Space of modular forms of level 4032 and weight 2

• Label: 4032.2
• Level: 4032
• Weight: 2
• Dimension: 187794
• Nonzero newspaces: 80
• Sturm bound: 1769472

Defining parameters

Level:	$N$	=	$4032 = 2^{6} \cdot 3^{2} \cdot 7$
Weight:	$k$	=	$2$
Nonzero newspaces:			$80$
Sturm bound:			$1769472$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4032))$.

	Total	New	Old
Modular forms	449280	189774	259506
Cusp forms	435457	187794	247663
Eisenstein series	13823	1980	11843

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4032))$

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
4032.2.a	$\chi_{4032}(1, \cdot)$	4032.2.a.a	1	1
		4032.2.a.b	1
		4032.2.a.c	1
		4032.2.a.d	1
		4032.2.a.e	1
		4032.2.a.f	1
		4032.2.a.g	1
		4032.2.a.h	1
		4032.2.a.i	1
		4032.2.a.j	1
		4032.2.a.k	1
		4032.2.a.l	1
		4032.2.a.m	1
		4032.2.a.n	1
		4032.2.a.o	1
		4032.2.a.p	1
		4032.2.a.q	1
		4032.2.a.r	1
		4032.2.a.s	1
		4032.2.a.t	1
		4032.2.a.u	1
		4032.2.a.v	1
		4032.2.a.w	1
		4032.2.a.x	1
		4032.2.a.y	1
		4032.2.a.z	1
		4032.2.a.ba	1
		4032.2.a.bb	1
		4032.2.a.bc	1
		4032.2.a.bd	1
		4032.2.a.be	1
		4032.2.a.bf	1
		4032.2.a.bg	1
		4032.2.a.bh	1
		4032.2.a.bi	1
		4032.2.a.bj	1
		4032.2.a.bk	1
		4032.2.a.bl	1
		4032.2.a.bm	1
		4032.2.a.bn	1
		4032.2.a.bo	2
		4032.2.a.bp	2
		4032.2.a.bq	2
		4032.2.a.br	2
		4032.2.a.bs	2
		4032.2.a.bt	2
		4032.2.a.bu	2
		4032.2.a.bv	2
		4032.2.a.bw	2
		4032.2.a.bx	2
4032.2.b	$\chi_{4032}(3583, \cdot)$	4032.2.b.a	2	1
		4032.2.b.b	2
		4032.2.b.c	2
		4032.2.b.d	2
		4032.2.b.e	2
		4032.2.b.f	2
		4032.2.b.g	2
		4032.2.b.h	2
		4032.2.b.i	2
		4032.2.b.j	4
		4032.2.b.k	4
		4032.2.b.l	4
		4032.2.b.m	4
		4032.2.b.n	4
		4032.2.b.o	8
		4032.2.b.p	8
		4032.2.b.q	8
		4032.2.b.r	16
4032.2.c	$\chi_{4032}(2017, \cdot)$	4032.2.c.a	2	1
		4032.2.c.b	2
		4032.2.c.c	2
		4032.2.c.d	2
		4032.2.c.e	2
		4032.2.c.f	2
		4032.2.c.g	2
		4032.2.c.h	2
		4032.2.c.i	2
		4032.2.c.j	2
		4032.2.c.k	4
		4032.2.c.l	4
		4032.2.c.m	4
		4032.2.c.n	4
		4032.2.c.o	4
		4032.2.c.p	4
		4032.2.c.q	8
		4032.2.c.r	8
4032.2.h	$\chi_{4032}(575, \cdot)$	4032.2.h.a	4	1
		4032.2.h.b	4
		4032.2.h.c	4
		4032.2.h.d	4
		4032.2.h.e	4
		4032.2.h.f	8
		4032.2.h.g	8
		4032.2.h.h	12
4032.2.i	$\chi_{4032}(1889, \cdot)$	4032.2.i.a	8	1
		4032.2.i.b	8
		4032.2.i.c	48
4032.2.j	$\chi_{4032}(2591, \cdot)$	4032.2.j.a	4	1
		4032.2.j.b	4
		4032.2.j.c	4
		4032.2.j.d	4
		4032.2.j.e	16
		4032.2.j.f	16
4032.2.k	$\chi_{4032}(3905, \cdot)$	4032.2.k.a	4	1
		4032.2.k.b	4
		4032.2.k.c	4
		4032.2.k.d	4
		4032.2.k.e	8
		4032.2.k.f	8
		4032.2.k.g	16
		4032.2.k.h	16
