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Properties

Label 7200.2
Level 7200
Weight 2
Dimension 565533
Nonzero newspaces 80
Sturm bound 5529600

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Defining parameters

Level: \( N \) = \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(5529600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7200))\).

Total New Old
Modular forms 1396736 569223 827513
Cusp forms 1368065 565533 802532
Eisenstein series 28671 3690 24981

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7200))\)

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
7200.2.a \(\chi_{7200}(1, \cdot)\) 7200.2.a.a 1 1
7200.2.a.b 1
7200.2.a.c 1
7200.2.a.d 1
7200.2.a.e 1
7200.2.a.f 1
7200.2.a.g 1
7200.2.a.h 1
7200.2.a.i 1
7200.2.a.j 1
7200.2.a.k 1
7200.2.a.l 1
7200.2.a.m 1
7200.2.a.n 1
7200.2.a.o 1
7200.2.a.p 1
7200.2.a.q 1
7200.2.a.r 1
7200.2.a.s 1
7200.2.a.t 1
7200.2.a.u 1
7200.2.a.v 1
7200.2.a.w 1
7200.2.a.x 1
7200.2.a.y 1
7200.2.a.z 1
7200.2.a.ba 1
7200.2.a.bb 1
7200.2.a.bc 1
7200.2.a.bd 1
7200.2.a.be 1
7200.2.a.bf 1
7200.2.a.bg 1
7200.2.a.bh 1
7200.2.a.bi 1
7200.2.a.bj 1
7200.2.a.bk 1
7200.2.a.bl 1
7200.2.a.bm 1
7200.2.a.bn 1
7200.2.a.bo 1
7200.2.a.bp 1
7200.2.a.bq 1
7200.2.a.br 1
7200.2.a.bs 1
7200.2.a.bt 1
7200.2.a.bu 1
7200.2.a.bv 1
7200.2.a.bw 1
7200.2.a.bx 1
7200.2.a.by 1
7200.2.a.bz 1
7200.2.a.ca 1
7200.2.a.cb 2
7200.2.a.cc 2
7200.2.a.cd 2
7200.2.a.ce 2
7200.2.a.cf 2
7200.2.a.cg 2
7200.2.a.ch 2
7200.2.a.ci 2
7200.2.a.cj 2
7200.2.a.ck 2
7200.2.a.cl 2
7200.2.a.cm 2
7200.2.a.cn 2
7200.2.a.co 2
7200.2.a.cp 2
7200.2.a.cq 2
7200.2.a.cr 2
7200.2.a.cs 4
7200.2.a.ct 4
7200.2.b \(\chi_{7200}(4751, \cdot)\) 7200.2.b.a 2 1
7200.2.b.b 2
7200.2.b.c 4
7200.2.b.d 6
7200.2.b.e 6
7200.2.b.f 8
7200.2.b.g 16
7200.2.b.h 16
7200.2.b.i 16
7200.2.d \(\chi_{7200}(2449, \cdot)\) 7200.2.d.a 2 1
7200.2.d.b 2
7200.2.d.c 2
7200.2.d.d 2
7200.2.d.e 2
7200.2.d.f 2
7200.2.d.g 2
7200.2.d.h 2
7200.2.d.i 2
7200.2.d.j 2
7200.2.d.k 4
7200.2.d.l 4
7200.2.d.m 4
7200.2.d.n 4
7200.2.d.o 4
7200.2.d.p 4
7200.2.d.q 6
7200.2.d.r 6
7200.2.d.s 8
7200.2.d.t 8
7200.2.d.u 16
7200.2.f \(\chi_{7200}(6049, \cdot)\) 7200.2.f.a 2 1
7200.2.f.b 2
