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Properties

Label 6200.2
Level 6200
Weight 2
Dimension 593618
Nonzero newspaces 126
Sturm bound 4608000

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Defining parameters

Level: \( N \) = \( 6200 = 2^{3} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 126 \)
Sturm bound: \(4608000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6200))\).

Total New Old
Modular forms 1162080 598374 563706
Cusp forms 1141921 593618 548303
Eisenstein series 20159 4756 15403

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6200))\)

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
6200.2.a \(\chi_{6200}(1, \cdot)\) 6200.2.a.a 1 1
6200.2.a.b 1
6200.2.a.c 1
6200.2.a.d 1
6200.2.a.e 1
6200.2.a.f 1
6200.2.a.g 1
6200.2.a.h 1
6200.2.a.i 1
6200.2.a.j 1
6200.2.a.k 1
6200.2.a.l 1
6200.2.a.m 2
6200.2.a.n 2
6200.2.a.o 2
6200.2.a.p 3
6200.2.a.q 3
6200.2.a.r 4
6200.2.a.s 5
6200.2.a.t 5
6200.2.a.u 6
6200.2.a.v 6
6200.2.a.w 6
6200.2.a.x 6
6200.2.a.y 8
6200.2.a.z 8
6200.2.a.ba 10
6200.2.a.bb 10
6200.2.a.bc 11
6200.2.a.bd 11
6200.2.a.be 11
6200.2.a.bf 11
6200.2.b \(\chi_{6200}(2851, \cdot)\) n/a 602 1
6200.2.d \(\chi_{6200}(249, \cdot)\) n/a 136 1
6200.2.g \(\chi_{6200}(3101, \cdot)\) n/a 570 1
6200.2.i \(\chi_{6200}(6199, \cdot)\) None 0 1
6200.2.j \(\chi_{6200}(3349, \cdot)\) n/a 540 1
6200.2.l \(\chi_{6200}(5951, \cdot)\) None 0 1
6200.2.o \(\chi_{6200}(3099, \cdot)\) n/a 572 1
6200.2.q \(\chi_{6200}(3001, \cdot)\) n/a 304 2
6200.2.r \(\chi_{6200}(3657, \cdot)\) n/a 288 2
6200.2.u \(\chi_{6200}(807, \cdot)\) None 0 2
6200.2.v \(\chi_{6200}(3907, \cdot)\) n/a 1080 2
6200.2.y \(\chi_{6200}(557, \cdot)\) n/a 1144 2
6200.2.z \(\chi_{6200}(721, \cdot)\) n/a 960 4
6200.2.ba \(\chi_{6200}(3201, \cdot)\) n/a 608 4
6200.2.bb \(\chi_{6200}(281, \cdot)\) n/a 960 4
6200.2.bc \(\chi_{6200}(2761, \cdot)\) n/a 960 4
6200.2.bd \(\chi_{6200}(1241, \cdot)\) n/a 904 4
6200.2.be \(\chi_{6200}(481, \cdot)\) n/a 960 4
6200.2.bg \(\chi_{6200}(99, \cdot)\) n/a 1144 2
6200.2.bj \(\chi_{6200}(2351, \cdot)\) None 0 2
6200.2.bl \(\chi_{6200}(149, \cdot)\) n/a 1144 2
6200.2.bm \(\chi_{6200}(2599, \cdot)\) None 0 2
6200.2.bo \(\chi_{6200}(501, \cdot)\) n/a 1204 2
6200.2.br \(\chi_{6200}(3249, \cdot)\) n/a 288 2
6200.2.bt \(\chi_{6200}(5451, \cdot)\) n/a 1204 2
6200.2.bu \(\chi_{6200}(3581, \cdot)\) n/a 3824 4
