# Properties

 Label 4950.2 Level 4950 Weight 2 Dimension 154979 Nonzero newspaces 84 Sturm bound 2592000

## Defining parameters

 Level: $$N$$ = $$4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$2592000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4950))$$.

Total New Old
Modular forms 656960 154979 501981
Cusp forms 639041 154979 484062
Eisenstein series 17919 0 17919

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4950))$$

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
4950.2.a $$\chi_{4950}(1, \cdot)$$ 4950.2.a.a 1 1
4950.2.a.b 1
4950.2.a.c 1
4950.2.a.d 1
4950.2.a.e 1
4950.2.a.f 1
4950.2.a.g 1
4950.2.a.h 1
4950.2.a.i 1
4950.2.a.j 1
4950.2.a.k 1
4950.2.a.l 1
4950.2.a.m 1
4950.2.a.n 1
4950.2.a.o 1
4950.2.a.p 1
4950.2.a.q 1
4950.2.a.r 1
4950.2.a.s 1
4950.2.a.t 1
4950.2.a.u 1
4950.2.a.v 1
4950.2.a.w 1
4950.2.a.x 1
4950.2.a.y 1
4950.2.a.z 1
4950.2.a.ba 1
4950.2.a.bb 1
4950.2.a.bc 1
4950.2.a.bd 1
4950.2.a.be 1
4950.2.a.bf 1
4950.2.a.bg 1
4950.2.a.bh 1
4950.2.a.bi 1
4950.2.a.bj 1
4950.2.a.bk 1
4950.2.a.bl 1
4950.2.a.bm 1
4950.2.a.bn 1
4950.2.a.bo 1
4950.2.a.bp 1
4950.2.a.bq 1
4950.2.a.br 1
4950.2.a.bs 1
4950.2.a.bt 1
4950.2.a.bu 1
4950.2.a.bv 2
4950.2.a.bw 2
4950.2.a.bx 2
4950.2.a.by 2
4950.2.a.bz 2
4950.2.a.ca 2
4950.2.a.cb 2
4950.2.a.cc 2
4950.2.a.cd 2
4950.2.a.ce 2
4950.2.a.cf 2
4950.2.a.cg 3
4950.2.a.ch 3
4950.2.a.ci 3
4950.2.a.cj 3
4950.2.c $$\chi_{4950}(199, \cdot)$$ 4950.2.c.a 2 1
4950.2.c.b 2
4950.2.c.c 2
4950.2.c.d 2
4950.2.c.e 2
4950.2.c.f 2
4950.2.c.g 2
4950.2.c.h 2
4950.2.c.i 2
4950.2.c.j 2
4950.2.c.k 2
4950.2.c.l 2
4950.2.c.m 2
4950.2.c.n 2
4950.2.c.o 2
4950.2.c.p 2
4950.2.c.q 2
4950.2.c.r 2
4950.2.c.s 2
4950.2.c.t 2
4950.2.c.u 2
4950.2.c.v 2
4950.2.c.w 2
4950.2.c.x 2
4950.2.c.y 2
4950.2.c.z 2
4950.2.c.ba 2
4950.2.c.bb 4
4950.2.c.bc 4
4950.2.c.bd 6
4950.2.c.be 6
4950.2.d $$\chi_{4950}(4751, \cdot)$$ 4950.2.d.a 2 1
4950.2.d.b 2
4950.2.d.c 2
4950.2.d.d 2
4950.2.d.e 2
4950.2.d.f 2
4950.2.d.g 8
4950.2.d.h 8
4950.2.d.i 8
4950.2.d.j 8
4950.2.d.k 8
4950.2.d.l 8
4950.2.d.m 8
4950.2.d.n 8
4950.2.f $$\chi_{4950}(4949, \cdot)$$ 4950.2.f.a 4 1
4950.2.f.b 4
4950.2.f.c 8
4950.2.f.d 8
4950.2.f.e 8
4950.2.f.f 8
4950.2.f.g 16
4950.2.f.h 16
4950.2.i $$\chi_{4950}(1651, \cdot)$$ n/a 380 2
4950.2.k $$\chi_{4950}(3257, \cdot)$$ n/a 120 2
4950.2.m $$\chi_{4950}(307, \cdot)$$ n/a 180 2
4950.2.n $$\chi_{4950}(361, \cdot)$$ n/a 600 4
4950.2.o $$\chi_{4950}(1351, \cdot)$$ n/a 380 4
4950.2.p $$\chi_{4950}(91, \cdot)$$ n/a 600 4
4950.2.q $$\chi_{4950}(631, \cdot)$$ n/a 600 4
4950.2.r $$\chi_{4950}(181, \cdot)$$ n/a 600 4
4950.2.s $$\chi_{4950}(991, \cdot)$$ n/a 496 4
4950.2.t $$\chi_{4950}(1649, \cdot)$$ n/a 432 2
4950.2.x $$\chi_{4950}(1849, \cdot)$$ n/a 360 2