7200.2.f.c 2
7200.2.f.d 2
7200.2.f.e 2
7200.2.f.f 2
7200.2.f.g 2
7200.2.f.h 2
7200.2.f.i 2
7200.2.f.j 2
7200.2.f.k 2
7200.2.f.l 2
7200.2.f.m 2
7200.2.f.n 2
7200.2.f.o 2
7200.2.f.p 2
7200.2.f.q 2
7200.2.f.r 2
7200.2.f.s 2
7200.2.f.t 2
7200.2.f.u 2
7200.2.f.v 2
7200.2.f.w 2
7200.2.f.x 2
7200.2.f.y 2
7200.2.f.z 2
7200.2.f.ba 2
7200.2.f.bb 2
7200.2.f.bc 2
7200.2.f.bd 4
7200.2.f.be 4
7200.2.f.bf 4
7200.2.f.bg 4
7200.2.f.bh 4
7200.2.f.bi 4
7200.2.f.bj 4
7200.2.f.bk 4
7200.2.h \(\chi_{7200}(1151, \cdot)\) 7200.2.h.a 4 1
7200.2.h.b 4
7200.2.h.c 4
7200.2.h.d 4
7200.2.h.e 4
7200.2.h.f 4
7200.2.h.g 4
7200.2.h.h 4
7200.2.h.i 4
7200.2.h.j 8
7200.2.h.k 8
7200.2.h.l 12
7200.2.h.m 12
7200.2.k \(\chi_{7200}(3601, \cdot)\) 7200.2.k.a 2 1
7200.2.k.b 2
7200.2.k.c 2
7200.2.k.d 2
7200.2.k.e 2
7200.2.k.f 2
7200.2.k.g 2
7200.2.k.h 2
7200.2.k.i 2
7200.2.k.j 4
7200.2.k.k 4
7200.2.k.l 4
7200.2.k.m 4
7200.2.k.n 4
7200.2.k.o 4
7200.2.k.p 6
7200.2.k.q 8
7200.2.k.r 8
7200.2.k.s 8
7200.2.k.t 8
7200.2.k.u 12
7200.2.m \(\chi_{7200}(3599, \cdot)\) 7200.2.m.a 4 1
7200.2.m.b 4
7200.2.m.c 8
7200.2.m.d 12
7200.2.m.e 12
7200.2.m.f 32
7200.2.o \(\chi_{7200}(7199, \cdot)\) 7200.2.o.a 4 1
7200.2.o.b 4
7200.2.o.c 4
7200.2.o.d 4
7200.2.o.e 4
7200.2.o.f 4
7200.2.o.g 4
7200.2.o.h 4
7200.2.o.i 4
7200.2.o.j 4
7200.2.o.k 4
7200.2.o.l 4
7200.2.o.m 4
7200.2.o.n 4
7200.2.o.o 8
7200.2.o.p 8
7200.2.q \(\chi_{7200}(2401, \cdot)\) n/a 456 2
7200.2.t \(\chi_{7200}(1801, \cdot)\) None 0 2
7200.2.u \(\chi_{7200}(1799, \cdot)\) None 0 2
7200.2.w \(\chi_{7200}(4193, \cdot)\) n/a 144 2
7200.2.x \(\chi_{7200}(2143, \cdot)\) n/a 180 2
7200.2.z \(\chi_{7200}(343, \cdot)\) None 0 2
7200.2.bc \(\chi_{7200}(3257, \cdot)\) None 0 2
7200.2.bd \(\chi_{7200}(1207, \cdot)\) None 0 2
7200.2.bg \(\chi_{7200}(2393, \cdot)\) None 0 2
7200.2.bi \(\chi_{7200}(5743, \cdot)\) n/a 176 2
7200.2.bj \(\chi_{7200}(593, \cdot)\) n/a 144 2
7200.2.bl \(\chi_{7200}(2951, \cdot)\) None 0 2
7200.2.bm \(\chi_{7200}(649, \cdot)\) None 0 2
7200.2.bp \(\chi_{7200}(1441, \cdot)\) n/a 600 4
7200.2.bs \(\chi_{7200}(2399, \cdot)\) n/a 432 2
7200.2.bu \(\chi_{7200}(1199, \cdot)\) n/a 424 2
7200.2.bw \(\chi_{7200}(1201, \cdot)\) n/a 444 2
