Space of modular forms of level 5733 and weight 2

• Label: 5733.2
• Level: 5733
• Weight: 2
• Dimension: 885021
• Nonzero newspaces: 168
• Sturm bound: 4741632

Defining parameters

Level:	$N$	=	$5733 = 3^{2} \cdot 7^{2} \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$168$
Sturm bound:			$4741632$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(5733))$.

	Total	New	Old
Modular forms	1196928	894623	302305
Cusp forms	1173889	885021	288868
Eisenstein series	23039	9602	13437

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(5733))$

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
5733.2.a	$\chi_{5733}(1, \cdot)$	5733.2.a.a	1	1
		5733.2.a.b	1
		5733.2.a.c	1
		5733.2.a.d	1
		5733.2.a.e	1
		5733.2.a.f	1
		5733.2.a.g	1
		5733.2.a.h	1
		5733.2.a.i	1
		5733.2.a.j	1
		5733.2.a.k	1
		5733.2.a.l	1
		5733.2.a.m	1
		5733.2.a.n	2
		5733.2.a.o	2
		5733.2.a.p	2
		5733.2.a.q	2
		5733.2.a.r	2
		5733.2.a.s	2
		5733.2.a.t	2
		5733.2.a.u	2
		5733.2.a.v	2
		5733.2.a.w	2
		5733.2.a.x	3
		5733.2.a.y	3
		5733.2.a.z	3
		5733.2.a.ba	3
		5733.2.a.bb	3
		5733.2.a.bc	3
		5733.2.a.bd	3
		5733.2.a.be	3
		5733.2.a.bf	4
		5733.2.a.bg	4
		5733.2.a.bh	4
		5733.2.a.bi	4
		5733.2.a.bj	4
		5733.2.a.bk	4
		5733.2.a.bl	5
		5733.2.a.bm	5
		5733.2.a.bn	5
		5733.2.a.bo	5
		5733.2.a.bp	5
		5733.2.a.bq	5
		5733.2.a.br	6
		5733.2.a.bs	6
		5733.2.a.bt	6
		5733.2.a.bu	6
		5733.2.a.bv	6
		5733.2.a.bw	10
		5733.2.a.bx	10
		5733.2.a.by	10
		5733.2.a.bz	10
		5733.2.a.ca	12
		5733.2.a.cb	12
5733.2.c	$\chi_{5733}(883, \cdot)$	n/a	234	1
5733.2.e	$\chi_{5733}(4850, \cdot)$	n/a	160	1
5733.2.g	$\chi_{5733}(5732, \cdot)$	n/a	184	1
5733.2.i	$\chi_{5733}(295, \cdot)$	n/a	1128	2
5733.2.j	$\chi_{5733}(1990, \cdot)$	n/a	400	2
5733.2.k	$\chi_{5733}(3019, \cdot)$	n/a	1104	2
5733.2.l	$\chi_{5733}(373, \cdot)$	n/a	1104	2
5733.2.m	$\chi_{5733}(1912, \cdot)$	n/a	984	2
5733.2.n	$\chi_{5733}(3448, \cdot)$	n/a	458	2
5733.2.o	$\chi_{5733}(2206, \cdot)$	n/a	468	2
5733.2.p	$\chi_{5733}(2713, \cdot)$	n/a	1104	2
5733.2.q	$\chi_{5733}(79, \cdot)$	n/a	960	2
5733.2.r	$\chi_{5733}(2419, \cdot)$	n/a	960	2
5733.2.s	$\chi_{5733}(802, \cdot)$	n/a	458	2
5733.2.t	$\chi_{5733}(2941, \cdot)$	n/a	1128	2
5733.2.u	$\chi_{5733}(2284, \cdot)$	n/a	1104	2
5733.2.w	$\chi_{5733}(3284, \cdot)$	n/a	380	2
5733.2.y	$\chi_{5733}(1126, \cdot)$	n/a	456	2
5733.2.z	$\chi_{5733}(2272, \cdot)$	n/a	1104	2
5733.2.bb	$\chi_{5733}(146, \cdot)$	n/a	1104	2
