Space of modular forms of level 4608 and weight 2

• Label: 4608.2
• Level: 4608
• Weight: 2
• Dimension: 261648
• Nonzero newspaces: 28
• Sturm bound: 2359296

Defining parameters

Level:	$N$	=	$4608 = 2^{9} \cdot 3^{2}$
Weight:	$k$	=	$2$
Nonzero newspaces:			$28$
Sturm bound:			$2359296$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4608))$.

	Total	New	Old
Modular forms	595968	263664	332304
Cusp forms	583681	261648	322033
Eisenstein series	12287	2016	10271

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4608))$

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
4608.2.a	$\chi_{4608}(1, \cdot)$	4608.2.a.a	2	1
		4608.2.a.b	2
		4608.2.a.c	2
		4608.2.a.d	2
		4608.2.a.e	2
		4608.2.a.f	2
		4608.2.a.g	2
		4608.2.a.h	2
		4608.2.a.i	2
		4608.2.a.j	2
		4608.2.a.k	2
		4608.2.a.l	2
		4608.2.a.m	2
		4608.2.a.n	2
		4608.2.a.o	2
		4608.2.a.p	2
		4608.2.a.q	2
		4608.2.a.r	2
		4608.2.a.s	4
		4608.2.a.t	4
		4608.2.a.u	4
		4608.2.a.v	4
		4608.2.a.w	4
		4608.2.a.x	4
		4608.2.a.y	4
		4608.2.a.z	4
		4608.2.a.ba	4
		4608.2.a.bb	4
		4608.2.a.bc	4
4608.2.c	$\chi_{4608}(4607, \cdot)$	4608.2.c.a	2	1
		4608.2.c.b	2
		4608.2.c.c	2
		4608.2.c.d	2
		4608.2.c.e	2
		4608.2.c.f	2
		4608.2.c.g	2
		4608.2.c.h	2
		4608.2.c.i	4
		4608.2.c.j	4
		4608.2.c.k	4
		4608.2.c.l	4
		4608.2.c.m	4
		4608.2.c.n	4
		4608.2.c.o	4
		4608.2.c.p	4
		4608.2.c.q	8
		4608.2.c.r	8
4608.2.d	$\chi_{4608}(2305, \cdot)$	4608.2.d.a	2	1
		4608.2.d.b	2
		4608.2.d.c	4
		4608.2.d.d	4
		4608.2.d.e	4
		4608.2.d.f	4
		4608.2.d.g	4
		4608.2.d.h	4
		4608.2.d.i	4
		4608.2.d.j	4
		4608.2.d.k	4
		4608.2.d.l	4
		4608.2.d.m	4
		4608.2.d.n	4
		4608.2.d.o	4
		4608.2.d.p	8
		4608.2.d.q	8
		4608.2.d.r	8
4608.2.f	$\chi_{4608}(2303, \cdot)$	4608.2.f.a	2	1
		4608.2.f.b	2
		4608.2.f.c	2
		4608.2.f.d	2
		4608.2.f.e	2
		4608.2.f.f	2
		4608.2.f.g	2
		4608.2.f.h	2
		4608.2.f.i	4
		4608.2.f.j	4
		4608.2.f.k	4
		4608.2.f.l	4
		4608.2.f.m	8
		4608.2.f.n	8
		4608.2.f.o	8
		4608.2.f.p	8
4608.2.i	$\chi_{4608}(1537, \cdot)$	n/a	384	2
4608.2.k	$\chi_{4608}(1153, \cdot)$	4608.2.k.a	2	2
		4608.2.k.b	2
		4608.2.k.c	2
		4608.2.k.d	2
		4608.2.k.e	2
		4608.2.k.f	2
		4608.2.k.g	2
		4608.2.k.h	2
		4608.2.k.i	2
		4608.2.k.j	2
		4608.2.k.k	2
		4608.2.k.l	2
		4608.2.k.m	2
		4608.2.k.n	2
		4608.2.k.o	2
		4608.2.k.p	2
		4608.2.k.q	2
		4608.2.k.r	2
		4608.2.k.s	2
		4608.2.k.t	2
		4608.2.k.u	2
		4608.2.k.v	2
		4608.2.k.w	2
		4608.2.k.x	2
		4608.2.k.y	4
		4608.2.k.z	4
		4608.2.k.ba	4
		4608.2.k.bb	4
		4608.2.k.bc	8
		4608.2.k.bd	8
		4608.2.k.be	8
		4608.2.k.bf	8
		4608.2.k.bg	8
		4608.2.k.bh	8
		4608.2.k.bi	8
		4608.2.k.bj	8
		4608.2.k.bk	16
		4608.2.k.bl	16
4608.2.l	$\chi_{4608}(1151, \cdot)$	n/a	128	2
4608.2.p	$\chi_{4608}(767, \cdot)$	n/a	384	2
4608.2.r	$\chi_{4608}(769, \cdot)$	n/a	384	2
4608.2.s	$\chi_{4608}(1535, \cdot)$	n/a	384	2
4608.2.v	$\chi_{4608}(577, \cdot)$	n/a	304	4
4608.2.w	$\chi_{4608}(575, \cdot)$	n/a	256	4
4608.2.y	$\chi_{4608}(383, \cdot)$	n/a	768	4
4608.2.bb	$\chi_{4608}(385, \cdot)$	n/a	768	4
4608.2.bd	$\chi_{4608}(289, \cdot)$	n/a	624	8
4608.2.be	$\chi_{4608}(287, \cdot)$	n/a	512	8
4608.2.bg	$\chi_{4608}(193, \cdot)$	n/a	1472	8
4608.2.bj	$\chi_{4608}(191, \cdot)$	n/a	1472	8
4608.2.bl	$\chi_{4608}(145, \cdot)$	n/a	1264	16
4608.2.bm	$\chi_{4608}(143, \cdot)$	n/a	1024	16
4608.2.bp	$\chi_{4608}(95, \cdot)$	n/a	3008	16
4608.2.bq	$\chi_{4608}(97, \cdot)$	n/a	3008	16
4608.2.bt	$\chi_{4608}(73, \cdot)$	None	0	32
4608.2.bu	$\chi_{4608}(71, \cdot)$	None	0	32
4608.2.bw	$\chi_{4608}(47, \cdot)$	n/a	6080	32
4608.2.bz	$\chi_{4608}(49, \cdot)$	n/a	6080	32
4608.2.cb	$\chi_{4608}(37, \cdot)$	n/a	20416	64
4608.2.cc	$\chi_{4608}(35, \cdot)$	n/a	16384	64
4608.2.ce	$\chi_{4608}(25, \cdot)$	None	0	64
4608.2.ch	$\chi_{4608}(23, \cdot)$	None	0	64
4608.2.cj	$\chi_{4608}(11, \cdot)$	n/a	98048	128
4608.2.ck	$\chi_{4608}(13, \cdot)$	n/a	98048	128

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4608))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4608)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 30}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 27}$$\oplus$$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(6))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 21}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 15}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(384))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(768))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1152))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1536))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2304))$$^{\oplus 2}$