Space of modular forms of level 4368 and weight 2

• Label: 4368.2
• Level: 4368
• Weight: 2
• Dimension: 205184
• Nonzero newspaces: 140
• Sturm bound: 2064384

Defining parameters

Level:	$N$	=	$4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$140$
Sturm bound:			$2064384$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(4368))$.

	Total	New	Old
Modular forms	524160	207160	317000
Cusp forms	508033	205184	302849
Eisenstein series	16127	1976	14151

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(4368))$

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
4368.2.a	$\chi_{4368}(1, \cdot)$	4368.2.a.a	1	1
		4368.2.a.b	1
		4368.2.a.c	1
		4368.2.a.d	1
		4368.2.a.e	1
		4368.2.a.f	1
		4368.2.a.g	1
		4368.2.a.h	1
		4368.2.a.i	1
		4368.2.a.j	1
		4368.2.a.k	1
		4368.2.a.l	1
		4368.2.a.m	1
		4368.2.a.n	1
		4368.2.a.o	1
		4368.2.a.p	1
		4368.2.a.q	1
		4368.2.a.r	1
		4368.2.a.s	1
		4368.2.a.t	1
		4368.2.a.u	1
		4368.2.a.v	1
		4368.2.a.w	1
		4368.2.a.x	1
		4368.2.a.y	1
		4368.2.a.z	1
		4368.2.a.ba	1
		4368.2.a.bb	2
		4368.2.a.bc	2
		4368.2.a.bd	2
		4368.2.a.be	2
		4368.2.a.bf	2
		4368.2.a.bg	2
		4368.2.a.bh	2
		4368.2.a.bi	2
		4368.2.a.bj	2
		4368.2.a.bk	2
		4368.2.a.bl	2
		4368.2.a.bm	3
		4368.2.a.bn	3
		4368.2.a.bo	3
		4368.2.a.bp	3
		4368.2.a.bq	3
		4368.2.a.br	4
		4368.2.a.bs	4
4368.2.b	$\chi_{4368}(727, \cdot)$	None	0	1
4368.2.e	$\chi_{4368}(2575, \cdot)$	4368.2.e.a	16	1
		4368.2.e.b	16
		4368.2.e.c	32
		4368.2.e.d	32
4368.2.g	$\chi_{4368}(2185, \cdot)$	None	0	1
4368.2.h	$\chi_{4368}(337, \cdot)$	4368.2.h.a	2	1
		4368.2.h.b	2
		4368.2.h.c	2
		4368.2.h.d	2
		4368.2.h.e	2
		4368.2.h.f	2
		4368.2.h.g	2
		4368.2.h.h	2
		4368.2.h.i	2
		4368.2.h.j	2
		4368.2.h.k	2
		4368.2.h.l	4
		4368.2.h.m	4
		4368.2.h.n	4
		4368.2.h.o	6
		4368.2.h.p	6
		4368.2.h.q	8
		4368.2.h.r	10
		4368.2.h.s	10
		4368.2.h.t	10
4368.2.j	$\chi_{4368}(911, \cdot)$	n/a	144	1
4368.2.m	$\chi_{4368}(3431, \cdot)$	None	0	1
4368.2.o	$\chi_{4368}(545, \cdot)$	n/a	220	1
4368.2.p	$\chi_{4368}(2393, \cdot)$	None	0	1
4368.2.s	$\chi_{4368}(1247, \cdot)$	n/a	168	1
4368.2.t	$\chi_{4368}(3095, \cdot)$	None	0	1
4368.2.v	$\chi_{4368}(209, \cdot)$	n/a	192	1
4368.2.y	$\chi_{4368}(2729, \cdot)$	None	0	1
4368.2.ba	$\chi_{4368}(391, \cdot)$	None	0	1
4368.2.bb	$\chi_{4368}(2911, \cdot)$	n/a	112	1
