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Properties

Label 24200.2
Level 24200
Weight 2
Dimension 8873046
Nonzero newspaces 126
Sturm bound 69696000

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Defining parameters

Level: \( N \) = \( 24200 = 2^{3} \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 126 \)
Sturm bound: \(69696000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(24200))\).

Total New Old
Modular forms 17477760 8896088 8581672
Cusp forms 17370241 8873046 8497195
Eisenstein series 107519 23042 84477

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(24200))\)

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
24200.2.a \(\chi_{24200}(1, \cdot)\) 24200.2.a.a 1 1
24200.2.a.b 1
24200.2.a.c 1
24200.2.a.d 1
24200.2.a.e 1
24200.2.a.f 1
24200.2.a.g 1
24200.2.a.h 1
24200.2.a.i 1
24200.2.a.j 1
24200.2.a.k 1
24200.2.a.l 1
24200.2.a.m 1
24200.2.a.n 1
24200.2.a.o 1
24200.2.a.p 1
24200.2.a.q 1
24200.2.a.r 1
24200.2.a.s 1
24200.2.a.t 1
24200.2.a.u 1
24200.2.a.v 1
24200.2.a.w 1
24200.2.a.x 1
24200.2.a.y 1
24200.2.a.z 1
24200.2.a.ba 1
24200.2.a.bb 1
24200.2.a.bc 1
24200.2.a.bd 1
24200.2.a.be 1
24200.2.a.bf 1
24200.2.a.bg 2
24200.2.a.bh 2
24200.2.a.bi 2
24200.2.a.bj 2
24200.2.a.bk 2
24200.2.a.bl 2
24200.2.a.bm 2
24200.2.a.bn 2
24200.2.a.bo 2
24200.2.a.bp 2
24200.2.a.bq 2
24200.2.a.br 2
24200.2.a.bs 2
24200.2.a.bt 2
24200.2.a.bu 2
24200.2.a.bv 2
24200.2.a.bw 2
24200.2.a.bx 2
24200.2.a.by 2
24200.2.a.bz 2
24200.2.a.ca 2
24200.2.a.cb 2
24200.2.a.cc 2
24200.2.a.cd 2
24200.2.a.ce 2
24200.2.a.cf 2
24200.2.a.cg 3
24200.2.a.ch 3
24200.2.a.ci 3
24200.2.a.cj 3
24200.2.a.ck 3
24200.2.a.cl 3
24200.2.a.cm 3
24200.2.a.cn 3
24200.2.a.co 3
24200.2.a.cp 3
24200.2.a.cq 4
24200.2.a.cr 4
24200.2.a.cs 4
24200.2.a.ct 4
24200.2.a.cu 4
24200.2.a.cv 4
24200.2.a.cw 4
24200.2.a.cx 4
24200.2.a.cy 4
24200.2.a.cz 4
24200.2.a.da 4
24200.2.a.db 4
24200.2.a.dc 5
24200.2.a.dd 5
24200.2.a.de 5
24200.2.a.df 5
24200.2.a.dg 5
24200.2.a.dh 5
24200.2.a.di 5
24200.2.a.dj 5
24200.2.a.dk 6
24200.2.a.dl 6
24200.2.a.dm 6
24200.2.a.dn 6
24200.2.a.do 6
24200.2.a.dp 6
24200.2.a.dq 6
24200.2.a.dr 6
24200.2.a.ds 6
24200.2.a.dt 6
24200.2.a.du 8
24200.2.a.dv 8
24200.2.a.dw 8
24200.2.a.dx 8
24200.2.a.dy 8
24200.2.a.dz 8
24200.2.a.ea 8
24200.2.a.eb 8
24200.2.a.ec 10
24200.2.a.ed 10
24200.2.a.ee 10
24200.2.a.ef 10
24200.2.a.eg 12
