# Properties

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

## 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

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