6200.2.bw \(\chi_{6200}(4239, \cdot)\) None 0 4
6200.2.bz \(\chi_{6200}(1131, \cdot)\) n/a 3824 4
6200.2.cb \(\chi_{6200}(529, \cdot)\) n/a 960 4
6200.2.cd \(\chi_{6200}(991, \cdot)\) None 0 4
6200.2.cf \(\chi_{6200}(869, \cdot)\) n/a 3600 4
6200.2.cl \(\chi_{6200}(339, \cdot)\) n/a 3824 4
6200.2.cm \(\chi_{6200}(3499, \cdot)\) n/a 2288 4
6200.2.cn \(\chi_{6200}(139, \cdot)\) n/a 3824 4
6200.2.co \(\chi_{6200}(1379, \cdot)\) n/a 3824 4
6200.2.cs \(\chi_{6200}(711, \cdot)\) None 0 4
6200.2.cx \(\chi_{6200}(3991, \cdot)\) None 0 4
6200.2.cy \(\chi_{6200}(151, \cdot)\) None 0 4
6200.2.cz \(\chi_{6200}(271, \cdot)\) None 0 4
6200.2.dd \(\chi_{6200}(3829, \cdot)\) n/a 3824 4
6200.2.de \(\chi_{6200}(469, \cdot)\) n/a 3824 4
6200.2.df \(\chi_{6200}(349, \cdot)\) n/a 2288 4
6200.2.dg \(\chi_{6200}(109, \cdot)\) n/a 3824 4
6200.2.dj \(\chi_{6200}(619, \cdot)\) n/a 3824 4
6200.2.dm \(\chi_{6200}(1489, \cdot)\) n/a 896 4
6200.2.do \(\chi_{6200}(371, \cdot)\) n/a 3824 4
6200.2.dp \(\chi_{6200}(1639, \cdot)\) None 0 4
6200.2.dq \(\chi_{6200}(959, \cdot)\) None 0 4
6200.2.dr \(\chi_{6200}(399, \cdot)\) None 0 4
6200.2.dw \(\chi_{6200}(519, \cdot)\) None 0 4
6200.2.dy \(\chi_{6200}(221, \cdot)\) n/a 3824 4
6200.2.dz \(\chi_{6200}(1341, \cdot)\) n/a 3824 4
6200.2.ea \(\chi_{6200}(101, \cdot)\) n/a 2408 4
6200.2.eb \(\chi_{6200}(2141, \cdot)\) n/a 3824 4
6200.2.ef \(\chi_{6200}(969, \cdot)\) n/a 960 4
6200.2.ek \(\chi_{6200}(3449, \cdot)\) n/a 576 4
6200.2.el \(\chi_{6200}(3009, \cdot)\) n/a 960 4
6200.2.em \(\chi_{6200}(729, \cdot)\) n/a 960 4
6200.2.eq \(\chi_{6200}(91, \cdot)\) n/a 3824 4
6200.2.er \(\chi_{6200}(3251, \cdot)\) n/a 2408 4
6200.2.es \(\chi_{6200}(891, \cdot)\) n/a 3824 4
6200.2.et \(\chi_{6200}(771, \cdot)\) n/a 3824 4
6200.2.ev \(\chi_{6200}(1239, \cdot)\) None 0 4
6200.2.ex \(\chi_{6200}(621, \cdot)\) n/a 3600 4
6200.2.ez \(\chi_{6200}(1139, \cdot)\) n/a 3824 4
6200.2.fd \(\chi_{6200}(1589, \cdot)\) n/a 3824 4
6200.2.ff \(\chi_{6200}(1391, \cdot)\) None 0 4
6200.2.fg \(\chi_{6200}(3157, \cdot)\) n/a 2288 4
6200.2.fj \(\chi_{6200}(707, \cdot)\) n/a 2288 4
6200.2.fk \(\chi_{6200}(3807, \cdot)\) None 0 4
6200.2.fn \(\chi_{6200}(57, \cdot)\) n/a 576 4
6200.2.fo \(\chi_{6200}(441, \cdot)\) n/a 1920 8
6200.2.fp \(\chi_{6200}(521, \cdot)\) n/a 1920 8
6200.2.fq \(\chi_{6200}(1041, \cdot)\) n/a 1920 8