5733.2.be	$\chi_{5733}(950, \cdot)$	n/a	960	2
5733.2.bg	$\chi_{5733}(1979, \cdot)$	n/a	372	2
5733.2.bh	$\chi_{5733}(589, \cdot)$	n/a	1128	2
5733.2.bk	$\chi_{5733}(3301, \cdot)$	n/a	1104	2
5733.2.bm	$\chi_{5733}(3007, \cdot)$	n/a	458	2
5733.2.bn	$\chi_{5733}(1244, \cdot)$	n/a	1104	2
5733.2.bq	$\chi_{5733}(881, \cdot)$	n/a	376	2
5733.2.bs	$\chi_{5733}(803, \cdot)$	n/a	1104	2
5733.2.bt	$\chi_{5733}(5225, \cdot)$	n/a	1104	2
5733.2.cc	$\chi_{5733}(4196, \cdot)$	n/a	1104	2
5733.2.ce	$\chi_{5733}(1910, \cdot)$	n/a	1104	2
5733.2.cf	$\chi_{5733}(1538, \cdot)$	n/a	372	2
5733.2.ch	$\chi_{5733}(4703, \cdot)$	n/a	1104	2
5733.2.ci	$\chi_{5733}(1403, \cdot)$	n/a	376	2
5733.2.cm	$\chi_{5733}(1109, \cdot)$	n/a	1104	2
5733.2.cq	$\chi_{5733}(961, \cdot)$	n/a	1104	2
5733.2.ct	$\chi_{5733}(1765, \cdot)$	n/a	470	2
5733.2.cv	$\chi_{5733}(1843, \cdot)$	n/a	1104	2
5733.2.cw	$\chi_{5733}(5066, \cdot)$	n/a	372	2
5733.2.cz	$\chi_{5733}(1550, \cdot)$	n/a	1104	2
5733.2.db	$\chi_{5733}(1028, \cdot)$	n/a	960	2
5733.2.dd	$\chi_{5733}(68, \cdot)$	n/a	1104	2
5733.2.de	$\chi_{5733}(2057, \cdot)$	n/a	1104	2
5733.2.df	$\chi_{5733}(521, \cdot)$	n/a	320	2
5733.2.dj	$\chi_{5733}(1096, \cdot)$	n/a	1104	2
5733.2.dk	$\chi_{5733}(2500, \cdot)$	n/a	1128	2
5733.2.dl	$\chi_{5733}(2872, \cdot)$	n/a	460	2
5733.2.do	$\chi_{5733}(361, \cdot)$	n/a	458	2
5733.2.dr	$\chi_{5733}(2578, \cdot)$	n/a	1104	2
5733.2.dt	$\chi_{5733}(2794, \cdot)$	n/a	1128	2
5733.2.du	$\chi_{5733}(4343, \cdot)$	n/a	960	2
5733.2.dx	$\chi_{5733}(1322, \cdot)$	n/a	376	2
5733.2.dz	$\chi_{5733}(815, \cdot)$	n/a	1104	2
5733.2.ea	$\chi_{5733}(374, \cdot)$	n/a	1104	2
5733.2.eg	$\chi_{5733}(1832, \cdot)$	n/a	1104	2
5733.2.ei	$\chi_{5733}(4625, \cdot)$	n/a	372	2
5733.2.ej	$\chi_{5733}(1616, \cdot)$	n/a	1104	2
5733.2.em	$\chi_{5733}(820, \cdot)$	n/a	1680	6
5733.2.en	$\chi_{5733}(1892, \cdot)$	n/a	2208	4
5733.2.eq	$\chi_{5733}(619, \cdot)$	n/a	2208	4
5733.2.er	$\chi_{5733}(1861, \cdot)$	n/a	2208	4
5733.2.eu	$\chi_{5733}(1783, \cdot)$	n/a	916	4
5733.2.ew	$\chi_{5733}(3362, \cdot)$	n/a	2208	4
5733.2.ex	$\chi_{5733}(1814, \cdot)$	n/a	2256	4
5733.2.fa	$\chi_{5733}(2186, \cdot)$	n/a	744	4
5733.2.fb	$\chi_{5733}(1354, \cdot)$	n/a	2208	4
5733.2.fe	$\chi_{5733}(422, \cdot)$	n/a	744	4
5733.2.ff	$\chi_{5733}(704, \cdot)$	n/a	2208	4
5733.2.fi	$\chi_{5733}(785, \cdot)$	n/a	2256	4
5733.2.fl	$\chi_{5733}(31, \cdot)$	n/a	2208	4
5733.2.fm	$\chi_{5733}(97, \cdot)$	n/a	2208	4
