# Properties

 Label 4200.2 Level 4200 Weight 2 Dimension 170886 Nonzero newspaces 72 Sturm bound 1843200

## Defining parameters

 Level: $$N$$ = $$4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$1843200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4200))$$.

Total New Old
Modular forms 468864 172526 296338
Cusp forms 452737 170886 281851
Eisenstein series 16127 1640 14487

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4200))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
4200.2.a $$\chi_{4200}(1, \cdot)$$ 4200.2.a.a 1 1
4200.2.a.b 1
4200.2.a.c 1
4200.2.a.d 1
4200.2.a.e 1
4200.2.a.f 1
4200.2.a.g 1
4200.2.a.h 1
4200.2.a.i 1
4200.2.a.j 1
4200.2.a.k 1
4200.2.a.l 1
4200.2.a.m 1
4200.2.a.n 1
4200.2.a.o 1
4200.2.a.p 1
4200.2.a.q 1
4200.2.a.r 1
4200.2.a.s 1
4200.2.a.t 1
4200.2.a.u 1
4200.2.a.v 1
4200.2.a.w 1
4200.2.a.x 1
4200.2.a.y 1
4200.2.a.z 1
4200.2.a.ba 1
4200.2.a.bb 1
4200.2.a.bc 1
4200.2.a.bd 1
4200.2.a.be 1
4200.2.a.bf 1
4200.2.a.bg 2
4200.2.a.bh 2
4200.2.a.bi 2
4200.2.a.bj 2
4200.2.a.bk 2
4200.2.a.bl 2
4200.2.a.bm 2
4200.2.a.bn 3
4200.2.a.bo 3
4200.2.a.bp 3
4200.2.a.bq 3
4200.2.d $$\chi_{4200}(3751, \cdot)$$ None 0 1
4200.2.e $$\chi_{4200}(3851, \cdot)$$ n/a 456 1
4200.2.f $$\chi_{4200}(3401, \cdot)$$ n/a 152 1
4200.2.g $$\chi_{4200}(2101, \cdot)$$ n/a 228 1
4200.2.j $$\chi_{4200}(3949, \cdot)$$ n/a 216 1
4200.2.k $$\chi_{4200}(1049, \cdot)$$ n/a 144 1
4200.2.p $$\chi_{4200}(1499, \cdot)$$ n/a 432 1
4200.2.q $$\chi_{4200}(1399, \cdot)$$ None 0 1
4200.2.t $$\chi_{4200}(1849, \cdot)$$ 4200.2.t.a 2 1
4200.2.t.b 2
4200.2.t.c 2
4200.2.t.d 2
4200.2.t.e 2
4200.2.t.f 2
4200.2.t.g 2
4200.2.t.h 2
4200.2.t.i 2
4200.2.t.j 2
4200.2.t.k 2
4200.2.t.l 2
4200.2.t.m 2
4200.2.t.n 2
4200.2.t.o 2
4200.2.t.p 2
4200.2.t.q 2
4200.2.t.r 2
4200.2.t.s 2
4200.2.t.t 2
4200.2.t.u 4
4200.2.t.v 4
4200.2.t.w 4
4200.2.u $$\chi_{4200}(3149, \cdot)$$ n/a 568 1
4200.2.v $$\chi_{4200}(3599, \cdot)$$ None 0 1
4200.2.w $$\chi_{4200}(3499, \cdot)$$ n/a 288 1
4200.2.z $$\chi_{4200}(1651, \cdot)$$ n/a 304 1
4200.2.ba $$\chi_{4200}(1751, \cdot)$$ None 0 1
4200.2.bf $$\chi_{4200}(1301, \cdot)$$ n/a 596 1
4200.2.bg $$\chi_{4200}(1201, \cdot)$$ n/a 152 2
4200.2.bj $$\chi_{4200}(1357, \cdot)$$ n/a 576 2
4200.2.bk $$\chi_{4200}(1457, \cdot)$$ n/a 216 2
4200.2.bl $$\chi_{4200}(1807, \cdot)$$ None 0 2
4200.2.bm $$\chi_{4200}(3107, \cdot)$$ n/a 1136 2
4200.2.br $$\chi_{4200}(43, \cdot)$$ n/a 432 2
4200.2.bs $$\chi_{4200}(1007, \cdot)$$ None 0 2
4200.2.bt $$\chi_{4200}(3457, \cdot)$$ n/a 144 2
4200.2.bu $$\chi_{4200}(3557, \cdot)$$ n/a 864 2
4200.2.bx $$\chi_{4200}(841, \cdot)$$ n/a 352 4
4200.2.ca $$\chi_{4200}(1699, \cdot)$$ n/a 576 2
4200.2.cb $$\chi_{4200}(599, \cdot)$$ None 0 2
4200.2.cc $$\chi_{4200}(1349, \cdot)$$ n/a 1136 2
4200.2.cd $$\chi_{4200}(3049, \cdot)$$ n/a 144 2
4200.2.cg $$\chi_{4200}(101, \cdot)$$ n/a 1192 2
4200.2.cl $$\chi_{4200}(2951, \cdot)$$ None 0 2
4200.2.cm $$\chi_{4200}(451, \cdot)$$ n/a 608 2
4200.2.cp $$\chi_{4200}(3301, \cdot)$$ n/a 608 2
4200.2.cq $$\chi_{4200}(1601, \cdot)$$ n/a 304 2
4200.2.cr $$\chi_{4200}(851, \cdot)$$ n/a 1192 2
4200.2.cs $$\chi_{4200}(1951, \cdot)$$ None 0 2
4200.2.cv $$\chi_{4200}(199, \cdot)$$ None 0 2
4200.2.cw $$\chi_{4200}(2699, \cdot)$$ n/a 1136 2
