.cm \(\chi_{1200}(53, \cdot)\) n/a 1888 8
1200.2.cp \(\chi_{1200}(67, \cdot)\) n/a 960 8
1200.2.cq \(\chi_{1200}(173, \cdot)\) n/a 1888 8
1200.2.ct \(\chi_{1200}(163, \cdot)\) n/a 960 8
1200.2.cv \(\chi_{1200}(127, \cdot)\) n/a 240 8
1200.2.cw \(\chi_{1200}(17, \cdot)\) n/a 464 8
1200.2.da \(\chi_{1200}(109, \cdot)\) n/a 960 8
1200.2.db \(\chi_{1200}(11, \cdot)\) n/a 1888 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)