24200.2.a.eh 12
24200.2.a.ei 12
24200.2.a.ej 12
24200.2.a.ek 16
24200.2.a.el 16
24200.2.a.em 18
24200.2.a.en 18
24200.2.a.eo 18
24200.2.a.ep 18
24200.2.b \(\chi_{24200}(10649, \cdot)\) n/a 490 1
24200.2.c \(\chi_{24200}(12099, \cdot)\) n/a 1928 1
24200.2.g \(\chi_{24200}(12101, \cdot)\) n/a 2044 1
24200.2.l \(\chi_{24200}(22749, \cdot)\) n/a 1944 1
24200.2.p \(\chi_{24200}(1451, \cdot)\) n/a 2028 1
24200.2.r \(\chi_{24200}(243, \cdot)\) n/a 3888 2
24200.2.t \(\chi_{24200}(1693, \cdot)\) n/a 3856 2
24200.2.v \(\chi_{24200}(11857, \cdot)\) n/a 972 2
24200.2.y \(\chi_{24200}(4921, \cdot)\) n/a 3240 4
24200.2.z \(\chi_{24200}(4601, \cdot)\) n/a 2052 4
24200.2.ba \(\chi_{24200}(1721, \cdot)\) n/a 3240 4
24200.2.bb \(\chi_{24200}(81, \cdot)\) n/a 3240 4
24200.2.bc \(\chi_{24200}(4841, \cdot)\) n/a 3268 4
24200.2.bd \(\chi_{24200}(8721, \cdot)\) n/a 3240 4
24200.2.be \(\chi_{24200}(7341, \cdot)\) n/a 12896 4
24200.2.bi \(\chi_{24200}(3379, \cdot)\) n/a 12896 4
24200.2.bj \(\chi_{24200}(12369, \cdot)\) n/a 3240 4
24200.2.bn \(\chi_{24200}(3389, \cdot)\) n/a 13008 4
24200.2.bq \(\chi_{24200}(9411, \cdot)\) n/a 12896 4
24200.2.br \(\chi_{24200}(1691, \cdot)\) n/a 12896 4
24200.2.bs \(\chi_{24200}(1371, \cdot)\) n/a 12896 4
24200.2.bt \(\chi_{24200}(7251, \cdot)\) n/a 8112 4
24200.2.cc \(\chi_{24200}(3469, \cdot)\) n/a 12896 4
24200.2.cg \(\chi_{24200}(7269, \cdot)\) n/a 12896 4
24200.2.ch \(\chi_{24200}(3149, \cdot)\) n/a 7712 4
24200.2.ci \(\chi_{24200}(5109, \cdot)\) n/a 12896 4
24200.2.cs \(\chi_{24200}(6291, \cdot)\) n/a 12896 4
24200.2.cx \(\chi_{24200}(2419, \cdot)\) n/a 12896 4
24200.2.cy \(\chi_{24200}(969, \cdot)\) n/a 3272 4
24200.2.di \(\chi_{24200}(13821, \cdot)\) n/a 12896 4
24200.2.dj \(\chi_{24200}(2501, \cdot)\) n/a 8112 4
24200.2.dk \(\chi_{24200}(1461, \cdot)\) n/a 12896 4
24200.2.do \(\chi_{24200}(7021, \cdot)\) n/a 12896 4
24200.2.dx \(\chi_{24200}(9, \cdot)\) n/a 3240 4
24200.2.dy \(\chi_{24200}(2339, \cdot)\) n/a 12896 4
24200.2.dz \(\chi_{24200}(7179, \cdot)\) n/a 12896 4
24200.2.ea \(\chi_{24200}(699, \cdot)\) n/a 7712 4
24200.2.eb \(\chi_{24200}(5569, \cdot)\) n/a 3240 4
24200.2.ec \(\chi_{24200}(1049, \cdot)\) n/a 1944 4
24200.2.ed \(\chi_{24200}(5889, \cdot)\) n/a 3240 4
24200.2.ee \(\chi_{24200}(5539, \cdot)\) n/a 12896 4
24200.2.eh \(\chi_{24200}(2421, \cdot)\) n/a 13008 4
