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Properties

Label 5200.2
Level 5200
Weight 2
Dimension 411062
Nonzero newspaces 104
Sturm bound 3225600

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Defining parameters

Level: \( N \) = \( 5200 = 2^{4} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(3225600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5200))\).

Total New Old
Modular forms 815808 415120 400688
Cusp forms 796993 411062 385931
Eisenstein series 18815 4058 14757

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5200))\)

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
5200.2.a \(\chi_{5200}(1, \cdot)\) 5200.2.a.a 1 1
5200.2.a.b 1
5200.2.a.c 1
5200.2.a.d 1
5200.2.a.e 1
5200.2.a.f 1
5200.2.a.g 1
5200.2.a.h 1
5200.2.a.i 1
5200.2.a.j 1
5200.2.a.k 1
5200.2.a.l 1
5200.2.a.m 1
5200.2.a.n 1
5200.2.a.o 1
5200.2.a.p 1
5200.2.a.q 1
5200.2.a.r 1
5200.2.a.s 1
5200.2.a.t 1
5200.2.a.u 1
5200.2.a.v 1
5200.2.a.w 1
5200.2.a.x 1
5200.2.a.y 1
5200.2.a.z 1
5200.2.a.ba 1
5200.2.a.bb 1
5200.2.a.bc 1
5200.2.a.bd 1
5200.2.a.be 1
5200.2.a.bf 1
5200.2.a.bg 1
5200.2.a.bh 1
5200.2.a.bi 1
5200.2.a.bj 1
5200.2.a.bk 1
5200.2.a.bl 2
5200.2.a.bm 2
5200.2.a.bn 2
5200.2.a.bo 2
5200.2.a.bp 2
5200.2.a.bq 2
5200.2.a.br 2
5200.2.a.bs 2
5200.2.a.bt 2
5200.2.a.bu 2
5200.2.a.bv 2
5200.2.a.bw 2
5200.2.a.bx 2
5200.2.a.by 2
5200.2.a.bz 2
5200.2.a.ca 2
5200.2.a.cb 3
5200.2.a.cc 3
5200.2.a.cd 3
5200.2.a.ce 3
5200.2.a.cf 3
5200.2.a.cg 3
5200.2.a.ch 3
5200.2.a.ci 3
5200.2.a.cj 3
5200.2.a.ck 4
5200.2.a.cl 4
5200.2.a.cm 5
5200.2.a.cn 5
5200.2.d \(\chi_{5200}(1249, \cdot)\) n/a 108 1
5200.2.e \(\chi_{5200}(4601, \cdot)\) None 0 1
5200.2.f \(\chi_{5200}(3249, \cdot)\) n/a 124 1
5200.2.g \(\chi_{5200}(2601, \cdot)\) None 0 1
5200.2.j \(\chi_{5200}(3849, \cdot)\) None 0 1
5200.2.k \(\chi_{5200}(2001, \cdot)\) n/a 130 1
5200.2.p \(\chi_{5200}(649, \cdot)\) None 0 1
5200.2.q \(\chi_{5200}(2401, \cdot)\) n/a 260 2
5200.2.s \(\chi_{5200}(3557, \cdot)\) n/a 1000 2
5200.2.u \(\chi_{5200}(2751, \cdot)\) n/a 266 2
5200.2.v \(\chi_{5200}(443, \cdot)\) n/a 864 2
5200.2.y \(\chi_{5200}(1507, \cdot)\) n/a 1000 2
5200.2.z \(\chi_{5200}(1399, \cdot)\) None 0 2
5200.2.bb \(\chi_{5200}(3957, \cdot)\) n/a 1000 2
5200.2.be \(\chi_{5200}(1949, \cdot)\) n/a 1000 2
5200.2.bg \(\chi_{5200}(593, \cdot)\) n/a 248 2
5200.2.bi \(\chi_{5200}(57, \cdot)\) None 0 2
5200.2.bj \(\chi_{5200}(1301, \cdot)\) n/a 912 2
5200.2.bm \(\chi_{5200}(1451, \cdot)\) n/a 1052 2
5200.2.bp \(\chi_{5200}(1743, \cdot)\) n/a 216 2
5200.2.bq \(\chi_{5200}(1143, \cdot)\) None 0 2
5200.2.bs \(\chi_{5200}(499, \cdot)\) n/a 1000 2
5200.2.bt \(\chi_{5200}(1851, \cdot)\) n/a 1052 2
5200.2.bv \(\chi_{5200}(207, \cdot)\) n/a 252 2
5200.2.bw \(\chi_{5200}(807, \cdot)\) None 0 2
5200.2.bz \(\chi_{5200}(99, \cdot)\) n/a 1000 2
5200.2.cc \(\chi_{5200}(2549, \cdot)\) n/a 864 2