7200.2.bx \(\chi_{7200}(3551, \cdot)\) n/a 456 2
7200.2.bz \(\chi_{7200}(1249, \cdot)\) n/a 432 2
7200.2.cb \(\chi_{7200}(49, \cdot)\) n/a 424 2
7200.2.cd \(\chi_{7200}(2351, \cdot)\) n/a 444 2
7200.2.cf \(\chi_{7200}(307, \cdot)\) n/a 1432 4
7200.2.ci \(\chi_{7200}(2357, \cdot)\) n/a 1152 4
7200.2.cj \(\chi_{7200}(899, \cdot)\) n/a 1152 4
7200.2.cm \(\chi_{7200}(901, \cdot)\) n/a 1508 4
7200.2.co \(\chi_{7200}(251, \cdot)\) n/a 1216 4
7200.2.cp \(\chi_{7200}(1549, \cdot)\) n/a 1432 4
7200.2.cs \(\chi_{7200}(557, \cdot)\) n/a 1152 4
7200.2.ct \(\chi_{7200}(2107, \cdot)\) n/a 1432 4
7200.2.cw \(\chi_{7200}(2591, \cdot)\) n/a 480 4
7200.2.cy \(\chi_{7200}(289, \cdot)\) n/a 600 4
7200.2.da \(\chi_{7200}(1009, \cdot)\) n/a 592 4
7200.2.dc \(\chi_{7200}(431, \cdot)\) n/a 480 4
7200.2.de \(\chi_{7200}(1439, \cdot)\) n/a 480 4
7200.2.dg \(\chi_{7200}(719, \cdot)\) n/a 480 4
7200.2.di \(\chi_{7200}(721, \cdot)\) n/a 592 4
7200.2.dk \(\chi_{7200}(1849, \cdot)\) None 0 4
7200.2.dl \(\chi_{7200}(551, \cdot)\) None 0 4
7200.2.do \(\chi_{7200}(943, \cdot)\) n/a 848 4
7200.2.dr \(\chi_{7200}(2993, \cdot)\) n/a 848 4
7200.2.ds \(\chi_{7200}(2057, \cdot)\) None 0 4
7200.2.dv \(\chi_{7200}(1543, \cdot)\) None 0 4
7200.2.dw \(\chi_{7200}(857, \cdot)\) None 0 4
7200.2.dz \(\chi_{7200}(7, \cdot)\) None 0 4
7200.2.ea \(\chi_{7200}(257, \cdot)\) n/a 864 4
7200.2.ed \(\chi_{7200}(607, \cdot)\) n/a 864 4
7200.2.eg \(\chi_{7200}(599, \cdot)\) None 0 4
7200.2.eh \(\chi_{7200}(601, \cdot)\) None 0 4
7200.2.ei \(\chi_{7200}(481, \cdot)\) n/a 2880 8
7200.2.ej \(\chi_{7200}(359, \cdot)\) None 0 8
7200.2.ek \(\chi_{7200}(361, \cdot)\) None 0 8
7200.2.eo \(\chi_{7200}(17, \cdot)\) n/a 960 8
7200.2.ep \(\chi_{7200}(847, \cdot)\) n/a 1184 8
7200.2.er \(\chi_{7200}(953, \cdot)\) None 0 8
7200.2.eu \(\chi_{7200}(1063, \cdot)\) None 0 8
7200.2.ev \(\chi_{7200}(233, \cdot)\) None 0 8
7200.2.ey \(\chi_{7200}(487, \cdot)\) None 0 8
7200.2.fa \(\chi_{7200}(127, \cdot)\) n/a 1200 8
7200.2.fb \(\chi_{7200}(737, \cdot)\) n/a 960 8
7200.2.ff \(\chi_{7200}(1369, \cdot)\) None 0 8
7200.2.fg \(\chi_{7200}(71, \cdot)\) None 0 8
7200.2.fi \(\chi_{7200}(643, \cdot)\) n/a 6880 8
