# Properties

 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 the 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

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