5733.2.fn	$\chi_{5733}(1567, \cdot)$	n/a	920	4
5733.2.fo	$\chi_{5733}(460, \cdot)$	n/a	920	4
5733.2.ft	$\chi_{5733}(1060, \cdot)$	n/a	2208	4
5733.2.fu	$\chi_{5733}(1636, \cdot)$	n/a	2208	4
5733.2.fx	$\chi_{5733}(197, \cdot)$	n/a	768	4
5733.2.fy	$\chi_{5733}(1292, \cdot)$	n/a	2208	4
5733.2.fz	$\chi_{5733}(50, \cdot)$	n/a	2256	4
5733.2.ga	$\chi_{5733}(863, \cdot)$	n/a	752	4
5733.2.gf	$\chi_{5733}(275, \cdot)$	n/a	2208	4
5733.2.gg	$\chi_{5733}(128, \cdot)$	n/a	2208	4
5733.2.gi	$\chi_{5733}(19, \cdot)$	n/a	916	4
5733.2.gj	$\chi_{5733}(1489, \cdot)$	n/a	2208	4
5733.2.gm	$\chi_{5733}(538, \cdot)$	n/a	2208	4
5733.2.go	$\chi_{5733}(818, \cdot)$	n/a	1584	6
5733.2.gq	$\chi_{5733}(755, \cdot)$	n/a	1344	6
5733.2.gs	$\chi_{5733}(64, \cdot)$	n/a	1956	6
5733.2.gu	$\chi_{5733}(445, \cdot)$	n/a	9360	12
5733.2.gv	$\chi_{5733}(22, \cdot)$	n/a	9360	12
5733.2.gw	$\chi_{5733}(289, \cdot)$	n/a	3900	12
5733.2.gx	$\chi_{5733}(625, \cdot)$	n/a	8064	12
5733.2.gy	$\chi_{5733}(898, \cdot)$	n/a	8064	12
5733.2.gz	$\chi_{5733}(16, \cdot)$	n/a	9360	12
5733.2.ha	$\chi_{5733}(568, \cdot)$	n/a	3888	12
5733.2.hb	$\chi_{5733}(100, \cdot)$	n/a	3900	12
5733.2.hc	$\chi_{5733}(274, \cdot)$	n/a	8064	12
5733.2.hd	$\chi_{5733}(718, \cdot)$	n/a	9360	12
5733.2.he	$\chi_{5733}(529, \cdot)$	n/a	9360	12
5733.2.hf	$\chi_{5733}(235, \cdot)$	n/a	3360	12
5733.2.hg	$\chi_{5733}(211, \cdot)$	n/a	9360	12
5733.2.hh	$\chi_{5733}(307, \cdot)$	n/a	3912	12
5733.2.hj	$\chi_{5733}(8, \cdot)$	n/a	3168	12
5733.2.hn	$\chi_{5733}(335, \cdot)$	n/a	9360	12
5733.2.ho	$\chi_{5733}(17, \cdot)$	n/a	3144	12
5733.2.hq	$\chi_{5733}(38, \cdot)$	n/a	9360	12
5733.2.hw	$\chi_{5733}(173, \cdot)$	n/a	9360	12
5733.2.hx	$\chi_{5733}(614, \cdot)$	n/a	9360	12
5733.2.hz	$\chi_{5733}(503, \cdot)$	n/a	3120	12
5733.2.ic	$\chi_{5733}(248, \cdot)$	n/a	8064	12
5733.2.id	$\chi_{5733}(337, \cdot)$	n/a	9360	12
5733.2.if	$\chi_{5733}(88, \cdot)$	n/a	9360	12
5733.2.ii	$\chi_{5733}(1180, \cdot)$	n/a	3900	12
5733.2.il	$\chi_{5733}(298, \cdot)$	n/a	3888	12
5733.2.im	$\chi_{5733}(43, \cdot)$	n/a	9360	12
5733.2.in	$\chi_{5733}(277, \cdot)$	n/a	9360	12
5733.2.ir	$\chi_{5733}(404, \cdot)$	n/a	2688	12
5733.2.is	$\chi_{5733}(419, \cdot)$	n/a	9360	12
5733.2.it	$\chi_{5733}(542, \cdot)$	n/a	9360	12
5733.2.iv	$\chi_{5733}(209, \cdot)$	n/a	8064	12
5733.2.ix	$\chi_{5733}(698, \cdot)$	n/a	9360	12
5733.2.ja	$\chi_{5733}(152, \cdot)$	n/a	3144	12
5733.2.jb	$\chi_{5733}(4, \cdot)$	n/a	9360	12
