Properties

Label 3000.2
Level 3000
Weight 2
Dimension 92800
Nonzero newspaces 27
Sturm bound 960000
Trace bound 16

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Defining parameters

Level: N N = 3000=23353 3000 = 2^{3} \cdot 3 \cdot 5^{3}
Weight: k k = 2 2
Nonzero newspaces: 27 27
Sturm bound: 960000960000
Trace bound: 1616

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ1(3000))M_{2}(\Gamma_1(3000)).

Total New Old
Modular forms 244320 93824 150496
Cusp forms 235681 92800 142881
Eisenstein series 8639 1024 7615

Trace form

92800q64q3128q4116q6120q7126q9160q10+8q1176q12+4q1324q1480q15264q164q1792q18160q1916q21168q22++44q99+O(q100) 92800 q - 64 q^{3} - 128 q^{4} - 116 q^{6} - 120 q^{7} - 126 q^{9} - 160 q^{10} + 8 q^{11} - 76 q^{12} + 4 q^{13} - 24 q^{14} - 80 q^{15} - 264 q^{16} - 4 q^{17} - 92 q^{18} - 160 q^{19} - 16 q^{21} - 168 q^{22}+ \cdots + 44 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ1(3000))S_{2}^{\mathrm{new}}(\Gamma_1(3000))

We only show spaces with even 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
3000.2.a χ3000(1,)\chi_{3000}(1, \cdot) 3000.2.a.a 2 1
3000.2.a.b 2
3000.2.a.c 2
3000.2.a.d 2
3000.2.a.e 2
3000.2.a.f 2
3000.2.a.g 2
3000.2.a.h 2
3000.2.a.i 4
3000.2.a.j 4
3000.2.a.k 4
3000.2.a.l 4
3000.2.a.m 4
3000.2.a.n 4
3000.2.a.o 4
3000.2.a.p 4
3000.2.b χ3000(251,)\chi_{3000}(251, \cdot) n/a 384 1
3000.2.d χ3000(2749,)\chi_{3000}(2749, \cdot) n/a 192 1
3000.2.f χ3000(1249,)\chi_{3000}(1249, \cdot) 3000.2.f.a 4 1
3000.2.f.b 4
3000.2.f.c 4
3000.2.f.d 4
3000.2.f.e 8
3000.2.f.f 8
3000.2.f.g 8
3000.2.f.h 8
3000.2.h χ3000(1751,)\chi_{3000}(1751, \cdot) None 0 1
3000.2.k χ3000(1501,)\chi_{3000}(1501, \cdot) n/a 192 1
3000.2.m χ3000(1499,)\chi_{3000}(1499, \cdot) n/a 384 1
3000.2.o χ3000(2999,)\chi_{3000}(2999, \cdot) None 0 1
3000.2.r χ3000(1193,)\chi_{3000}(1193, \cdot) n/a 192 2
3000.2.s χ3000(943,)\chi_{3000}(943, \cdot) None 0 2
3000.2.v χ3000(307,)\chi_{3000}(307, \cdot) n/a 384 2
3000.2.w χ3000(557,)\chi_{3000}(557, \cdot) n/a 768 2
3000.2.y χ3000(601,)\chi_{3000}(601, \cdot) n/a 176 4
3000.2.ba χ3000(551,)\chi_{3000}(551, \cdot) None 0 4
3000.2.bc χ3000(49,)\chi_{3000}(49, \cdot) n/a 184 4
3000.2.be χ3000(349,)\chi_{3000}(349, \cdot) n/a 720 4
3000.2.bg χ3000(851,)\chi_{3000}(851, \cdot) n/a 1392 4
3000.2.bi χ3000(599,)\chi_{3000}(599, \cdot) None 0 4
3000.2.bk χ3000(299,)\chi_{3000}(299, \cdot) n/a 1392 4
3000.2.bm χ3000(301,)\chi_{3000}(301, \cdot) n/a 720 4
3000.2.bp χ3000(293,)\chi_{3000}(293, \cdot) n/a 2784 8
3000.2.bq χ3000(43,)\chi_{3000}(43, \cdot) n/a 1440 8
3000.2.bt χ3000(7,)\chi_{3000}(7, \cdot) None 0 8
3000.2.bu χ3000(257,)\chi_{3000}(257, \cdot) n/a 720 8
3000.2.bw χ3000(121,)\chi_{3000}(121, \cdot) n/a 1520 20
3000.2.bz χ3000(119,)\chi_{3000}(119, \cdot) None 0 20
3000.2.cb χ3000(59,)\chi_{3000}(59, \cdot) n/a 11920 20
3000.2.cc χ3000(61,)\chi_{3000}(61, \cdot) n/a 6000 20
3000.2.cf χ3000(11,)\chi_{3000}(11, \cdot) n/a 11920 20
3000.2.cg χ3000(109,)\chi_{3000}(109, \cdot) n/a 6000 20
3000.2.ci χ3000(169,)\chi_{3000}(169, \cdot) n/a 1480 20
3000.2.cl χ3000(71,)\chi_{3000}(71, \cdot) None 0 20
3000.2.cn χ3000(53,)\chi_{3000}(53, \cdot) n/a 23840 40
3000.2.co χ3000(103,)\chi_{3000}(103, \cdot) None 0 40
3000.2.cq χ3000(17,)\chi_{3000}(17, \cdot) n/a 6000 40
3000.2.ct χ3000(67,)\chi_{3000}(67, \cdot) n/a 12000 40

