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 N = 600=23352 600 = 2^{3} \cdot 3 \cdot 5^{2}
Weight: k k = 3 3
Nonzero newspaces: 18 18
Sturm bound: 5760057600
Trace bound: 88

Dimensions

The following table gives the dimensions of various subspaces of M3(Γ1(600))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+2q210q336q4+8q534q68q74q828q932q1064q1168q12132q13204q1488q15200q1664q176q184q19++768q99+O(q100) 7384 q + 2 q^{2} - 10 q^{3} - 36 q^{4} + 8 q^{5} - 34 q^{6} - 8 q^{7} - 4 q^{8} - 28 q^{9} - 32 q^{10} - 64 q^{11} - 68 q^{12} - 132 q^{13} - 204 q^{14} - 88 q^{15} - 200 q^{16} - 64 q^{17} - 6 q^{18} - 4 q^{19}+ \cdots + 768 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S3new(Γ1(600))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 Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
600.3.c χ600(449,)\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 χ600(151,)\chi_{600}(151, \cdot) None 0 1
600.3.g χ600(451,)\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 χ600(149,)\chi_{600}(149, \cdot) n/a 140 1
600.3.j χ600(199,)\chi_{600}(199, \cdot) None 0 1
600.3.l χ600(401,)\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 χ600(101,)\chi_{600}(101, \cdot) n/a 146 1
600.3.p χ600(499,)\chi_{600}(499, \cdot) 600.3.p.a 8 1
600.3.p.b 32
600.3.p.c 32
600.3.q χ600(107,)\chi_{600}(107, \cdot) n/a 280 2
600.3.t χ600(157,)\chi_{600}(157, \cdot) n/a 144 2
600.3.u χ600(193,)\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 χ600(143,)\chi_{600}(143, \cdot) None 0 2
600.3.z χ600(29,)\chi_{600}(29, \cdot) n/a 944 4
600.3.bb χ600(91,)\chi_{600}(91, \cdot) n/a 480 4
600.3.bd χ600(31,)\chi_{600}(31, \cdot) None 0 4
600.3.bf χ600(89,)\chi_{600}(89, \cdot) n/a 240 4
600.3.bh χ600(19,)\chi_{600}(19, \cdot) n/a 480 4
600.3.bj χ600(221,)\chi_{600}(221, \cdot) n/a 944 4
600.3.bl χ600(41,)\chi_{600}(41, \cdot) n/a 240 4
600.3.bn χ600(79,)\chi_{600}(79, \cdot) None 0 4
600.3.bo χ600(23,)\chi_{600}(23, \cdot) None 0 8
600.3.br χ600(73,)\chi_{600}(73, \cdot) n/a 240 8
600.3.bs χ600(13,)\chi_{600}(13, \cdot) n/a 960 8
600.3.bv χ600(83,)\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 S3old(Γ1(600))S_{3}^{\mathrm{old}}(\Gamma_1(600)) into lower level spaces

S3old(Γ1(600)) S_{3}^{\mathrm{old}}(\Gamma_1(600)) \cong S3new(Γ1(1))S_{3}^{\mathrm{new}}(\Gamma_1(1))24^{\oplus 24}\oplusS3new(Γ1(2))S_{3}^{\mathrm{new}}(\Gamma_1(2))18^{\oplus 18}\oplusS3new(Γ1(3))S_{3}^{\mathrm{new}}(\Gamma_1(3))12^{\oplus 12}\oplusS3new(Γ1(4))S_{3}^{\mathrm{new}}(\Gamma_1(4))12^{\oplus 12}\oplusS3new(Γ1(5))S_{3}^{\mathrm{new}}(\Gamma_1(5))16^{\oplus 16}\oplusS3new(Γ1(6))S_{3}^{\mathrm{new}}(\Gamma_1(6))9^{\oplus 9}\oplusS3new(Γ1(8))S_{3}^{\mathrm{new}}(\Gamma_1(8))6^{\oplus 6}\oplusS3new(Γ1(10))S_{3}^{\mathrm{new}}(\Gamma_1(10))12^{\oplus 12}\oplusS3new(Γ1(12))S_{3}^{\mathrm{new}}(\Gamma_1(12))6^{\oplus 6}\oplusS3new(Γ1(15))S_{3}^{\mathrm{new}}(\Gamma_1(15))8^{\oplus 8}\oplusS3new(Γ1(20))S_{3}^{\mathrm{new}}(\Gamma_1(20))8^{\oplus 8}\oplusS3new(Γ1(24))S_{3}^{\mathrm{new}}(\Gamma_1(24))3^{\oplus 3}\oplusS3new(Γ1(25))S_{3}^{\mathrm{new}}(\Gamma_1(25))8^{\oplus 8}\oplusS3new(Γ1(30))S_{3}^{\mathrm{new}}(\Gamma_1(30))6^{\oplus 6}\oplusS3new(Γ1(40))S_{3}^{\mathrm{new}}(\Gamma_1(40))4^{\oplus 4}\oplusS3new(Γ1(50))S_{3}^{\mathrm{new}}(\Gamma_1(50))6^{\oplus 6}\oplusS3new(Γ1(60))S_{3}^{\mathrm{new}}(\Gamma_1(60))4^{\oplus 4}\oplusS3new(Γ1(75))S_{3}^{\mathrm{new}}(\Gamma_1(75))4^{\oplus 4}\oplusS3new(Γ1(100))S_{3}^{\mathrm{new}}(\Gamma_1(100))4^{\oplus 4}\oplusS3new(Γ1(120))S_{3}^{\mathrm{new}}(\Gamma_1(120))2^{\oplus 2}\oplusS3new(Γ1(150))S_{3}^{\mathrm{new}}(\Gamma_1(150))3^{\oplus 3}\oplusS3new(Γ1(200))S_{3}^{\mathrm{new}}(\Gamma_1(200))2^{\oplus 2}\oplusS3new(Γ1(300))S_{3}^{\mathrm{new}}(\Gamma_1(300))2^{\oplus 2}