24200.2.el \(\chi_{24200}(15891, \cdot)\) n/a 12896 4
24200.2.ep \(\chi_{24200}(269, \cdot)\) n/a 12896 4
24200.2.eq \(\chi_{24200}(2201, \cdot)\) n/a 6270 10
24200.2.eu \(\chi_{24200}(6937, \cdot)\) n/a 6480 8
24200.2.ew \(\chi_{24200}(1613, \cdot)\) n/a 25792 8
24200.2.ey \(\chi_{24200}(4867, \cdot)\) n/a 25792 8
24200.2.ez \(\chi_{24200}(717, \cdot)\) n/a 25792 8
24200.2.fb \(\chi_{24200}(323, \cdot)\) n/a 25792 8
24200.2.fd \(\chi_{24200}(457, \cdot)\) n/a 3888 8
24200.2.fl \(\chi_{24200}(2177, \cdot)\) n/a 6480 8
24200.2.fm \(\chi_{24200}(3137, \cdot)\) n/a 6480 8
24200.2.fp \(\chi_{24200}(2097, \cdot)\) n/a 6480 8
24200.2.ft \(\chi_{24200}(2907, \cdot)\) n/a 15424 8
24200.2.fv \(\chi_{24200}(4597, \cdot)\) n/a 25792 8
24200.2.fw \(\chi_{24200}(2877, \cdot)\) n/a 25792 8
24200.2.fz \(\chi_{24200}(1933, \cdot)\) n/a 25792 8
24200.2.gb \(\chi_{24200}(1963, \cdot)\) n/a 25792 8
24200.2.gd \(\chi_{24200}(3147, \cdot)\) n/a 26016 8
24200.2.ge \(\chi_{24200}(3, \cdot)\) n/a 25792 8
24200.2.gh \(\chi_{24200}(5557, \cdot)\) n/a 15424 8
24200.2.gl \(\chi_{24200}(233, \cdot)\) n/a 6480 8
24200.2.gp \(\chi_{24200}(1101, \cdot)\) n/a 25020 10
24200.2.gt \(\chi_{24200}(1099, \cdot)\) n/a 23720 10
24200.2.gu \(\chi_{24200}(1849, \cdot)\) n/a 5940 10
24200.2.gv \(\chi_{24200}(3651, \cdot)\) n/a 25020 10
24200.2.gz \(\chi_{24200}(749, \cdot)\) n/a 23720 10
24200.2.he \(\chi_{24200}(593, \cdot)\) n/a 11880 20
24200.2.hg \(\chi_{24200}(1957, \cdot)\) n/a 47440 20
24200.2.hi \(\chi_{24200}(507, \cdot)\) n/a 47440 20
24200.2.hk \(\chi_{24200}(441, \cdot)\) n/a 39600 40
24200.2.hl \(\chi_{24200}(1241, \cdot)\) n/a 39600 40
24200.2.hm \(\chi_{24200}(641, \cdot)\) n/a 39600 40
24200.2.hn \(\chi_{24200}(201, \cdot)\) n/a 25080 40
24200.2.ho \(\chi_{24200}(361, \cdot)\) n/a 39600 40
24200.2.hp \(\chi_{24200}(1281, \cdot)\) n/a 39600 40
24200.2.hs \(\chi_{24200}(289, \cdot)\) n/a 39600 40
24200.2.ht \(\chi_{24200}(1179, \cdot)\) n/a 158240 40
24200.2.hx \(\chi_{24200}(181, \cdot)\) n/a 158240 40
24200.2.ia \(\chi_{24200}(131, \cdot)\) n/a 158240 40
24200.2.ik \(\chi_{24200}(69, \cdot)\) n/a 158240 40
24200.2.il \(\chi_{24200}(949, \cdot)\) n/a 94880 40
24200.2.im \(\chi_{24200}(389, \cdot)\) n/a 158240 40
24200.2.iq \(\chi_{24200}(1109, \cdot)\) n/a 158240 40
24200.2.iz \(\chi_{24200}(51, \cdot)\) n/a 100080 40
24200.2.ja \(\chi_{24200}(211, \cdot)\) n/a 158240 40
