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Properties

Label 4800.2
Level 4800
Weight 2
Dimension 237994
Nonzero newspaces 56
Sturm bound 2457600

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Defining parameters

Level: \( N \) = \( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(2457600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4800))\).

Total New Old
Modular forms 622464 239798 382666
Cusp forms 606337 237994 368343
Eisenstein series 16127 1804 14323

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4800))\)

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
4800.2.a \(\chi_{4800}(1, \cdot)\) 4800.2.a.a 1 1
4800.2.a.b 1
4800.2.a.c 1
4800.2.a.d 1
4800.2.a.e 1
4800.2.a.f 1
4800.2.a.g 1
4800.2.a.h 1
4800.2.a.i 1
4800.2.a.j 1
4800.2.a.k 1
4800.2.a.l 1
4800.2.a.m 1
4800.2.a.n 1
4800.2.a.o 1
4800.2.a.p 1
4800.2.a.q 1
4800.2.a.r 1
4800.2.a.s 1
4800.2.a.t 1
4800.2.a.u 1
4800.2.a.v 1
4800.2.a.w 1
4800.2.a.x 1
4800.2.a.y 1
4800.2.a.z 1
4800.2.a.ba 1
4800.2.a.bb 1
4800.2.a.bc 1
4800.2.a.bd 1
4800.2.a.be 1
4800.2.a.bf 1
4800.2.a.bg 1
4800.2.a.bh 1
4800.2.a.bi 1
4800.2.a.bj 1
4800.2.a.bk 1
4800.2.a.bl 1
4800.2.a.bm 1
4800.2.a.bn 1
4800.2.a.bo 1
4800.2.a.bp 1
4800.2.a.bq 1
4800.2.a.br 1
4800.2.a.bs 1
4800.2.a.bt 1
4800.2.a.bu 1
4800.2.a.bv 1
4800.2.a.bw 1
4800.2.a.bx 1
4800.2.a.by 1
4800.2.a.bz 1
4800.2.a.ca 1
4800.2.a.cb 1
4800.2.a.cc 1
4800.2.a.cd 1
4800.2.a.ce 1
4800.2.a.cf 1
4800.2.a.cg 1
4800.2.a.ch 1
4800.2.a.ci 1
4800.2.a.cj 1
4800.2.a.ck 1
4800.2.a.cl 1
4800.2.a.cm 1
4800.2.a.cn 1
4800.2.a.co 1
4800.2.a.cp 1
4800.2.a.cq 1
4800.2.a.cr 1
4800.2.a.cs 1
4800.2.a.ct 1
4800.2.a.cu 2
4800.2.a.cv 2
4800.2.b \(\chi_{4800}(3551, \cdot)\) n/a 152 1
4800.2.d \(\chi_{4800}(1249, \cdot)\) 4800.2.d.a 2 1
4800.2.d.b 2
4800.2.d.c 2
4800.2.d.d 2
4800.2.d.e 2
4800.2.d.f 2
4800.2.d.g 2
4800.2.d.h 2
4800.2.d.i 4
4800.2.d.j 4
4800.2.d.k 4
4800.2.d.l 4
4800.2.d.m 4
4800.2.d.n 4
4800.2.d.o 4
4800.2.d.p 4
4800.2.d.q 4
4800.2.d.r 4
4800.2.d.s 8
4800.2.d.t 8
4800.2.f \(\chi_{4800}(3649, \cdot)\) 4800.2.f.a 2 1
4800.2.f.b 2
4800.2.f.c 2
4800.2.f.d 2
4800.2.f.e 2
4800.2.f.f 2
4800.2.f.g 2
4800.2.f.h 2
4800.2.f.i 2
4800.2.f.j 2
4800.2.f.k 2
4800.2.f.l 2
4800.2.f.m 2
4800.2.f.n 2
4800.2.f.o 2
4800.2.f.p 2
4800.2.f.q 2
4800.2.f.r 2
4800.2.f.s 2
4800.2.f.t 2
4800.2.f.u 2
4800.2.f.v 2
4800.2.f.w 2
4800.2.f.x 2
4800.2.f.y 2
4800.2.f.z 2
4800.2.f.ba 2
4800.2.f.bb 2
4800.2.f.bc 2
4800.2.f.bd 2
4800.2.f.be 2
4800.2.f.bf 2
4800.2.f.bg 2
4800.2.f.bh 2
4800.2.f.bi 2
4800.2.f.bj 2
4800.2.h \(\chi_{4800}(1151, \cdot)\) n/a 146 1
4800.2.k \(\chi_{4800}(2401, \cdot)\) 4800.2.k.a 2 1
4800.2.k.b 2
4800.2.k.c 2
4800.2.k.d 2
4800.2.k.e 2
4800.2.k.f 2
4800.2.k.g 2
4800.2.k.h 2
4800.2.k.i 4
4800.2.k.j 4
4800.2.k.k 4
4800.2.k.l 4
4800.2.k.m 4
4800.2.k.n 4
4800.2.k.o 4
4800.2.k.p 8
4800.2.k.q 8
4800.2.k.r 8
4800.2.k.s 8
4800.2.m \(\chi_{4800}(2399, \cdot)\) n/a 144 1
4800.2.o \(\chi_{4800}(4799, \cdot)\) n/a 140 1
4800.2.s \(\chi_{4800}(1201, \cdot)\) n/a 152 2
4800.2.t \(\chi_{4800}(1199, \cdot)\) n/a 280 2
