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Properties

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

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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

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