↑

Properties

Label 6000.2
Level 6000
Weight 2
Dimension 372096
Nonzero newspaces 42
Sturm bound 3840000

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 6000 = 2^{4} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(3840000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6000))\).

Total New Old
Modular forms 970080 374400 595680
Cusp forms 949921 372096 577825
Eisenstein series 20159 2304 17855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6000))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6000.2.a \(\chi_{6000}(1, \cdot)\) 6000.2.a.a 2 1
6000.2.a.b 2
6000.2.a.c 2
6000.2.a.d 2
6000.2.a.e 2
6000.2.a.f 2
6000.2.a.g 2
6000.2.a.h 2
6000.2.a.i 2
6000.2.a.j 2
6000.2.a.k 2
6000.2.a.l 2
6000.2.a.m 2
6000.2.a.n 2
6000.2.a.o 2
6000.2.a.p 2
6000.2.a.q 2
6000.2.a.r 2
6000.2.a.s 2
6000.2.a.t 2
6000.2.a.u 2
6000.2.a.v 2
6000.2.a.w 2
6000.2.a.x 2
6000.2.a.y 2
6000.2.a.z 2
6000.2.a.ba 2
6000.2.a.bb 2
6000.2.a.bc 4
6000.2.a.bd 4
6000.2.a.be 4
6000.2.a.bf 4
6000.2.a.bg 4
6000.2.a.bh 4
6000.2.a.bi 4
6000.2.a.bj 4
6000.2.a.bk 4
6000.2.a.bl 4
6000.2.b \(\chi_{6000}(1751, \cdot)\) None 0 1
6000.2.d \(\chi_{6000}(4249, \cdot)\) None 0 1
6000.2.f \(\chi_{6000}(1249, \cdot)\) 6000.2.f.a 4 1
6000.2.f.b 4
6000.2.f.c 4
6000.2.f.d 4
6000.2.f.e 4
6000.2.f.f 4
6000.2.f.g 4
6000.2.f.h 4
6000.2.f.i 4
6000.2.f.j 4
6000.2.f.k 4
6000.2.f.l 4
6000.2.f.m 4
6000.2.f.n 4
6000.2.f.o 8
6000.2.f.p 8
6000.2.f.q 8
6000.2.f.r 8
6000.2.f.s 8
6000.2.h \(\chi_{6000}(4751, \cdot)\) n/a 192 1
6000.2.k \(\chi_{6000}(3001, \cdot)\) None 0 1
6000.2.m \(\chi_{6000}(2999, \cdot)\) None 0 1
6000.2.o \(\chi_{6000}(5999, \cdot)\) n/a 192 1
6000.2.s \(\chi_{6000}(1501, \cdot)\) n/a 768 2
6000.2.t \(\chi_{6000}(1499, \cdot)\) n/a 1536 2
6000.2.v \(\chi_{6000}(4193, \cdot)\) n/a 384 2
6000.2.w \(\chi_{6000}(943, \cdot)\) n/a 192 2
6000.2.y \(\chi_{6000}(3307, \cdot)\) n/a 768 2
6000.2.bb \(\chi_{6000}(3557, \cdot)\) n/a 1536 2
6000.2.bc \(\chi_{6000}(307, \cdot)\) n/a 768 2
6000.2.bf \(\chi_{6000}(557, \cdot)\) n/a 1536 2
6000.2.bh \(\chi_{6000}(3943, \cdot)\) None 0 2
6000.2.bi \(\chi_{6000}(1193, \cdot)\) None 0 2
6000.2.bk \(\chi_{6000}(251, \cdot)\) n/a 1536 2
6000.2.bl \(\chi_{6000}(2749, \cdot)\) n/a 768 2
6000.2.bo \(\chi_{6000}(1201, \cdot)\) n/a 360 4
6000.2.bq \(\chi_{6000}(1151, \cdot)\) n/a 720 4
6000.2.bs \(\chi_{6000}(49, \cdot)\) n/a 360 4
6000.2.bu \(\chi_{6000}(649, \cdot)\) None 0 4
6000.2.bw \(\chi_{6000}(551, \cdot)\) None 0 4
6000.2.by \(\chi_{6000}(1199, \cdot)\) n/a 720 4
6000.2.ca \(\chi_{6000}(599, \cdot)\) None 0 4
6000.2.cc \(\chi_{6000}(601, \cdot)\) None 0 4
6000.2.ce \(\chi_{6000}(299, \cdot)\) n/a 5664 8
6000.2.cf \(\chi_{6000}(301, \cdot)\) n/a 2880 8
6000.2.cj \(\chi_{6000}(857, \cdot)\) None 0 8
6000.2.ck \(\chi_{6000}(7, \cdot)\) None 0 8
6000.2.cm \(\chi_{6000}(293, \cdot)\) n/a 5664 8
6000.2.cp \(\chi_{6000}(43, \cdot)\) n/a 2880 8
6000.2.cq \(\chi_{6000}(893, \cdot)\) n/a 5664 8
6000.2.ct \(\chi_{6000}(643, \cdot)\) n/a 2880 8
6000.2.cv \(\chi_{6000}(607, \cdot)\) n/a 720 8
6000.2.cw \(\chi_{6000}(257, \cdot)\) n/a 1392 8
6000.2.da \(\chi_{6000}(349, \cdot)\) n/a 2880 8
6000.2.db \(\chi_{6000}(851, \cdot)\) n/a 5664 8
6000.2.dc \(\chi_{6000}(241, \cdot)\) n/a 3000 20
6000.2.df \(\chi_{6000}(239, \cdot)\) n/a 6000 20
6000.2.dh \(\chi_{6000}(119, \cdot)\) None 0 20
6000.2.di \(\chi_{6000}(121, \cdot)\) None 0 20
6000.2.dl \(\chi_{6000}(71, \cdot)\) None 0 20
6000.2.dm \(\chi_{6000}(169, \cdot)\) None 0 20
6000.2.do \(\chi_{6000}(289, \cdot)\) n/a 3000 20
6000.2.dr \(\chi_{6000}(191, \cdot)\) n/a 6000 20
6000.2.ds \(\chi_{6000}(11, \cdot)\) n/a 47840 40
6000.2.dv \(\chi_{6000}(109, \cdot)\) n/a 24000 40
6000.2.dx \(\chi_{6000}(173, \cdot)\) n/a 47840 40
6000.2.dy \(\chi_{6000}(67, \cdot)\) n/a 24000 40
6000.2.eb \(\chi_{6000}(137, \cdot)\) None 0 40
6000.2.ec \(\chi_{6000}(127, \cdot)\) n/a 6000 40
6000.2.ee \(\chi_{6000}(17, \cdot)\) n/a 11920 40
6000.2.eh \(\chi_{6000}(103, \cdot)\) None 0 40
6000.2.ei \(\chi_{6000}(163, \cdot)\) n/a 24000 40
6000.2.el \(\chi_{6000}(53, \cdot)\) n/a 47840 40
6000.2.en \(\chi_{6000}(61, \cdot)\) n/a 24000 40
6000.2.eo \(\chi_{6000}(59, \cdot)\) n/a 47840 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6000))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1500))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6000))\)\(^{\oplus 1}\)