5200.2.cd \(\chi_{5200}(993, \cdot)\) n/a 248 2
5200.2.cf \(\chi_{5200}(3593, \cdot)\) None 0 2
5200.2.ch \(\chi_{5200}(701, \cdot)\) n/a 1052 2
5200.2.cj \(\chi_{5200}(957, \cdot)\) n/a 1000 2
5200.2.cm \(\chi_{5200}(151, \cdot)\) None 0 2
5200.2.cn \(\chi_{5200}(2107, \cdot)\) n/a 864 2
5200.2.cq \(\chi_{5200}(4107, \cdot)\) n/a 1000 2
5200.2.cr \(\chi_{5200}(3999, \cdot)\) n/a 252 2
5200.2.cu \(\chi_{5200}(1357, \cdot)\) n/a 1000 2
5200.2.cv \(\chi_{5200}(1041, \cdot)\) n/a 720 4
5200.2.cw \(\chi_{5200}(2649, \cdot)\) None 0 2
5200.2.db \(\chi_{5200}(4001, \cdot)\) n/a 260 2
5200.2.dc \(\chi_{5200}(1049, \cdot)\) None 0 2
5200.2.df \(\chi_{5200}(601, \cdot)\) None 0 2
5200.2.dg \(\chi_{5200}(49, \cdot)\) n/a 248 2
5200.2.dh \(\chi_{5200}(1401, \cdot)\) None 0 2
5200.2.di \(\chi_{5200}(3649, \cdot)\) n/a 248 2
5200.2.dn \(\chi_{5200}(961, \cdot)\) n/a 832 4
5200.2.do \(\chi_{5200}(729, \cdot)\) None 0 4
5200.2.dp \(\chi_{5200}(1689, \cdot)\) None 0 4
5200.2.ds \(\chi_{5200}(441, \cdot)\) None 0 4
5200.2.dt \(\chi_{5200}(209, \cdot)\) n/a 720 4
5200.2.dy \(\chi_{5200}(521, \cdot)\) None 0 4
5200.2.dz \(\chi_{5200}(129, \cdot)\) n/a 832 4
5200.2.ea \(\chi_{5200}(293, \cdot)\) n/a 2000 4
5200.2.ed \(\chi_{5200}(799, \cdot)\) n/a 504 4
5200.2.ef \(\chi_{5200}(107, \cdot)\) n/a 2000 4
5200.2.eg \(\chi_{5200}(907, \cdot)\) n/a 2000 4
5200.2.ei \(\chi_{5200}(951, \cdot)\) None 0 4
5200.2.el \(\chi_{5200}(557, \cdot)\) n/a 2000 4
5200.2.en \(\chi_{5200}(101, \cdot)\) n/a 2104 4
5200.2.ep \(\chi_{5200}(3257, \cdot)\) None 0 4
5200.2.er \(\chi_{5200}(657, \cdot)\) n/a 496 4
5200.2.es \(\chi_{5200}(549, \cdot)\) n/a 2000 4
5200.2.eu \(\chi_{5200}(3499, \cdot)\) n/a 2000 4
5200.2.ew \(\chi_{5200}(1543, \cdot)\) None 0 4
5200.2.ex \(\chi_{5200}(543, \cdot)\) n/a 504 4
5200.2.fa \(\chi_{5200}(2251, \cdot)\) n/a 2104 4
5200.2.fd \(\chi_{5200}(899, \cdot)\) n/a 2000 4
5200.2.fg \(\chi_{5200}(407, \cdot)\) None 0 4
5200.2.fh \(\chi_{5200}(607, \cdot)\) n/a 504 4
5200.2.fj \(\chi_{5200}(851, \cdot)\) n/a 2104 4
5200.2.fl \(\chi_{5200}(1101, \cdot)\) n/a 2104 4
5200.2.fm \(\chi_{5200}(457, \cdot)\) None 0 4
5200.2.fo \(\chi_{5200}(193, \cdot)\) n/a 496 4
5200.2.fq \(\chi_{5200}(1349, \cdot)\) n/a 2000 4
5200.2.ft \(\chi_{5200}(357, \cdot)\) n/a 2000 4
5200.2.fv \(\chi_{5200}(999, \cdot)\) None 0 4
5200.2.fx \(\chi_{5200}(1907, \cdot)\) n/a 2000 4
5200.2.fy \(\chi_{5200}(43, \cdot)\) n/a 2000 4
5200.2.ga \(\chi_{5200}(1151, \cdot)\) n/a 532 4
5200.2.gc \(\chi_{5200}(93, \cdot)\) n/a 2000 4
5200.2.ge \(\chi_{5200}(81, \cdot)\) n/a 1664 8
5200.2.gg \(\chi_{5200}(213, \cdot)\) n/a 6688 8
5200.2.gi \(\chi_{5200}(239, \cdot)\) n/a 1680 8
5200.2.gj \(\chi_{5200}(883, \cdot)\) n/a 6688 8
5200.2.gm \(\chi_{5200}(27, \cdot)\) n/a 5760 8
5200.2.gn \(\chi_{5200}(1191, \cdot)\) None 0 8
5200.2.gp \(\chi_{5200}(317, \cdot)\) n/a 6688 8