4032.2.p	$\chi_{4032}(1567, \cdot)$	4032.2.p.a	4	1
		4032.2.p.b	4
		4032.2.p.c	4
		4032.2.p.d	4
		4032.2.p.e	8
		4032.2.p.f	8
		4032.2.p.g	8
		4032.2.p.h	8
		4032.2.p.i	8
		4032.2.p.j	12
		4032.2.p.k	12
4032.2.q	$\chi_{4032}(1537, \cdot)$	n/a	376	2
4032.2.r	$\chi_{4032}(1345, \cdot)$	n/a	288	2
4032.2.s	$\chi_{4032}(2305, \cdot)$	n/a	156	2
4032.2.t	$\chi_{4032}(193, \cdot)$	n/a	376	2
4032.2.v	$\chi_{4032}(1583, \cdot)$	4032.2.v.a	4	2
		4032.2.v.b	4
		4032.2.v.c	12
		4032.2.v.d	36
		4032.2.v.e	40
4032.2.x	$\chi_{4032}(559, \cdot)$	n/a	156	2
4032.2.z	$\chi_{4032}(1009, \cdot)$	n/a	120	2
4032.2.bb	$\chi_{4032}(881, \cdot)$	n/a	128	2
4032.2.be	$\chi_{4032}(2209, \cdot)$	n/a	384	2
4032.2.bf	$\chi_{4032}(2047, \cdot)$	n/a	376	2
4032.2.bg	$\chi_{4032}(929, \cdot)$	n/a	384	2
4032.2.bh	$\chi_{4032}(191, \cdot)$	n/a	376	2
4032.2.bm	$\chi_{4032}(223, \cdot)$	n/a	384	2
4032.2.bn	$\chi_{4032}(607, \cdot)$	n/a	384	2
4032.2.bs	$\chi_{4032}(2719, \cdot)$	n/a	160	2
4032.2.bt	$\chi_{4032}(1025, \cdot)$	n/a	128	2
4032.2.bu	$\chi_{4032}(863, \cdot)$	n/a	128	2
4032.2.bz	$\chi_{4032}(1247, \cdot)$	n/a	288	2
4032.2.ca	$\chi_{4032}(257, \cdot)$	n/a	376	2
4032.2.cb	$\chi_{4032}(2783, \cdot)$	n/a	384	2
4032.2.cc	$\chi_{4032}(1217, \cdot)$	n/a	376	2
4032.2.ch	$\chi_{4032}(1919, \cdot)$	n/a	288	2
4032.2.ci	$\chi_{4032}(353, \cdot)$	n/a	384	2
4032.2.cj	$\chi_{4032}(767, \cdot)$	n/a	376	2
4032.2.ck	$\chi_{4032}(545, \cdot)$	n/a	384	2
4032.2.cp	$\chi_{4032}(3041, \cdot)$	n/a	128	2
4032.2.cq	$\chi_{4032}(2879, \cdot)$	n/a	128	2
4032.2.cr	$\chi_{4032}(289, \cdot)$	n/a	160	2
4032.2.cs	$\chi_{4032}(703, \cdot)$	n/a	156	2
4032.2.cx	$\chi_{4032}(895, \cdot)$	n/a	376	2
4032.2.cy	$\chi_{4032}(1633, \cdot)$	n/a	384	2
4032.2.cz	$\chi_{4032}(2623, \cdot)$	n/a	376	2
4032.2.da	$\chi_{4032}(673, \cdot)$	n/a	288	2
4032.2.df	$\chi_{4032}(2945, \cdot)$	n/a	376	2
4032.2.dg	$\chi_{4032}(95, \cdot)$	n/a	384	2
4032.2.dh	$\chi_{4032}(31, \cdot)$	n/a	384	2
4032.2.dk	$\chi_{4032}(377, \cdot)$	None	0	4
4032.2.dm	$\chi_{4032}(505, \cdot)$	None	0	4
4032.2.do	$\chi_{4032}(71, \cdot)$	None	0	4
4032.2.dq	$\chi_{4032}(55, \cdot)$	None	0	4
4032.2.ds	$\chi_{4032}(1231, \cdot)$	n/a	752	4
4032.2.du	$\chi_{4032}(239, \cdot)$	n/a	576	4
4032.2.dw	$\chi_{4032}(1201, \cdot)$	n/a	752	4
4032.2.dz	$\chi_{4032}(1265, \cdot)$	n/a	752	4
4032.2.ea	$\chi_{4032}(17, \cdot)$	n/a	256	4
4032.2.ec	$\chi_{4032}(1297, \cdot)$	n/a	312	4
4032.2.ef	$\chi_{4032}(529, \cdot)$	n/a	752	4
4032.2.eg	$\chi_{4032}(689, \cdot)$	n/a	752	4
4032.2.ei	$\chi_{4032}(1103, \cdot)$	n/a	752	4
4032.2.ek	$\chi_{4032}(271, \cdot)$	n/a	312	4