7200.2.fj \(\chi_{7200}(293, \cdot)\) n/a 6880 8
7200.2.fl \(\chi_{7200}(301, \cdot)\) n/a 7248 8
7200.2.fo \(\chi_{7200}(299, \cdot)\) n/a 6880 8
7200.2.fq \(\chi_{7200}(349, \cdot)\) n/a 6880 8
7200.2.fr \(\chi_{7200}(851, \cdot)\) n/a 7248 8
7200.2.ft \(\chi_{7200}(893, \cdot)\) n/a 6880 8
7200.2.fw \(\chi_{7200}(43, \cdot)\) n/a 6880 8
7200.2.fx \(\chi_{7200}(241, \cdot)\) n/a 2848 8
7200.2.fz \(\chi_{7200}(239, \cdot)\) n/a 2848 8
7200.2.gb \(\chi_{7200}(479, \cdot)\) n/a 2880 8
7200.2.gf \(\chi_{7200}(911, \cdot)\) n/a 2848 8
7200.2.gh \(\chi_{7200}(529, \cdot)\) n/a 2848 8
7200.2.gj \(\chi_{7200}(769, \cdot)\) n/a 2880 8
7200.2.gl \(\chi_{7200}(191, \cdot)\) n/a 2880 8
7200.2.gm \(\chi_{7200}(197, \cdot)\) n/a 7680 16
7200.2.gp \(\chi_{7200}(523, \cdot)\) n/a 9568 16
7200.2.gr \(\chi_{7200}(109, \cdot)\) n/a 9568 16
7200.2.gs \(\chi_{7200}(611, \cdot)\) n/a 7680 16
7200.2.gu \(\chi_{7200}(181, \cdot)\) n/a 9568 16
7200.2.gx \(\chi_{7200}(179, \cdot)\) n/a 7680 16
7200.2.gz \(\chi_{7200}(163, \cdot)\) n/a 9568 16
7200.2.ha \(\chi_{7200}(53, \cdot)\) n/a 7680 16
7200.2.he \(\chi_{7200}(311, \cdot)\) None 0 16
7200.2.hf \(\chi_{7200}(169, \cdot)\) None 0 16
7200.2.hg \(\chi_{7200}(223, \cdot)\) n/a 5760 16
7200.2.hj \(\chi_{7200}(353, \cdot)\) n/a 5760 16
7200.2.hk \(\chi_{7200}(823, \cdot)\) None 0 16
7200.2.hn \(\chi_{7200}(713, \cdot)\) None 0 16
7200.2.ho \(\chi_{7200}(103, \cdot)\) None 0 16
7200.2.hr \(\chi_{7200}(137, \cdot)\) None 0 16
7200.2.hs \(\chi_{7200}(113, \cdot)\) n/a 5696 16
7200.2.hv \(\chi_{7200}(367, \cdot)\) n/a 5696 16
7200.2.hw \(\chi_{7200}(121, \cdot)\) None 0 16
7200.2.hx \(\chi_{7200}(119, \cdot)\) None 0 16
7200.2.ib \(\chi_{7200}(77, \cdot)\) n/a 45952 32
7200.2.ic \(\chi_{7200}(187, \cdot)\) n/a 45952 32
7200.2.if \(\chi_{7200}(11, \cdot)\) n/a 45952 32
7200.2.ig \(\chi_{7200}(229, \cdot)\) n/a 45952 32
7200.2.ii \(\chi_{7200}(59, \cdot)\) n/a 45952 32
7200.2.il \(\chi_{7200}(61, \cdot)\) n/a 45952 32
7200.2.im \(\chi_{7200}(67, \cdot)\) n/a 45952 32
7200.2.ip \(\chi_{7200}(173, \cdot)\) n/a 45952 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3600))\)\(^{\oplus 2}\)