4368.2.bd	$\chi_{4368}(2521, \cdot)$	None	0	1
4368.2.bg	$\chi_{4368}(625, \cdot)$	n/a	192	2
4368.2.bh	$\chi_{4368}(289, \cdot)$	n/a	224	2
4368.2.bi	$\chi_{4368}(1537, \cdot)$	n/a	224	2
4368.2.bj	$\chi_{4368}(3025, \cdot)$	n/a	168	2
4368.2.bk	$\chi_{4368}(3739, \cdot)$	n/a	672	2
4368.2.bn	$\chi_{4368}(3037, \cdot)$	n/a	896	2
4368.2.bo	$\chi_{4368}(83, \cdot)$	n/a	1776	2
4368.2.br	$\chi_{4368}(1373, \cdot)$	n/a	1344	2
4368.2.bs	$\chi_{4368}(671, \cdot)$	n/a	448	2
4368.2.bv	$\chi_{4368}(2003, \cdot)$	n/a	1152	2
4368.2.bw	$\chi_{4368}(155, \cdot)$	n/a	1344	2
4368.2.by	$\chi_{4368}(1175, \cdot)$	None	0	2
4368.2.ca	$\chi_{4368}(967, \cdot)$	None	0	2
4368.2.cc	$\chi_{4368}(1819, \cdot)$	n/a	896	2
4368.2.cf	$\chi_{4368}(1483, \cdot)$	n/a	768	2
4368.2.cg	$\chi_{4368}(463, \cdot)$	n/a	168	2
4368.2.cj	$\chi_{4368}(265, \cdot)$	None	0	2
4368.2.ck	$\chi_{4368}(1429, \cdot)$	n/a	672	2
4368.2.cn	$\chi_{4368}(1093, \cdot)$	n/a	576	2
4368.2.cp	$\chi_{4368}(2449, \cdot)$	n/a	224	2
4368.2.cr	$\chi_{4368}(785, \cdot)$	n/a	336	2
4368.2.ct	$\chi_{4368}(1301, \cdot)$	n/a	1536	2
4368.2.cu	$\chi_{4368}(1637, \cdot)$	n/a	1776	2
4368.2.cx	$\chi_{4368}(281, \cdot)$	None	0	2
4368.2.cz	$\chi_{4368}(1763, \cdot)$	n/a	1776	2
4368.2.da	$\chi_{4368}(3557, \cdot)$	n/a	1344	2
4368.2.dd	$\chi_{4368}(1555, \cdot)$	n/a	672	2
4368.2.de	$\chi_{4368}(853, \cdot)$	n/a	896	2
4368.2.dg	$\chi_{4368}(1049, \cdot)$	None	0	2
4368.2.dj	$\chi_{4368}(881, \cdot)$	n/a	440	2
4368.2.dl	$\chi_{4368}(407, \cdot)$	None	0	2
4368.2.dm	$\chi_{4368}(575, \cdot)$	n/a	336	2
4368.2.do	$\chi_{4368}(673, \cdot)$	n/a	168	2
4368.2.dr	$\chi_{4368}(841, \cdot)$	None	0	2
4368.2.dt	$\chi_{4368}(1231, \cdot)$	n/a	224	2
4368.2.du	$\chi_{4368}(1063, \cdot)$	None	0	2
4368.2.dw	$\chi_{4368}(1193, \cdot)$	None	0	2
4368.2.dz	$\chi_{4368}(2369, \cdot)$	n/a	440	2
4368.2.eb	$\chi_{4368}(263, \cdot)$	None	0	2
4368.2.ec	$\chi_{4368}(3215, \cdot)$	n/a	448	2
4368.2.ef	$\chi_{4368}(2383, \cdot)$	n/a	224	2
4368.2.eg	$\chi_{4368}(1543, \cdot)$	None	0	2
4368.2.ej	$\chi_{4368}(25, \cdot)$	None	0	2
4368.2.el	$\chi_{4368}(2887, \cdot)$	None	0	2
4368.2.eo	$\chi_{4368}(1039, \cdot)$	n/a	224	2
4368.2.er	$\chi_{4368}(1369, \cdot)$	None	0	2
4368.2.et	$\chi_{4368}(3383, \cdot)$	None	0	2