4032.2.en	$\chi_{4032}(367, \cdot)$	n/a	752	4
4032.2.ep	$\chi_{4032}(527, \cdot)$	n/a	752	4
4032.2.eq	$\chi_{4032}(431, \cdot)$	n/a	256	4
4032.2.es	$\chi_{4032}(943, \cdot)$	n/a	752	4
4032.2.eu	$\chi_{4032}(209, \cdot)$	n/a	752	4
4032.2.ew	$\chi_{4032}(337, \cdot)$	n/a	576	4
4032.2.fa	$\chi_{4032}(253, \cdot)$	n/a	1920	8
4032.2.fb	$\chi_{4032}(307, \cdot)$	n/a	2544	8
4032.2.fc	$\chi_{4032}(323, \cdot)$	n/a	1536	8
4032.2.fd	$\chi_{4032}(125, \cdot)$	n/a	2048	8
4032.2.fh	$\chi_{4032}(169, \cdot)$	None	0	8
4032.2.fj	$\chi_{4032}(41, \cdot)$	None	0	8
4032.2.fk	$\chi_{4032}(23, \cdot)$	None	0	8
4032.2.fo	$\chi_{4032}(199, \cdot)$	None	0	8
4032.2.fp	$\chi_{4032}(439, \cdot)$	None	0	8
4032.2.fs	$\chi_{4032}(599, \cdot)$	None	0	8
4032.2.ft	$\chi_{4032}(359, \cdot)$	None	0	8
4032.2.fu	$\chi_{4032}(103, \cdot)$	None	0	8
4032.2.fw	$\chi_{4032}(761, \cdot)$	None	0	8
4032.2.ga	$\chi_{4032}(457, \cdot)$	None	0	8
4032.2.gb	$\chi_{4032}(361, \cdot)$	None	0	8
4032.2.ge	$\chi_{4032}(89, \cdot)$	None	0	8
4032.2.gf	$\chi_{4032}(185, \cdot)$	None	0	8
4032.2.gg	$\chi_{4032}(25, \cdot)$	None	0	8
4032.2.gj	$\chi_{4032}(391, \cdot)$	None	0	8
4032.2.gl	$\chi_{4032}(407, \cdot)$	None	0	8
4032.2.go	$\chi_{4032}(277, \cdot)$	n/a	12224	16
4032.2.gp	$\chi_{4032}(115, \cdot)$	n/a	12224	16
4032.2.gw	$\chi_{4032}(293, \cdot)$	n/a	12224	16
4032.2.gx	$\chi_{4032}(173, \cdot)$	n/a	12224	16
4032.2.gy	$\chi_{4032}(269, \cdot)$	n/a	4096	16
4032.2.gz	$\chi_{4032}(107, \cdot)$	n/a	4096	16
4032.2.ha	$\chi_{4032}(347, \cdot)$	n/a	12224	16
4032.2.hb	$\chi_{4032}(155, \cdot)$	n/a	9216	16
4032.2.hc	$\chi_{4032}(187, \cdot)$	n/a	12224	16
4032.2.hd	$\chi_{4032}(139, \cdot)$	n/a	12224	16
4032.2.he	$\chi_{4032}(19, \cdot)$	n/a	5088	16
4032.2.hf	$\chi_{4032}(37, \cdot)$	n/a	5088	16
4032.2.hg	$\chi_{4032}(85, \cdot)$	n/a	9216	16
4032.2.hh	$\chi_{4032}(205, \cdot)$	n/a	12224	16
4032.2.ho	$\chi_{4032}(11, \cdot)$	n/a	12224	16
4032.2.hp	$\chi_{4032}(5, \cdot)$	n/a	12224	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4032))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4032)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 42}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 28}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 30}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 21}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 15}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1008))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1344))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2016))$$^{\oplus 2}$