Properties

Label 600.2
Level 600
Weight 2
Dimension 3651
Nonzero newspaces 18
Newform subspaces 81
Sturm bound 38400
Trace bound 8

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 81 \)
Sturm bound: \(38400\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(600))\).

Total New Old
Modular forms 10272 3815 6457
Cusp forms 8929 3651 5278
Eisenstein series 1343 164 1179

Trace form

\( 3651q - 2q^{2} - 15q^{3} - 28q^{4} - 2q^{5} - 18q^{6} - 44q^{7} + 4q^{8} - 31q^{9} + O(q^{10}) \) \( 3651q - 2q^{2} - 15q^{3} - 28q^{4} - 2q^{5} - 18q^{6} - 44q^{7} + 4q^{8} - 31q^{9} - 32q^{10} - 12q^{11} + 20q^{12} - 10q^{13} + 52q^{14} - 8q^{15} + 24q^{16} + 6q^{17} + 38q^{18} + 40q^{19} + 40q^{20} + 32q^{21} + 48q^{22} + 48q^{23} + 32q^{24} - 58q^{25} + 56q^{26} + 45q^{27} - 40q^{28} + 30q^{29} - 12q^{30} + 36q^{31} - 72q^{32} + 28q^{33} - 132q^{34} + 48q^{35} - 32q^{36} + 72q^{37} - 104q^{38} + 78q^{39} - 112q^{40} + 46q^{41} - 96q^{42} + 136q^{43} - 112q^{44} + 70q^{45} - 176q^{46} + 120q^{47} - 140q^{48} + 55q^{49} - 40q^{50} - 62q^{51} - 72q^{52} + 64q^{53} - 110q^{54} + 64q^{55} - 8q^{56} + 16q^{57} - 36q^{58} + 20q^{59} - 92q^{60} - 50q^{61} - 4q^{62} - 120q^{63} - 88q^{64} + 6q^{65} - 188q^{66} - 160q^{67} - 112q^{68} - 24q^{69} - 104q^{70} - 128q^{71} - 200q^{72} + 74q^{73} - 160q^{74} - 88q^{75} - 232q^{76} - 188q^{78} - 204q^{79} - 80q^{80} + 57q^{81} - 348q^{82} - 268q^{83} - 300q^{84} - 82q^{85} - 184q^{86} - 206q^{87} - 472q^{88} + 128q^{89} - 172q^{90} - 184q^{91} - 384q^{92} - 32q^{93} - 496q^{94} - 256q^{95} - 84q^{96} - 86q^{97} - 378q^{98} - 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)

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
600.2.a \(\chi_{600}(1, \cdot)\) 600.2.a.a 1 1
600.2.a.b 1
600.2.a.c 1
600.2.a.d 1
600.2.a.e 1
600.2.a.f 1
600.2.a.g 1
600.2.a.h 1
600.2.a.i 1
600.2.b \(\chi_{600}(251, \cdot)\) 600.2.b.a 2 1
600.2.b.b 4
600.2.b.c 4
600.2.b.d 4
600.2.b.e 8
600.2.b.f 8
600.2.b.g 12
600.2.b.h 12
600.2.b.i 16
600.2.d \(\chi_{600}(349, \cdot)\) 600.2.d.a 2 1
600.2.d.b 2
600.2.d.c 2
600.2.d.d 2
600.2.d.e 6
600.2.d.f 6
600.2.d.g 8
600.2.d.h 8
600.2.f \(\chi_{600}(49, \cdot)\) 600.2.f.a 2 1
600.2.f.b 2
600.2.f.c 2
600.2.f.d 2
600.2.f.e 2
600.2.h \(\chi_{600}(551, \cdot)\) None 0 1
600.2.k \(\chi_{600}(301, \cdot)\) 600.2.k.a 2 1
600.2.k.b 2
600.2.k.c 6
600.2.k.d 8
600.2.k.e 8
600.2.k.f 12
600.2.m \(\chi_{600}(299, \cdot)\) 600.2.m.a 4 1
600.2.m.b 8
600.2.m.c 16
600.2.m.d 16
600.2.m.e 24
600.2.o \(\chi_{600}(599, \cdot)\) None 0 1
600.2.r \(\chi_{600}(257, \cdot)\) 600.2.r.a 4 2
600.2.r.b 4
600.2.r.c 4
600.2.r.d 4
600.2.r.e 4
600.2.r.f 16
600.2.s \(\chi_{600}(7, \cdot)\) None 0 2
600.2.v \(\chi_{600}(43, \cdot)\) 600.2.v.a 16 2
600.2.v.b 24
600.2.v.c 32
600.2.w \(\chi_{600}(293, \cdot)\) 600.2.w.a 4 2
600.2.w.b 4
600.2.w.c 4
600.2.w.d 4
600.2.w.e 4
600.2.w.f 4
600.2.w.g 4
600.2.w.h 4
600.2.w.i 8
600.2.w.j 32
600.2.w.k 64
600.2.y \(\chi_{600}(121, \cdot)\) 600.2.y.a 4 4
600.2.y.b 4
600.2.y.c 12
600.2.y.d 12
600.2.y.e 16
600.2.y.f 16
600.2.ba \(\chi_{600}(71, \cdot)\) None 0 4
600.2.bc \(\chi_{600}(169, \cdot)\) 600.2.bc.a 8 4
600.2.bc.b 24
600.2.bc.c 24
600.2.be \(\chi_{600}(109, \cdot)\) 600.2.be.a 120 4
600.2.be.b 120
600.2.bg \(\chi_{600}(11, \cdot)\) 600.2.bg.a 464 4
600.2.bi \(\chi_{600}(119, \cdot)\) None 0 4
600.2.bk \(\chi_{600}(59, \cdot)\) 600.2.bk.a 464 4
600.2.bm \(\chi_{600}(61, \cdot)\) 600.2.bm.a 240 4
600.2.bp \(\chi_{600}(53, \cdot)\) 600.2.bp.a 16 8
600.2.bp.b 16
600.2.bp.c 896
600.2.bq \(\chi_{600}(67, \cdot)\) 600.2.bq.a 480 8
600.2.bt \(\chi_{600}(103, \cdot)\) None 0 8
600.2.bu \(\chi_{600}(17, \cdot)\) 600.2.bu.a 240 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)