24200.2.jb \(\chi_{24200}(171, \cdot)\) n/a 158240 40
24200.2.jc \(\chi_{24200}(371, \cdot)\) n/a 158240 40
24200.2.jf \(\chi_{24200}(309, \cdot)\) n/a 158240 40
24200.2.ji \(\chi_{24200}(221, \cdot)\) n/a 158240 40
24200.2.jl \(\chi_{24200}(1019, \cdot)\) n/a 158240 40
24200.2.jm \(\chi_{24200}(929, \cdot)\) n/a 39600 40
24200.2.jn \(\chi_{24200}(49, \cdot)\) n/a 23760 40
24200.2.jo \(\chi_{24200}(889, \cdot)\) n/a 39600 40
24200.2.jp \(\chi_{24200}(299, \cdot)\) n/a 94880 40
24200.2.jq \(\chi_{24200}(19, \cdot)\) n/a 158240 40
24200.2.jr \(\chi_{24200}(139, \cdot)\) n/a 158240 40
24200.2.js \(\chi_{24200}(169, \cdot)\) n/a 39600 40
24200.2.kb \(\chi_{24200}(141, \cdot)\) n/a 158240 40
24200.2.kf \(\chi_{24200}(1621, \cdot)\) n/a 158240 40
24200.2.kg \(\chi_{24200}(301, \cdot)\) n/a 100080 40
24200.2.kh \(\chi_{24200}(581, \cdot)\) n/a 158240 40
24200.2.kr \(\chi_{24200}(89, \cdot)\) n/a 39600 40
24200.2.ks \(\chi_{24200}(219, \cdot)\) n/a 158240 40
24200.2.kv \(\chi_{24200}(229, \cdot)\) n/a 158240 40
24200.2.kz \(\chi_{24200}(491, \cdot)\) n/a 158240 40
24200.2.lc \(\chi_{24200}(467, \cdot)\) n/a 316480 80
24200.2.le \(\chi_{24200}(173, \cdot)\) n/a 316480 80
24200.2.lg \(\chi_{24200}(17, \cdot)\) n/a 79200 80
24200.2.ll \(\chi_{24200}(73, \cdot)\) n/a 79200 80
24200.2.lp \(\chi_{24200}(293, \cdot)\) n/a 189760 80
24200.2.ls \(\chi_{24200}(163, \cdot)\) n/a 316480 80
24200.2.lt \(\chi_{24200}(67, \cdot)\) n/a 316480 80
24200.2.lv \(\chi_{24200}(147, \cdot)\) n/a 316480 80
24200.2.lx \(\chi_{24200}(237, \cdot)\) n/a 316480 80
24200.2.ma \(\chi_{24200}(13, \cdot)\) n/a 316480 80
24200.2.mb \(\chi_{24200}(197, \cdot)\) n/a 316480 80
24200.2.md \(\chi_{24200}(443, \cdot)\) n/a 189760 80
24200.2.mh \(\chi_{24200}(217, \cdot)\) n/a 79200 80
24200.2.mk \(\chi_{24200}(937, \cdot)\) n/a 79200 80
24200.2.ml \(\chi_{24200}(153, \cdot)\) n/a 79200 80
24200.2.mt \(\chi_{24200}(57, \cdot)\) n/a 47520 80
24200.2.mv \(\chi_{24200}(203, \cdot)\) n/a 316480 80
24200.2.mx \(\chi_{24200}(437, \cdot)\) n/a 316480 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(24200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(24200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3025))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6050))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12100))\)\(^{\oplus 2}\)