Space of modular forms of level 4160 and weight 2

• Label: 4160.2
• Level: 4160
• Weight: 2
• Dimension: 261492
• Nonzero newspaces: 104
• Sturm bound: 2064384

Defining parameters

Level:	$N$	=	$4160 = 2^{6} \cdot 5 \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$104$
Sturm bound:			$2064384$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4160))$.

	Total	New	Old
Modular forms	523008	264396	258612
Cusp forms	509185	261492	247693
Eisenstein series	13823	2904	10919

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4160))$

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
4160.2.a	$\chi_{4160}(1, \cdot)$	4160.2.a.a	1	1
		4160.2.a.b	1
		4160.2.a.c	1
		4160.2.a.d	1
		4160.2.a.e	1
		4160.2.a.f	1
		4160.2.a.g	1
		4160.2.a.h	1
		4160.2.a.i	1
		4160.2.a.j	1
		4160.2.a.k	1
		4160.2.a.l	1
		4160.2.a.m	1
		4160.2.a.n	1
		4160.2.a.o	1
		4160.2.a.p	1
		4160.2.a.q	1
		4160.2.a.r	1
		4160.2.a.s	1
		4160.2.a.t	1
		4160.2.a.u	2
		4160.2.a.v	2
		4160.2.a.w	2
		4160.2.a.x	2
		4160.2.a.y	2
		4160.2.a.z	2
		4160.2.a.ba	2
		4160.2.a.bb	2
		4160.2.a.bc	2
		4160.2.a.bd	2
		4160.2.a.be	2
		4160.2.a.bf	2
		4160.2.a.bg	2
		4160.2.a.bh	2
		4160.2.a.bi	2
		4160.2.a.bj	2
		4160.2.a.bk	2
		4160.2.a.bl	2
		4160.2.a.bm	2
		4160.2.a.bn	2
		4160.2.a.bo	3
		4160.2.a.bp	3
		4160.2.a.bq	3
		4160.2.a.br	3
		4160.2.a.bs	4
		4160.2.a.bt	4
		4160.2.a.bu	4
		4160.2.a.bv	4
		4160.2.a.bw	4
		4160.2.a.bx	4
4160.2.d	$\chi_{4160}(3329, \cdot)$	n/a	144	1
4160.2.e	$\chi_{4160}(3041, \cdot)$	n/a	112	1
4160.2.f	$\chi_{4160}(129, \cdot)$	n/a	164	1
4160.2.g	$\chi_{4160}(2081, \cdot)$	4160.2.g.a	2	1
		4160.2.g.b	2
		4160.2.g.c	6
		4160.2.g.d	6
		4160.2.g.e	8
		4160.2.g.f	8
		4160.2.g.g	16
		4160.2.g.h	16
		4160.2.g.i	16
		4160.2.g.j	16
4160.2.j	$\chi_{4160}(1249, \cdot)$	n/a	144	1
4160.2.k	$\chi_{4160}(961, \cdot)$	n/a	112	1
4160.2.p	$\chi_{4160}(2209, \cdot)$	n/a	168	1
4160.2.q	$\chi_{4160}(321, \cdot)$	n/a	224	2
4160.2.s	$\chi_{4160}(177, \cdot)$	n/a	328	2
4160.2.u	$\chi_{4160}(2111, \cdot)$	n/a	224	2
4160.2.v	$\chi_{4160}(1327, \cdot)$	n/a	288	2
4160.2.y	$\chi_{4160}(2287, \cdot)$	n/a	328	2
4160.2.z	$\chi_{4160}(3359, \cdot)$	n/a	336	2
4160.2.bb	$\chi_{4160}(593, \cdot)$	n/a	328	2
4160.2.be	$\chi_{4160}(1169, \cdot)$	n/a	328	2
4160.2.bg	$\chi_{4160}(577, \cdot)$	n/a	328	2
4160.2.bi	$\chi_{4160}(1633, \cdot)$	n/a	336	2
4160.2.bj	$\chi_{4160}(1041, \cdot)$	n/a	192	2
4160.2.bm	$\chi_{4160}(1071, \cdot)$	n/a	224	2
4160.2.bp	$\chi_{4160}(703, \cdot)$	n/a	288	2
4160.2.bq	$\chi_{4160}(1247, \cdot)$	n/a	336	2
4160.2.bs	$\chi_{4160}(239, \cdot)$	n/a	328	2
4160.2.bt	$\chi_{4160}(1711, \cdot)$	n/a	224	2
4160.2.bv	$\chi_{4160}(1663, \cdot)$	n/a	328	2
4160.2.bw	$\chi_{4160}(287, \cdot)$	n/a	288	2