5200.2.gs \(\chi_{5200}(261, \cdot)\) n/a 5760 8
5200.2.gt \(\chi_{5200}(73, \cdot)\) None 0 8
5200.2.gv \(\chi_{5200}(577, \cdot)\) n/a 1664 8
5200.2.gx \(\chi_{5200}(389, \cdot)\) n/a 6688 8
5200.2.ha \(\chi_{5200}(1019, \cdot)\) n/a 6688 8
5200.2.hd \(\chi_{5200}(183, \cdot)\) None 0 8
5200.2.he \(\chi_{5200}(623, \cdot)\) n/a 1680 8
5200.2.hg \(\chi_{5200}(811, \cdot)\) n/a 6688 8
5200.2.hh \(\chi_{5200}(619, \cdot)\) n/a 6688 8
5200.2.hj \(\chi_{5200}(103, \cdot)\) None 0 8
5200.2.hk \(\chi_{5200}(287, \cdot)\) n/a 1440 8
5200.2.hn \(\chi_{5200}(291, \cdot)\) n/a 6688 8
5200.2.hq \(\chi_{5200}(181, \cdot)\) n/a 6688 8
5200.2.hs \(\chi_{5200}(473, \cdot)\) None 0 8
5200.2.hu \(\chi_{5200}(177, \cdot)\) n/a 1664 8
5200.2.hv \(\chi_{5200}(469, \cdot)\) n/a 5760 8
5200.2.hx \(\chi_{5200}(437, \cdot)\) n/a 6688 8
5200.2.ia \(\chi_{5200}(359, \cdot)\) None 0 8
5200.2.ib \(\chi_{5200}(363, \cdot)\) n/a 6688 8
5200.2.ie \(\chi_{5200}(547, \cdot)\) n/a 5760 8
5200.2.if \(\chi_{5200}(31, \cdot)\) n/a 1680 8
5200.2.ii \(\chi_{5200}(333, \cdot)\) n/a 6688 8
5200.2.ij \(\chi_{5200}(1089, \cdot)\) n/a 1664 8
5200.2.ik \(\chi_{5200}(841, \cdot)\) None 0 8
5200.2.ip \(\chi_{5200}(289, \cdot)\) n/a 1664 8
5200.2.iq \(\chi_{5200}(121, \cdot)\) None 0 8
5200.2.it \(\chi_{5200}(329, \cdot)\) None 0 8
5200.2.iu \(\chi_{5200}(9, \cdot)\) None 0 8
5200.2.iv \(\chi_{5200}(641, \cdot)\) n/a 1664 8
5200.2.iy \(\chi_{5200}(197, \cdot)\) n/a 13376 16
5200.2.jb \(\chi_{5200}(111, \cdot)\) n/a 3360 16
5200.2.jd \(\chi_{5200}(147, \cdot)\) n/a 13376 16
5200.2.je \(\chi_{5200}(523, \cdot)\) n/a 13376 16
5200.2.jg \(\chi_{5200}(119, \cdot)\) None 0 16
5200.2.jj \(\chi_{5200}(37, \cdot)\) n/a 13376 16
5200.2.jl \(\chi_{5200}(29, \cdot)\) n/a 13376 16
5200.2.jm \(\chi_{5200}(353, \cdot)\) n/a 3328 16
5200.2.jo \(\chi_{5200}(137, \cdot)\) None 0 16
5200.2.jq \(\chi_{5200}(381, \cdot)\) n/a 13376 16
5200.2.js \(\chi_{5200}(11, \cdot)\) n/a 13376 16
5200.2.ju \(\chi_{5200}(367, \cdot)\) n/a 3360 16
5200.2.jv \(\chi_{5200}(23, \cdot)\) None 0 16
5200.2.jy \(\chi_{5200}(19, \cdot)\) n/a 13376 16
5200.2.kb \(\chi_{5200}(171, \cdot)\) n/a 13376 16
5200.2.ke \(\chi_{5200}(127, \cdot)\) n/a 3360 16
5200.2.kf \(\chi_{5200}(87, \cdot)\) None 0 16
5200.2.kh \(\chi_{5200}(379, \cdot)\) n/a 13376 16
5200.2.kj \(\chi_{5200}(69, \cdot)\) n/a 13376 16
5200.2.kl \(\chi_{5200}(33, \cdot)\) n/a 3328 16
5200.2.kn \(\chi_{5200}(553, \cdot)\) None 0 16
5200.2.ko \(\chi_{5200}(61, \cdot)\) n/a 13376 16
5200.2.kr \(\chi_{5200}(453, \cdot)\) n/a 13376 16
5200.2.kt \(\chi_{5200}(71, \cdot)\) None 0 16
5200.2.kv \(\chi_{5200}(563, \cdot)\) n/a 13376 16
5200.2.kw \(\chi_{5200}(3, \cdot)\) n/a 13376 16
5200.2.ky \(\chi_{5200}(319, \cdot)\) n/a 3360 16
5200.2.la \(\chi_{5200}(397, \cdot)\) n/a 13376 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2600))\)\(^{\oplus 2}\)