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

Decomposition of S2old(Γ1(3000))S_{2}^{\mathrm{old}}(\Gamma_1(3000)) into lower level spaces

S2old(Γ1(3000)) S_{2}^{\mathrm{old}}(\Gamma_1(3000)) \cong S2new(Γ1(1))S_{2}^{\mathrm{new}}(\Gamma_1(1))32^{\oplus 32}\oplusS2new(Γ1(2))S_{2}^{\mathrm{new}}(\Gamma_1(2))24^{\oplus 24}\oplusS2new(Γ1(3))S_{2}^{\mathrm{new}}(\Gamma_1(3))16^{\oplus 16}\oplusS2new(Γ1(4))S_{2}^{\mathrm{new}}(\Gamma_1(4))16^{\oplus 16}\oplusS2new(Γ1(5))S_{2}^{\mathrm{new}}(\Gamma_1(5))24^{\oplus 24}\oplusS2new(Γ1(6))S_{2}^{\mathrm{new}}(\Gamma_1(6))12^{\oplus 12}\oplusS2new(Γ1(8))S_{2}^{\mathrm{new}}(\Gamma_1(8))8^{\oplus 8}\oplusS2new(Γ1(10))S_{2}^{\mathrm{new}}(\Gamma_1(10))18^{\oplus 18}\oplusS2new(Γ1(12))S_{2}^{\mathrm{new}}(\Gamma_1(12))8^{\oplus 8}\oplusS2new(Γ1(15))S_{2}^{\mathrm{new}}(\Gamma_1(15))12^{\oplus 12}\oplusS2new(Γ1(20))S_{2}^{\mathrm{new}}(\Gamma_1(20))12^{\oplus 12}\oplusS2new(Γ1(24))S_{2}^{\mathrm{new}}(\Gamma_1(24))4^{\oplus 4}\oplusS2new(Γ1(25))S_{2}^{\mathrm{new}}(\Gamma_1(25))16^{\oplus 16}\oplusS2new(Γ1(30))S_{2}^{\mathrm{new}}(\Gamma_1(30))9^{\oplus 9}\oplusS2new(Γ1(40))S_{2}^{\mathrm{new}}(\Gamma_1(40))6^{\oplus 6}\oplusS2new(Γ1(50))S_{2}^{\mathrm{new}}(\Gamma_1(50))12^{\oplus 12}\oplusS2new(Γ1(60))S_{2}^{\mathrm{new}}(\Gamma_1(60))6^{\oplus 6}\oplusS2new(Γ1(75))S_{2}^{\mathrm{new}}(\Gamma_1(75))8^{\oplus 8}\oplusS2new(Γ1(100))S_{2}^{\mathrm{new}}(\Gamma_1(100))8^{\oplus 8}\oplusS2new(Γ1(120))S_{2}^{\mathrm{new}}(\Gamma_1(120))3^{\oplus 3}\oplusS2new(Γ1(125))S_{2}^{\mathrm{new}}(\Gamma_1(125))8^{\oplus 8}\oplusS2new(Γ1(150))S_{2}^{\mathrm{new}}(\Gamma_1(150))6^{\oplus 6}\oplusS2new(Γ1(200))S_{2}^{\mathrm{new}}(\Gamma_1(200))4^{\oplus 4}\oplusS2new(Γ1(250))S_{2}^{\mathrm{new}}(\Gamma_1(250))6^{\oplus 6}\oplusS2new(Γ1(300))S_{2}^{\mathrm{new}}(\Gamma_1(300))4^{\oplus 4}\oplusS2new(Γ1(375))S_{2}^{\mathrm{new}}(\Gamma_1(375))4^{\oplus 4}\oplusS2new(Γ1(500))S_{2}^{\mathrm{new}}(\Gamma_1(500))4^{\oplus 4}\oplusS2new(Γ1(600))S_{2}^{\mathrm{new}}(\Gamma_1(600))2^{\oplus 2}\oplusS2new(Γ1(750))S_{2}^{\mathrm{new}}(\Gamma_1(750))3^{\oplus 3}\oplusS2new(Γ1(1000))S_{2}^{\mathrm{new}}(\Gamma_1(1000))2^{\oplus 2}\oplusS2new(Γ1(1500))S_{2}^{\mathrm{new}}(\Gamma_1(1500))2^{\oplus 2}