4160.2.bz	$\chi_{4160}(879, \cdot)$	n/a	328	2
4160.2.cc	$\chi_{4160}(209, \cdot)$	n/a	288	2
4160.2.cd	$\chi_{4160}(1217, \cdot)$	n/a	328	2
4160.2.cf	$\chi_{4160}(993, \cdot)$	n/a	336	2
4160.2.ch	$\chi_{4160}(2001, \cdot)$	n/a	224	2
4160.2.cj	$\chi_{4160}(2033, \cdot)$	n/a	328	2
4160.2.cm	$\chi_{4160}(31, \cdot)$	n/a	224	2
4160.2.cn	$\chi_{4160}(3407, \cdot)$	n/a	288	2
4160.2.cq	$\chi_{4160}(207, \cdot)$	n/a	328	2
4160.2.cr	$\chi_{4160}(1279, \cdot)$	n/a	328	2
4160.2.cu	$\chi_{4160}(1617, \cdot)$	n/a	328	2
4160.2.cv	$\chi_{4160}(1889, \cdot)$	n/a	336	2
4160.2.da	$\chi_{4160}(641, \cdot)$	n/a	224	2
4160.2.db	$\chi_{4160}(289, \cdot)$	n/a	336	2
4160.2.de	$\chi_{4160}(1121, \cdot)$	n/a	224	2
4160.2.df	$\chi_{4160}(1089, \cdot)$	n/a	328	2
4160.2.dg	$\chi_{4160}(2721, \cdot)$	n/a	224	2
4160.2.dh	$\chi_{4160}(2369, \cdot)$	n/a	328	2
4160.2.dk	$\chi_{4160}(1399, \cdot)$	None	0	4
4160.2.dm	$\chi_{4160}(1223, \cdot)$	None	0	4
4160.2.dp	$\chi_{4160}(1143, \cdot)$	None	0	4
4160.2.dr	$\chi_{4160}(1191, \cdot)$	None	0	4
4160.2.ds	$\chi_{4160}(441, \cdot)$	None	0	4
4160.2.dv	$\chi_{4160}(521, \cdot)$	None	0	4
4160.2.dw	$\chi_{4160}(473, \cdot)$	None	0	4
4160.2.dz	$\chi_{4160}(1097, \cdot)$	None	0	4
4160.2.eb	$\chi_{4160}(697, \cdot)$	None	0	4
4160.2.ec	$\chi_{4160}(57, \cdot)$	None	0	4
4160.2.ef	$\chi_{4160}(649, \cdot)$	None	0	4
4160.2.eg	$\chi_{4160}(729, \cdot)$	None	0	4
4160.2.ej	$\chi_{4160}(359, \cdot)$	None	0	4
4160.2.el	$\chi_{4160}(103, \cdot)$	None	0	4
4160.2.em	$\chi_{4160}(183, \cdot)$	None	0	4
4160.2.eo	$\chi_{4160}(151, \cdot)$	None	0	4
4160.2.eq	$\chi_{4160}(977, \cdot)$	n/a	656	4
4160.2.et	$\chi_{4160}(319, \cdot)$	n/a	656	4
4160.2.ev	$\chi_{4160}(2447, \cdot)$	n/a	656	4
4160.2.ew	$\chi_{4160}(303, \cdot)$	n/a	656	4
4160.2.ey	$\chi_{4160}(1311, \cdot)$	n/a	448	4
4160.2.fb	$\chi_{4160}(657, \cdot)$	n/a	656	4
4160.2.fd	$\chi_{4160}(881, \cdot)$	n/a	448	4
4160.2.ff	$\chi_{4160}(353, \cdot)$	n/a	672	4
4160.2.fh	$\chi_{4160}(513, \cdot)$	n/a	656	4
4160.2.fi	$\chi_{4160}(529, \cdot)$	n/a	656	4
4160.2.fk	$\chi_{4160}(1519, \cdot)$	n/a	656	4
4160.2.fm	$\chi_{4160}(607, \cdot)$	n/a	672	4
4160.2.fn	$\chi_{4160}(127, \cdot)$	n/a	656	4
4160.2.fq	$\chi_{4160}(111, \cdot)$	n/a	448	4
4160.2.ft	$\chi_{4160}(1359, \cdot)$	n/a	656	4
4160.2.fw	$\chi_{4160}(543, \cdot)$	n/a	672	4
4160.2.fx	$\chi_{4160}(1023, \cdot)$	n/a	656	4
4160.2.fz	$\chi_{4160}(271, \cdot)$	n/a	448	4
4160.2.gb	$\chi_{4160}(81, \cdot)$	n/a	448	4
4160.2.gc	$\chi_{4160}(33, \cdot)$	n/a	672	4
4160.2.ge	$\chi_{4160}(193, \cdot)$	n/a	656	4
4160.2.gg	$\chi_{4160}(49, \cdot)$	n/a	656	4
4160.2.gj	$\chi_{4160}(1137, \cdot)$	n/a	656	4
4160.2.gl	$\chi_{4160}(479, \cdot)$	n/a	672	4
4160.2.gn	$\chi_{4160}(367, \cdot)$	n/a	656	4