4800.2.v \(\chi_{4800}(257, \cdot)\) n/a 280 2
4800.2.w \(\chi_{4800}(3007, \cdot)\) n/a 144 2
4800.2.y \(\chi_{4800}(943, \cdot)\) n/a 144 2
4800.2.bb \(\chi_{4800}(593, \cdot)\) n/a 280 2
4800.2.bc \(\chi_{4800}(3343, \cdot)\) n/a 144 2
4800.2.bf \(\chi_{4800}(2993, \cdot)\) n/a 280 2
4800.2.bh \(\chi_{4800}(607, \cdot)\) n/a 144 2
4800.2.bi \(\chi_{4800}(2657, \cdot)\) n/a 288 2
4800.2.bk \(\chi_{4800}(2351, \cdot)\) n/a 292 2
4800.2.bl \(\chi_{4800}(49, \cdot)\) n/a 144 2
4800.2.bo \(\chi_{4800}(961, \cdot)\) n/a 480 4
4800.2.bp \(\chi_{4800}(1207, \cdot)\) None 0 4
4800.2.bs \(\chi_{4800}(857, \cdot)\) None 0 4
4800.2.bt \(\chi_{4800}(599, \cdot)\) None 0 4
4800.2.bw \(\chi_{4800}(601, \cdot)\) None 0 4
4800.2.by \(\chi_{4800}(551, \cdot)\) None 0 4
4800.2.bz \(\chi_{4800}(649, \cdot)\) None 0 4
4800.2.cc \(\chi_{4800}(2057, \cdot)\) None 0 4
4800.2.cd \(\chi_{4800}(7, \cdot)\) None 0 4
4800.2.cg \(\chi_{4800}(191, \cdot)\) n/a 944 4
4800.2.ci \(\chi_{4800}(769, \cdot)\) n/a 480 4
4800.2.ck \(\chi_{4800}(289, \cdot)\) n/a 480 4
4800.2.cm \(\chi_{4800}(671, \cdot)\) n/a 960 4
4800.2.co \(\chi_{4800}(959, \cdot)\) n/a 944 4
4800.2.cq \(\chi_{4800}(479, \cdot)\) n/a 960 4
4800.2.cs \(\chi_{4800}(481, \cdot)\) n/a 480 4
4800.2.cv \(\chi_{4800}(893, \cdot)\) n/a 4576 8
4800.2.cw \(\chi_{4800}(43, \cdot)\) n/a 2304 8
4800.2.cy \(\chi_{4800}(301, \cdot)\) n/a 2432 8
4800.2.da \(\chi_{4800}(349, \cdot)\) n/a 2304 8
4800.2.dd \(\chi_{4800}(251, \cdot)\) n/a 4816 8
4800.2.df \(\chi_{4800}(299, \cdot)\) n/a 4576 8
4800.2.dh \(\chi_{4800}(293, \cdot)\) n/a 4576 8
4800.2.di \(\chi_{4800}(643, \cdot)\) n/a 2304 8
4800.2.dk \(\chi_{4800}(239, \cdot)\) n/a 1888 8
4800.2.dl \(\chi_{4800}(241, \cdot)\) n/a 960 8
4800.2.dp \(\chi_{4800}(353, \cdot)\) n/a 1920 8
4800.2.dq \(\chi_{4800}(223, \cdot)\) n/a 960 8
4800.2.ds \(\chi_{4800}(17, \cdot)\) n/a 1888 8
4800.2.dv \(\chi_{4800}(367, \cdot)\) n/a 960 8
4800.2.dw \(\chi_{4800}(497, \cdot)\) n/a 1888 8
4800.2.dz \(\chi_{4800}(847, \cdot)\) n/a 960 8
4800.2.eb \(\chi_{4800}(127, \cdot)\) n/a 960 8
4800.2.ec \(\chi_{4800}(833, \cdot)\) n/a 1888 8
4800.2.eg \(\chi_{4800}(529, \cdot)\) n/a 960 8
4800.2.eh \(\chi_{4800}(431, \cdot)\) n/a 1888 8
4800.2.ei \(\chi_{4800}(233, \cdot)\) None 0 16
4800.2.el \(\chi_{4800}(103, \cdot)\) None 0 16
4800.2.en \(\chi_{4800}(169, \cdot)\) None 0 16
4800.2.eo \(\chi_{4800}(71, \cdot)\) None 0 16
4800.2.eq \(\chi_{4800}(121, \cdot)\) None 0 16
4800.2.et \(\chi_{4800}(119, \cdot)\) None 0 16
4800.2.ev \(\chi_{4800}(487, \cdot)\) None 0 16
4800.2.ew \(\chi_{4800}(137, \cdot)\) None 0 16
4800.2.ez \(\chi_{4800}(163, \cdot)\) n/a 15360 32
4800.2.fa \(\chi_{4800}(53, \cdot)\) n/a 30592 32
4800.2.fc \(\chi_{4800}(59, \cdot)\) n/a 30592 32
4800.2.fe \(\chi_{4800}(11, \cdot)\) n/a 30592 32
4800.2.fh \(\chi_{4800}(109, \cdot)\) n/a 15360 32
4800.2.fj \(\chi_{4800}(61, \cdot)\) n/a 15360 32
4800.2.fl \(\chi_{4800}(67, \cdot)\) n/a 15360 32
4800.2.fm \(\chi_{4800}(173, \cdot)\) n/a 30592 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 2}\)