6200.2.fr \(\chi_{6200}(81, \cdot)\) n/a 1920 8
6200.2.fs \(\chi_{6200}(1001, \cdot)\) n/a 1216 8
6200.2.ft \(\chi_{6200}(41, \cdot)\) n/a 1920 8
6200.2.fv \(\chi_{6200}(153, \cdot)\) n/a 1920 8
6200.2.fw \(\chi_{6200}(1527, \cdot)\) None 0 8
6200.2.fz \(\chi_{6200}(667, \cdot)\) n/a 7648 8
6200.2.ga \(\chi_{6200}(213, \cdot)\) n/a 7648 8
6200.2.gd \(\chi_{6200}(1053, \cdot)\) n/a 7648 8
6200.2.ge \(\chi_{6200}(957, \cdot)\) n/a 4576 8
6200.2.gf \(\chi_{6200}(277, \cdot)\) n/a 7648 8
6200.2.gg \(\chi_{6200}(77, \cdot)\) n/a 7648 8
6200.2.gl \(\chi_{6200}(1517, \cdot)\) n/a 7648 8
6200.2.gm \(\chi_{6200}(163, \cdot)\) n/a 7648 8
6200.2.gr \(\chi_{6200}(187, \cdot)\) n/a 7200 8
6200.2.gs \(\chi_{6200}(1163, \cdot)\) n/a 7648 8
6200.2.gt \(\chi_{6200}(907, \cdot)\) n/a 4576 8
6200.2.gu \(\chi_{6200}(283, \cdot)\) n/a 7648 8
6200.2.gx \(\chi_{6200}(63, \cdot)\) None 0 8
6200.2.gy \(\chi_{6200}(343, \cdot)\) None 0 8
6200.2.gz \(\chi_{6200}(783, \cdot)\) None 0 8
6200.2.ha \(\chi_{6200}(1087, \cdot)\) None 0 8
6200.2.hf \(\chi_{6200}(47, \cdot)\) None 0 8
6200.2.hg \(\chi_{6200}(697, \cdot)\) n/a 1920 8
6200.2.hl \(\chi_{6200}(433, \cdot)\) n/a 1920 8
6200.2.hm \(\chi_{6200}(1937, \cdot)\) n/a 1920 8
6200.2.hn \(\chi_{6200}(457, \cdot)\) n/a 1152 8
6200.2.ho \(\chi_{6200}(833, \cdot)\) n/a 1920 8
6200.2.hq \(\chi_{6200}(1791, \cdot)\) None 0 8
6200.2.hs \(\chi_{6200}(669, \cdot)\) n/a 7648 8
6200.2.hw \(\chi_{6200}(259, \cdot)\) n/a 7648 8
6200.2.hy \(\chi_{6200}(1141, \cdot)\) n/a 7648 8
6200.2.ia \(\chi_{6200}(119, \cdot)\) None 0 8
6200.2.ic \(\chi_{6200}(1171, \cdot)\) n/a 7648 8
6200.2.id \(\chi_{6200}(11, \cdot)\) n/a 7648 8
6200.2.ie \(\chi_{6200}(251, \cdot)\) n/a 4816 8
6200.2.if \(\chi_{6200}(291, \cdot)\) n/a 7648 8
6200.2.ij \(\chi_{6200}(9, \cdot)\) n/a 1920 8
6200.2.ik \(\chi_{6200}(1289, \cdot)\) n/a 1920 8
6200.2.il \(\chi_{6200}(49, \cdot)\) n/a 1152 8
6200.2.iq \(\chi_{6200}(169, \cdot)\) n/a 1920 8
6200.2.iu \(\chi_{6200}(981, \cdot)\) n/a 7648 8
6200.2.iv \(\chi_{6200}(701, \cdot)\) n/a 4816 8
6200.2.iw \(\chi_{6200}(421, \cdot)\) n/a 7648 8
6200.2.ix \(\chi_{6200}(381, \cdot)\) n/a 7648 8
6200.2.iz \(\chi_{6200}(879, \cdot)\) None 0 8
6200.2.je \(\chi_{6200}(199, \cdot)\) None 0 8
6200.2.jf \(\chi_{6200}(79, \cdot)\) None 0 8
6200.2.jg \(\chi_{6200}(2039, \cdot)\) None 0 8
