Properties

Label 600.3
Level 600
Weight 3
Dimension 7384
Nonzero newspaces 18
Sturm bound 57600
Trace bound 8

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Defining parameters

Level: \( N \) = \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(57600\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(600))\).

Total New Old
Modular forms 19872 7548 12324
Cusp forms 18528 7384 11144
Eisenstein series 1344 164 1180

Trace form

\( 7384q + 2q^{2} - 10q^{3} - 36q^{4} + 8q^{5} - 34q^{6} - 8q^{7} - 4q^{8} - 28q^{9} + O(q^{10}) \) \( 7384q + 2q^{2} - 10q^{3} - 36q^{4} + 8q^{5} - 34q^{6} - 8q^{7} - 4q^{8} - 28q^{9} - 32q^{10} - 64q^{11} - 68q^{12} - 132q^{13} - 204q^{14} - 88q^{15} - 200q^{16} - 64q^{17} - 6q^{18} - 4q^{19} + 40q^{20} - 28q^{21} + 264q^{22} + 192q^{23} + 216q^{24} - 28q^{25} + 352q^{26} + 86q^{27} + 488q^{28} + 228q^{30} - 536q^{31} + 472q^{32} - 52q^{33} + 548q^{34} - 192q^{35} + 136q^{36} - 204q^{37} + 152q^{38} + 48q^{39} - 112q^{40} + 136q^{41} + 72q^{42} + 396q^{43} - 496q^{44} - 220q^{45} - 784q^{46} + 672q^{47} - 44q^{48} + 332q^{49} - 440q^{50} + 528q^{51} - 1016q^{52} + 384q^{53} + 306q^{54} + 664q^{55} - 168q^{56} + 516q^{57} - 20q^{58} + 672q^{59} - 12q^{60} + 212q^{61} + 204q^{62} + 300q^{63} + 936q^{64} - 84q^{65} + 244q^{66} + 1004q^{67} + 1344q^{68} - 544q^{69} + 616q^{70} + 960q^{71} - 336q^{72} - 1088q^{73} + 760q^{74} - 248q^{75} + 232q^{76} - 480q^{77} - 340q^{78} - 728q^{79} - 80q^{80} + 204q^{81} + 716q^{82} + 224q^{83} + 628q^{84} + 1448q^{85} - 184q^{86} + 296q^{87} + 1512q^{88} + 1700q^{89} + 188q^{90} - 640q^{91} - 96q^{92} + 1300q^{93} + 48q^{94} + 224q^{95} - 1076q^{96} + 1904q^{97} - 406q^{98} + 768q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(600))\)

We only show spaces with odd 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
600.3.c \(\chi_{600}(449, \cdot)\) 600.3.c.a 4 1
600.3.c.b 4
600.3.c.c 12
600.3.c.d 16
600.3.e \(\chi_{600}(151, \cdot)\) None 0 1
600.3.g \(\chi_{600}(451, \cdot)\) 600.3.g.a 4 1
600.3.g.b 16
600.3.g.c 16
600.3.g.d 16
600.3.g.e 24
600.3.i \(\chi_{600}(149, \cdot)\) n/a 140 1
600.3.j \(\chi_{600}(199, \cdot)\) None 0 1
600.3.l \(\chi_{600}(401, \cdot)\) 600.3.l.a 2 1
600.3.l.b 2
600.3.l.c 2
600.3.l.d 6
600.3.l.e 6
600.3.l.f 8
600.3.l.g 12
600.3.n \(\chi_{600}(101, \cdot)\) n/a 146 1
600.3.p \(\chi_{600}(499, \cdot)\) 600.3.p.a 8 1
600.3.p.b 32
600.3.p.c 32
600.3.q \(\chi_{600}(107, \cdot)\) n/a 280 2
600.3.t \(\chi_{600}(157, \cdot)\) n/a 144 2
600.3.u \(\chi_{600}(193, \cdot)\) 600.3.u.a 4 2
600.3.u.b 4
600.3.u.c 4
600.3.u.d 4
600.3.u.e 4
600.3.u.f 4
600.3.u.g 4
600.3.u.h 8
600.3.x \(\chi_{600}(143, \cdot)\) None 0 2
600.3.z \(\chi_{600}(29, \cdot)\) n/a 944 4
600.3.bb \(\chi_{600}(91, \cdot)\) n/a 480 4
600.3.bd \(\chi_{600}(31, \cdot)\) None 0 4
600.3.bf \(\chi_{600}(89, \cdot)\) n/a 240 4
600.3.bh \(\chi_{600}(19, \cdot)\) n/a 480 4
600.3.bj \(\chi_{600}(221, \cdot)\) n/a 944 4
600.3.bl \(\chi_{600}(41, \cdot)\) n/a 240 4
600.3.bn \(\chi_{600}(79, \cdot)\) None 0 4
600.3.bo \(\chi_{600}(23, \cdot)\) None 0 8
600.3.br \(\chi_{600}(73, \cdot)\) n/a 240 8
600.3.bs \(\chi_{600}(13, \cdot)\) n/a 960 8
600.3.bv \(\chi_{600}(83, \cdot)\) n/a 1888 8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(600))\) into lower level spaces

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