4200.2.db $$\chi_{4200}(3449, \cdot)$$ n/a 288 2
4200.2.dc $$\chi_{4200}(949, \cdot)$$ n/a 576 2
4200.2.dd $$\chi_{4200}(461, \cdot)$$ n/a 3808 4
4200.2.di $$\chi_{4200}(71, \cdot)$$ None 0 4
4200.2.dj $$\chi_{4200}(811, \cdot)$$ n/a 1920 4
4200.2.dm $$\chi_{4200}(139, \cdot)$$ n/a 1920 4
4200.2.dn $$\chi_{4200}(239, \cdot)$$ None 0 4
4200.2.do $$\chi_{4200}(629, \cdot)$$ n/a 3808 4
4200.2.dp $$\chi_{4200}(169, \cdot)$$ n/a 368 4
4200.2.ds $$\chi_{4200}(559, \cdot)$$ None 0 4
4200.2.dt $$\chi_{4200}(659, \cdot)$$ n/a 2880 4
4200.2.dy $$\chi_{4200}(209, \cdot)$$ n/a 960 4
4200.2.dz $$\chi_{4200}(589, \cdot)$$ n/a 1440 4
4200.2.ec $$\chi_{4200}(421, \cdot)$$ n/a 1440 4
4200.2.ed $$\chi_{4200}(41, \cdot)$$ n/a 960 4
4200.2.ee $$\chi_{4200}(491, \cdot)$$ n/a 2880 4
4200.2.ef $$\chi_{4200}(391, \cdot)$$ None 0 4
4200.2.ei $$\chi_{4200}(557, \cdot)$$ n/a 2272 4
4200.2.ej $$\chi_{4200}(1657, \cdot)$$ n/a 288 4
4200.2.eo $$\chi_{4200}(143, \cdot)$$ None 0 4
4200.2.ep $$\chi_{4200}(907, \cdot)$$ n/a 1152 4
4200.2.eq $$\chi_{4200}(1307, \cdot)$$ n/a 2272 4
4200.2.er $$\chi_{4200}(3007, \cdot)$$ None 0 4
4200.2.ew $$\chi_{4200}(2657, \cdot)$$ n/a 576 4
4200.2.ex $$\chi_{4200}(157, \cdot)$$ n/a 1152 4
4200.2.ey $$\chi_{4200}(121, \cdot)$$ n/a 960 8
4200.2.fb $$\chi_{4200}(197, \cdot)$$ n/a 5760 8
4200.2.fc $$\chi_{4200}(97, \cdot)$$ n/a 960 8
4200.2.fd $$\chi_{4200}(167, \cdot)$$ None 0 8
4200.2.fe $$\chi_{4200}(547, \cdot)$$ n/a 2880 8
4200.2.fj $$\chi_{4200}(83, \cdot)$$ n/a 7616 8
4200.2.fk $$\chi_{4200}(127, \cdot)$$ None 0 8
4200.2.fl $$\chi_{4200}(113, \cdot)$$ n/a 1440 8
4200.2.fm $$\chi_{4200}(13, \cdot)$$ n/a 3840 8
4200.2.fp $$\chi_{4200}(109, \cdot)$$ n/a 3840 8
4200.2.fq $$\chi_{4200}(89, \cdot)$$ n/a 1920 8
4200.2.fv $$\chi_{4200}(179, \cdot)$$ n/a 7616 8
4200.2.fw $$\chi_{4200}(439, \cdot)$$ None 0 8
4200.2.fz $$\chi_{4200}(31, \cdot)$$ None 0 8
4200.2.ga $$\chi_{4200}(11, \cdot)$$ n/a 7616 8
4200.2.gb $$\chi_{4200}(521, \cdot)$$ n/a 1920 8
4200.2.gc $$\chi_{4200}(541, \cdot)$$ n/a 3840 8
4200.2.gf $$\chi_{4200}(691, \cdot)$$ n/a 3840 8
4200.2.gg $$\chi_{4200}(191, \cdot)$$ None 0 8
4200.2.gl $$\chi_{4200}(341, \cdot)$$ n/a 7616 8
4200.2.go $$\chi_{4200}(289, \cdot)$$ n/a 960 8
4200.2.gp $$\chi_{4200}(269, \cdot)$$ n/a 7616 8
4200.2.gq $$\chi_{4200}(359, \cdot)$$ None 0 8
4200.2.gr $$\chi_{4200}(19, \cdot)$$ n/a 3840 8
4200.2.gu $$\chi_{4200}(397, \cdot)$$ n/a 7680 16
4200.2.gv $$\chi_{4200}(137, \cdot)$$ n/a 3840 16
4200.2.ha $$\chi_{4200}(247, \cdot)$$ None 0 16
4200.2.hb $$\chi_{4200}(227, \cdot)$$ n/a 15232 16
4200.2.hc $$\chi_{4200}(67, \cdot)$$ n/a 7680 16
4200.2.hd $$\chi_{4200}(47, \cdot)$$ None 0 16
4200.2.hi $$\chi_{4200}(73, \cdot)$$ n/a 1920 16
4200.2.hj $$\chi_{4200}(53, \cdot)$$ n/a 15232 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4200))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4200)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(600))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(700))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(840))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1050))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1400))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2100))$$$$^{\oplus 2}$$