4160.2.go	$\chi_{4160}(1967, \cdot)$	n/a	656	4
4160.2.gq	$\chi_{4160}(1151, \cdot)$	n/a	448	4
4160.2.gs	$\chi_{4160}(817, \cdot)$	n/a	656	4
4160.2.gu	$\chi_{4160}(363, \cdot)$	n/a	5344	8
4160.2.gx	$\chi_{4160}(333, \cdot)$	n/a	5344	8
4160.2.gy	$\chi_{4160}(437, \cdot)$	n/a	5344	8
4160.2.ha	$\chi_{4160}(443, \cdot)$	n/a	4608	8
4160.2.hd	$\chi_{4160}(261, \cdot)$	n/a	3072	8
4160.2.he	$\chi_{4160}(469, \cdot)$	n/a	4608	8
4160.2.hh	$\chi_{4160}(811, \cdot)$	n/a	3584	8
4160.2.hi	$\chi_{4160}(499, \cdot)$	n/a	5344	8
4160.2.hk	$\chi_{4160}(99, \cdot)$	n/a	5344	8
4160.2.hn	$\chi_{4160}(291, \cdot)$	n/a	3584	8
4160.2.hp	$\chi_{4160}(389, \cdot)$	n/a	5344	8
4160.2.hq	$\chi_{4160}(181, \cdot)$	n/a	3584	8
4160.2.hs	$\chi_{4160}(883, \cdot)$	n/a	5344	8
4160.2.hv	$\chi_{4160}(317, \cdot)$	n/a	5344	8
4160.2.hw	$\chi_{4160}(213, \cdot)$	n/a	5344	8
4160.2.hy	$\chi_{4160}(27, \cdot)$	n/a	4608	8
4160.2.ib	$\chi_{4160}(71, \cdot)$	None	0	8
4160.2.ic	$\chi_{4160}(503, \cdot)$	None	0	8
4160.2.if	$\chi_{4160}(407, \cdot)$	None	0	8
4160.2.ig	$\chi_{4160}(119, \cdot)$	None	0	8
4160.2.ii	$\chi_{4160}(329, \cdot)$	None	0	8
4160.2.il	$\chi_{4160}(9, \cdot)$	None	0	8
4160.2.in	$\chi_{4160}(553, \cdot)$	None	0	8
4160.2.io	$\chi_{4160}(873, \cdot)$	None	0	8
4160.2.iq	$\chi_{4160}(457, \cdot)$	None	0	8
4160.2.it	$\chi_{4160}(137, \cdot)$	None	0	8
4160.2.iv	$\chi_{4160}(121, \cdot)$	None	0	8
4160.2.iw	$\chi_{4160}(601, \cdot)$	None	0	8
4160.2.iy	$\chi_{4160}(951, \cdot)$	None	0	8
4160.2.jb	$\chi_{4160}(23, \cdot)$	None	0	8
4160.2.jc	$\chi_{4160}(87, \cdot)$	None	0	8
4160.2.jf	$\chi_{4160}(1159, \cdot)$	None	0	8
4160.2.jh	$\chi_{4160}(563, \cdot)$	n/a	10688	16
4160.2.jj	$\chi_{4160}(397, \cdot)$	n/a	10688	16
4160.2.jk	$\chi_{4160}(293, \cdot)$	n/a	10688	16
4160.2.jn	$\chi_{4160}(3, \cdot)$	n/a	10688	16
4160.2.jp	$\chi_{4160}(29, \cdot)$	n/a	10688	16
4160.2.jq	$\chi_{4160}(61, \cdot)$	n/a	7168	16
4160.2.jt	$\chi_{4160}(19, \cdot)$	n/a	10688	16
4160.2.ju	$\chi_{4160}(171, \cdot)$	n/a	7168	16
4160.2.jw	$\chi_{4160}(11, \cdot)$	n/a	7168	16
4160.2.jz	$\chi_{4160}(379, \cdot)$	n/a	10688	16
4160.2.kb	$\chi_{4160}(101, \cdot)$	n/a	7168	16
4160.2.kc	$\chi_{4160}(69, \cdot)$	n/a	10688	16
4160.2.kf	$\chi_{4160}(43, \cdot)$	n/a	10688	16
4160.2.kh	$\chi_{4160}(37, \cdot)$	n/a	10688	16
4160.2.ki	$\chi_{4160}(197, \cdot)$	n/a	10688	16
4160.2.kl	$\chi_{4160}(523, \cdot)$	n/a	10688	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4160))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4160)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 28}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1040))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2080))$$^{\oplus 2}$