4368.2.eu	$\chi_{4368}(95, \cdot)$	n/a	448	2
4368.2.ex	$\chi_{4368}(2705, \cdot)$	n/a	384	2
4368.2.ey	$\chi_{4368}(857, \cdot)$	None	0	2
4368.2.fa	$\chi_{4368}(1871, \cdot)$	n/a	448	2
4368.2.fd	$\chi_{4368}(599, \cdot)$	None	0	2
4368.2.fe	$\chi_{4368}(2201, \cdot)$	None	0	2
4368.2.fh	$\chi_{4368}(1361, \cdot)$	n/a	440	2
4368.2.fk	$\chi_{4368}(121, \cdot)$	None	0	2
4368.2.fm	$\chi_{4368}(1375, \cdot)$	n/a	224	2
4368.2.fn	$\chi_{4368}(2551, \cdot)$	None	0	2
4368.2.fq	$\chi_{4368}(2305, \cdot)$	n/a	224	2
4368.2.fr	$\chi_{4368}(1465, \cdot)$	None	0	2
4368.2.ft	$\chi_{4368}(367, \cdot)$	n/a	224	2
4368.2.fw	$\chi_{4368}(1447, \cdot)$	None	0	2
4368.2.fx	$\chi_{4368}(23, \cdot)$	None	0	2
4368.2.ga	$\chi_{4368}(1199, \cdot)$	n/a	448	2
4368.2.gb	$\chi_{4368}(3041, \cdot)$	n/a	440	2
4368.2.ge	$\chi_{4368}(521, \cdot)$	None	0	2
4368.2.gg	$\chi_{4368}(1535, \cdot)$	n/a	384	2
4368.2.gh	$\chi_{4368}(935, \cdot)$	None	0	2
4368.2.gk	$\chi_{4368}(1433, \cdot)$	None	0	2
4368.2.gl	$\chi_{4368}(17, \cdot)$	n/a	440	2
4368.2.gn	$\chi_{4368}(1615, \cdot)$	n/a	224	2
4368.2.gq	$\chi_{4368}(199, \cdot)$	None	0	2
4368.2.gr	$\chi_{4368}(2809, \cdot)$	None	0	2
4368.2.gu	$\chi_{4368}(961, \cdot)$	n/a	224	2
4368.2.gw	$\chi_{4368}(103, \cdot)$	None	0	2
4368.2.gx	$\chi_{4368}(703, \cdot)$	n/a	192	2
4368.2.ha	$\chi_{4368}(1297, \cdot)$	n/a	224	2
4368.2.hb	$\chi_{4368}(2473, \cdot)$	None	0	2
4368.2.he	$\chi_{4368}(185, \cdot)$	None	0	2
4368.2.hf	$\chi_{4368}(1265, \cdot)$	n/a	440	2
4368.2.hh	$\chi_{4368}(1031, \cdot)$	None	0	2
4368.2.hk	$\chi_{4368}(191, \cdot)$	n/a	448	2
4368.2.hm	$\chi_{4368}(2857, \cdot)$	None	0	2
4368.2.ho	$\chi_{4368}(3247, \cdot)$	n/a	224	2
4368.2.hr	$\chi_{4368}(55, \cdot)$	None	0	2
4368.2.ht	$\chi_{4368}(3065, \cdot)$	None	0	2
4368.2.hu	$\chi_{4368}(3233, \cdot)$	n/a	440	2
4368.2.hw	$\chi_{4368}(1751, \cdot)$	None	0	2
4368.2.hz	$\chi_{4368}(1583, \cdot)$	n/a	336	2
4368.2.ia	$\chi_{4368}(197, \cdot)$	n/a	2688	4
4368.2.id	$\chi_{4368}(1259, \cdot)$	n/a	3552	4
4368.2.ie	$\chi_{4368}(349, \cdot)$	n/a	1792	4
4368.2.ih	$\chi_{4368}(1051, \cdot)$	n/a	1344	4
4368.2.ij	$\chi_{4368}(2165, \cdot)$	n/a	3552	4
4368.2.ik	$\chi_{4368}(1571, \cdot)$	n/a	3552	4
4368.2.in	$\chi_{4368}(1003, \cdot)$	n/a	1792	4
4368.2.ip	$\chi_{4368}(229, \cdot)$	n/a	1792	4