5733.2.jd	$\chi_{5733}(127, \cdot)$	n/a	3888	12
5733.2.jg	$\chi_{5733}(142, \cdot)$	n/a	9360	12
5733.2.jk	$\chi_{5733}(257, \cdot)$	n/a	9360	12
5733.2.jo	$\chi_{5733}(467, \cdot)$	n/a	3120	12
5733.2.jp	$\chi_{5733}(524, \cdot)$	n/a	9360	12
5733.2.jr	$\chi_{5733}(647, \cdot)$	n/a	3144	12
5733.2.js	$\chi_{5733}(272, \cdot)$	n/a	9360	12
5733.2.ju	$\chi_{5733}(101, \cdot)$	n/a	9360	12
5733.2.kd	$\chi_{5733}(311, \cdot)$	n/a	9360	12
5733.2.ke	$\chi_{5733}(563, \cdot)$	n/a	9360	12
5733.2.kg	$\chi_{5733}(62, \cdot)$	n/a	3120	12
5733.2.kj	$\chi_{5733}(185, \cdot)$	n/a	9360	12
5733.2.kk	$\chi_{5733}(478, \cdot)$	n/a	3900	12
5733.2.km	$\chi_{5733}(25, \cdot)$	n/a	9360	12
5733.2.kp	$\chi_{5733}(673, \cdot)$	n/a	9360	12
5733.2.kq	$\chi_{5733}(269, \cdot)$	n/a	3144	12
5733.2.ks	$\chi_{5733}(131, \cdot)$	n/a	8064	12
5733.2.kv	$\chi_{5733}(230, \cdot)$	n/a	9360	12
5733.2.kx	$\chi_{5733}(394, \cdot)$	n/a	9360	12
5733.2.ky	$\chi_{5733}(34, \cdot)$	n/a	18720	24
5733.2.lb	$\chi_{5733}(115, \cdot)$	n/a	18720	24
5733.2.lc	$\chi_{5733}(262, \cdot)$	n/a	7800	24
5733.2.le	$\chi_{5733}(2, \cdot)$	n/a	18720	24
5733.2.lf	$\chi_{5733}(137, \cdot)$	n/a	18720	24
5733.2.lk	$\chi_{5733}(44, \cdot)$	n/a	6240	24
5733.2.ll	$\chi_{5733}(722, \cdot)$	n/a	18720	24
5733.2.lm	$\chi_{5733}(317, \cdot)$	n/a	18720	24
5733.2.ln	$\chi_{5733}(71, \cdot)$	n/a	6240	24
5733.2.lq	$\chi_{5733}(409, \cdot)$	n/a	18720	24
5733.2.lr	$\chi_{5733}(241, \cdot)$	n/a	18720	24
5733.2.lw	$\chi_{5733}(73, \cdot)$	n/a	7776	24
5733.2.lx	$\chi_{5733}(370, \cdot)$	n/a	7776	24
5733.2.ly	$\chi_{5733}(76, \cdot)$	n/a	18720	24
5733.2.lz	$\chi_{5733}(187, \cdot)$	n/a	18720	24
5733.2.mc	$\chi_{5733}(239, \cdot)$	n/a	18720	24
5733.2.mf	$\chi_{5733}(11, \cdot)$	n/a	18720	24
5733.2.mg	$\chi_{5733}(431, \cdot)$	n/a	6288	24
5733.2.mj	$\chi_{5733}(124, \cdot)$	n/a	18720	24
5733.2.mk	$\chi_{5733}(305, \cdot)$	n/a	6288	24
5733.2.mn	$\chi_{5733}(176, \cdot)$	n/a	18720	24
5733.2.mo	$\chi_{5733}(86, \cdot)$	n/a	18720	24
5733.2.mq	$\chi_{5733}(136, \cdot)$	n/a	7800	24
5733.2.mt	$\chi_{5733}(202, \cdot)$	n/a	18720	24
5733.2.mu	$\chi_{5733}(229, \cdot)$	n/a	18720	24
5733.2.mx	$\chi_{5733}(158, \cdot)$	n/a	18720	24

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(5733))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(5733)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(819))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1911))$$^{\oplus 2}$