6200.2.jh \(\chi_{6200}(491, \cdot)\) n/a 7648 8
6200.2.jj \(\chi_{6200}(129, \cdot)\) n/a 1920 8
6200.2.jm \(\chi_{6200}(739, \cdot)\) n/a 7648 8
6200.2.jp \(\chi_{6200}(1229, \cdot)\) n/a 7648 8
6200.2.jq \(\chi_{6200}(949, \cdot)\) n/a 4576 8
6200.2.jr \(\chi_{6200}(69, \cdot)\) n/a 7648 8
6200.2.js \(\chi_{6200}(2229, \cdot)\) n/a 7648 8
6200.2.jw \(\chi_{6200}(631, \cdot)\) None 0 8
6200.2.jx \(\chi_{6200}(551, \cdot)\) None 0 8
6200.2.jy \(\chi_{6200}(871, \cdot)\) None 0 8
6200.2.kd \(\chi_{6200}(911, \cdot)\) None 0 8
6200.2.kh \(\chi_{6200}(859, \cdot)\) n/a 7648 8
6200.2.ki \(\chi_{6200}(1419, \cdot)\) n/a 7648 8
6200.2.kj \(\chi_{6200}(499, \cdot)\) n/a 4576 8
6200.2.kk \(\chi_{6200}(179, \cdot)\) n/a 7648 8
6200.2.kq \(\chi_{6200}(1389, \cdot)\) n/a 7648 8
6200.2.ks \(\chi_{6200}(471, \cdot)\) None 0 8
6200.2.ku \(\chi_{6200}(329, \cdot)\) n/a 1920 8
6200.2.kw \(\chi_{6200}(611, \cdot)\) n/a 7648 8
6200.2.kz \(\chi_{6200}(239, \cdot)\) None 0 8
6200.2.lb \(\chi_{6200}(1981, \cdot)\) n/a 7648 8
6200.2.ld \(\chi_{6200}(817, \cdot)\) n/a 3840 16
6200.2.le \(\chi_{6200}(393, \cdot)\) n/a 2304 16
6200.2.lf \(\chi_{6200}(17, \cdot)\) n/a 3840 16
6200.2.lg \(\chi_{6200}(553, \cdot)\) n/a 3840 16
6200.2.ll \(\chi_{6200}(73, \cdot)\) n/a 3840 16
6200.2.lm \(\chi_{6200}(423, \cdot)\) None 0 16
6200.2.lr \(\chi_{6200}(887, \cdot)\) None 0 16
6200.2.ls \(\chi_{6200}(503, \cdot)\) None 0 16
6200.2.lt \(\chi_{6200}(7, \cdot)\) None 0 16
6200.2.lu \(\chi_{6200}(87, \cdot)\) None 0 16
6200.2.lx \(\chi_{6200}(603, \cdot)\) n/a 15296 16
6200.2.ly \(\chi_{6200}(107, \cdot)\) n/a 9152 16
6200.2.lz \(\chi_{6200}(227, \cdot)\) n/a 15296 16
6200.2.ma \(\chi_{6200}(67, \cdot)\) n/a 15296 16
6200.2.mf \(\chi_{6200}(267, \cdot)\) n/a 15296 16
6200.2.mg \(\chi_{6200}(517, \cdot)\) n/a 15296 16
6200.2.ml \(\chi_{6200}(53, \cdot)\) n/a 15296 16
6200.2.mm \(\chi_{6200}(13, \cdot)\) n/a 15296 16
6200.2.mn \(\chi_{6200}(693, \cdot)\) n/a 9152 16
6200.2.mo \(\chi_{6200}(37, \cdot)\) n/a 15296 16
6200.2.mr \(\chi_{6200}(613, \cdot)\) n/a 15296 16
6200.2.ms \(\chi_{6200}(483, \cdot)\) n/a 15296 16
6200.2.mv \(\chi_{6200}(103, \cdot)\) None 0 16
6200.2.mw \(\chi_{6200}(177, \cdot)\) n/a 3840 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1550))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6200))\)\(^{\oplus 1}\)