4368.2.iq	$\chi_{4368}(2179, \cdot)$	n/a	1792	4
4368.2.is	$\chi_{4368}(1333, \cdot)$	n/a	1792	4
4368.2.iv	$\chi_{4368}(2243, \cdot)$	n/a	3552	4
4368.2.ix	$\chi_{4368}(317, \cdot)$	n/a	3552	4
4368.2.iy	$\chi_{4368}(395, \cdot)$	n/a	3552	4
4368.2.ja	$\chi_{4368}(1493, \cdot)$	n/a	3552	4
4368.2.jd	$\chi_{4368}(661, \cdot)$	n/a	1792	4
4368.2.je	$\chi_{4368}(163, \cdot)$	n/a	1792	4
4368.2.jh	$\chi_{4368}(1319, \cdot)$	None	0	4
4368.2.jj	$\chi_{4368}(1115, \cdot)$	n/a	3552	4
4368.2.jk	$\chi_{4368}(107, \cdot)$	n/a	3552	4
4368.2.jn	$\chi_{4368}(1055, \cdot)$	n/a	896	4
4368.2.jp	$\chi_{4368}(319, \cdot)$	n/a	448	4
4368.2.jq	$\chi_{4368}(451, \cdot)$	n/a	1792	4
4368.2.jt	$\chi_{4368}(1291, \cdot)$	n/a	1792	4
4368.2.jv	$\chi_{4368}(487, \cdot)$	None	0	4
4368.2.jx	$\chi_{4368}(617, \cdot)$	None	0	4
4368.2.jz	$\chi_{4368}(965, \cdot)$	n/a	3552	4
4368.2.ka	$\chi_{4368}(797, \cdot)$	n/a	3552	4
4368.2.kd	$\chi_{4368}(449, \cdot)$	n/a	672	4
4368.2.ke	$\chi_{4368}(1409, \cdot)$	n/a	880	4
4368.2.kg	$\chi_{4368}(1241, \cdot)$	None	0	4
4368.2.kj	$\chi_{4368}(101, \cdot)$	n/a	3552	4
4368.2.kl	$\chi_{4368}(1013, \cdot)$	n/a	3552	4
4368.2.km	$\chi_{4368}(677, \cdot)$	n/a	3072	4
4368.2.ko	$\chi_{4368}(1277, \cdot)$	n/a	3552	4
4368.2.kq	$\chi_{4368}(977, \cdot)$	n/a	880	4
4368.2.ks	$\chi_{4368}(473, \cdot)$	None	0	4
4368.2.kv	$\chi_{4368}(97, \cdot)$	n/a	448	4
4368.2.kw	$\chi_{4368}(589, \cdot)$	n/a	1344	4
4368.2.kz	$\chi_{4368}(757, \cdot)$	n/a	1344	4
4368.2.lb	$\chi_{4368}(2281, \cdot)$	None	0	4
4368.2.lc	$\chi_{4368}(73, \cdot)$	None	0	4
4368.2.le	$\chi_{4368}(1489, \cdot)$	n/a	448	4
4368.2.lg	$\chi_{4368}(781, \cdot)$	n/a	1536	4
4368.2.li	$\chi_{4368}(373, \cdot)$	n/a	1792	4
4368.2.ll	$\chi_{4368}(1213, \cdot)$	n/a	1792	4
4368.2.ln	$\chi_{4368}(1117, \cdot)$	n/a	1792	4
4368.2.lo	$\chi_{4368}(1081, \cdot)$	None	0	4
4368.2.lq	$\chi_{4368}(577, \cdot)$	n/a	448	4
4368.2.ls	$\chi_{4368}(799, \cdot)$	n/a	336	4
4368.2.lu	$\chi_{4368}(979, \cdot)$	n/a	1792	4
4368.2.lx	$\chi_{4368}(139, \cdot)$	n/a	1792	4
4368.2.ly	$\chi_{4368}(631, \cdot)$	None	0	4
4368.2.mb	$\chi_{4368}(151, \cdot)$	None	0	4
4368.2.md	$\chi_{4368}(1423, \cdot)$	n/a	448	4
4368.2.me	$\chi_{4368}(1459, \cdot)$	n/a	1792	4
4368.2.mg	$\chi_{4368}(859, \cdot)$	n/a	1536	4
4368.2.mj	$\chi_{4368}(1195, \cdot)$	n/a	1792	4
