Space of modular forms of level 6000 and weight 2

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

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}$