4368.2.ml	$\chi_{4368}(283, \cdot)$	n/a	1792	4
4368.2.mn	$\chi_{4368}(1159, \cdot)$	None	0	4
4368.2.mp	$\chi_{4368}(655, \cdot)$	n/a	448	4
4368.2.mq	$\chi_{4368}(167, \cdot)$	None	0	4
4368.2.mt	$\chi_{4368}(659, \cdot)$	n/a	2688	4
4368.2.mu	$\chi_{4368}(491, \cdot)$	n/a	2688	4
4368.2.mw	$\chi_{4368}(1007, \cdot)$	n/a	896	4
4368.2.mz	$\chi_{4368}(47, \cdot)$	n/a	896	4
4368.2.nb	$\chi_{4368}(215, \cdot)$	None	0	4
4368.2.nd	$\chi_{4368}(779, \cdot)$	n/a	3552	4
4368.2.nf	$\chi_{4368}(179, \cdot)$	n/a	3552	4
4368.2.ng	$\chi_{4368}(1283, \cdot)$	n/a	3552	4
4368.2.ni	$\chi_{4368}(443, \cdot)$	n/a	3072	4
4368.2.nl	$\chi_{4368}(383, \cdot)$	n/a	896	4
4368.2.nn	$\chi_{4368}(551, \cdot)$	None	0	4
4368.2.no	$\chi_{4368}(145, \cdot)$	n/a	448	4
4368.2.nq	$\chi_{4368}(1381, \cdot)$	n/a	1792	4
4368.2.nt	$\chi_{4368}(205, \cdot)$	n/a	1792	4
4368.2.nu	$\chi_{4368}(409, \cdot)$	None	0	4
4368.2.nw	$\chi_{4368}(137, \cdot)$	None	0	4
4368.2.nz	$\chi_{4368}(1109, \cdot)$	n/a	3552	4
4368.2.oa	$\chi_{4368}(269, \cdot)$	n/a	3552	4
4368.2.oc	$\chi_{4368}(305, \cdot)$	n/a	880	4
4368.2.oe	$\chi_{4368}(397, \cdot)$	n/a	1792	4
4368.2.oh	$\chi_{4368}(67, \cdot)$	n/a	1792	4
4368.2.oi	$\chi_{4368}(59, \cdot)$	n/a	3552	4
4368.2.ok	$\chi_{4368}(1997, \cdot)$	n/a	3552	4
4368.2.on	$\chi_{4368}(2075, \cdot)$	n/a	3552	4
4368.2.op	$\chi_{4368}(821, \cdot)$	n/a	3552	4
4368.2.oq	$\chi_{4368}(1675, \cdot)$	n/a	1792	4
4368.2.os	$\chi_{4368}(1165, \cdot)$	n/a	1792	4
4368.2.ov	$\chi_{4368}(499, \cdot)$	n/a	1792	4
4368.2.ox	$\chi_{4368}(1237, \cdot)$	n/a	1792	4
4368.2.oy	$\chi_{4368}(149, \cdot)$	n/a	3552	4
4368.2.pb	$\chi_{4368}(899, \cdot)$	n/a	3552	4
4368.2.pd	$\chi_{4368}(2533, \cdot)$	n/a	1792	4
4368.2.pe	$\chi_{4368}(379, \cdot)$	n/a	1344	4
4368.2.ph	$\chi_{4368}(869, \cdot)$	n/a	2688	4
4368.2.pi	$\chi_{4368}(587, \cdot)$	n/a	3552	4

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(4368))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(4368)) \cong$ $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(6))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(546))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1092))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1456))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2184))$$^{\oplus 2}$