4950.2.y $$\chi_{4950}(1451, \cdot)$$ n/a 456 2
4950.2.bb $$\chi_{4950}(791, \cdot)$$ n/a 480 4
4950.2.bc $$\chi_{4950}(1189, \cdot)$$ n/a 504 4
4950.2.bf $$\chi_{4950}(2609, \cdot)$$ n/a 480 4
4950.2.bj $$\chi_{4950}(1619, \cdot)$$ n/a 480 4
4950.2.bm $$\chi_{4950}(809, \cdot)$$ n/a 480 4
4950.2.bn $$\chi_{4950}(899, \cdot)$$ n/a 288 4
4950.2.bs $$\chi_{4950}(359, \cdot)$$ n/a 480 4
4950.2.bu $$\chi_{4950}(1421, \cdot)$$ n/a 480 4
4950.2.bv $$\chi_{4950}(289, \cdot)$$ n/a 600 4
4950.2.bx $$\chi_{4950}(559, \cdot)$$ n/a 600 4
4950.2.bz $$\chi_{4950}(161, \cdot)$$ n/a 480 4
4950.2.cc $$\chi_{4950}(701, \cdot)$$ n/a 304 4
4950.2.cd $$\chi_{4950}(2411, \cdot)$$ n/a 480 4
4950.2.cg $$\chi_{4950}(1549, \cdot)$$ n/a 360 4
4950.2.ch $$\chi_{4950}(829, \cdot)$$ n/a 600 4
4950.2.ck $$\chi_{4950}(379, \cdot)$$ n/a 600 4
4950.2.cm $$\chi_{4950}(611, \cdot)$$ n/a 480 4
4950.2.cp $$\chi_{4950}(989, \cdot)$$ n/a 480 4
4950.2.cq $$\chi_{4950}(1343, \cdot)$$ n/a 720 4
4950.2.cs $$\chi_{4950}(43, \cdot)$$ n/a 864 4
4950.2.cu $$\chi_{4950}(331, \cdot)$$ n/a 2400 8
4950.2.cv $$\chi_{4950}(1021, \cdot)$$ n/a 2880 8
4950.2.cw $$\chi_{4950}(301, \cdot)$$ n/a 1824 8
4950.2.cx $$\chi_{4950}(841, \cdot)$$ n/a 2880 8
4950.2.cy $$\chi_{4950}(31, \cdot)$$ n/a 2880 8
4950.2.cz $$\chi_{4950}(421, \cdot)$$ n/a 2880 8
4950.2.db $$\chi_{4950}(323, \cdot)$$ n/a 960 8
4950.2.dc $$\chi_{4950}(703, \cdot)$$ n/a 1200 8
4950.2.dd $$\chi_{4950}(127, \cdot)$$ n/a 1200 8
4950.2.de $$\chi_{4950}(1063, \cdot)$$ n/a 1200 8
4950.2.df $$\chi_{4950}(343, \cdot)$$ n/a 720 8
4950.2.dg $$\chi_{4950}(217, \cdot)$$ n/a 1200 8
4950.2.dm $$\chi_{4950}(287, \cdot)$$ n/a 800 8
4950.2.dn $$\chi_{4950}(1043, \cdot)$$ n/a 576 8
4950.2.do $$\chi_{4950}(53, \cdot)$$ n/a 960 8
4950.2.dp $$\chi_{4950}(917, \cdot)$$ n/a 960 8
4950.2.dq $$\chi_{4950}(863, \cdot)$$ n/a 960 8
4950.2.dx $$\chi_{4950}(73, \cdot)$$ n/a 1200 8
4950.2.ea $$\chi_{4950}(329, \cdot)$$ n/a 2880 8
4950.2.eb $$\chi_{4950}(169, \cdot)$$ n/a 2880 8
4950.2.ed $$\chi_{4950}(41, \cdot)$$ n/a 2880 8
4950.2.eg $$\chi_{4950}(761, \cdot)$$ n/a 2880 8
4950.2.eh $$\chi_{4950}(101, \cdot)$$ n/a 1824 8
4950.2.ek $$\chi_{4950}(619, \cdot)$$ n/a 2880 8
4950.2.el $$\chi_{4950}(49, \cdot)$$ n/a 1728 8
4950.2.eo $$\chi_{4950}(1219, \cdot)$$ n/a 2880 8
4950.2.eq $$\chi_{4950}(371, \cdot)$$ n/a 2880 8
4950.2.es $$\chi_{4950}(281, \cdot)$$ n/a 2880 8
4950.2.et $$\chi_{4950}(229, \cdot)$$ n/a 2880 8
4950.2.ex $$\chi_{4950}(239, \cdot)$$ n/a 2880 8
4950.2.ez $$\chi_{4950}(959, \cdot)$$ n/a 2880 8
4950.2.fd $$\chi_{4950}(479, \cdot)$$ n/a 2880 8
4950.2.fg $$\chi_{4950}(149, \cdot)$$ n/a 1728 8
4950.2.fh $$\chi_{4950}(29, \cdot)$$ n/a 2880 8
4950.2.fl $$\chi_{4950}(131, \cdot)$$ n/a 2880 8
4950.2.fm $$\chi_{4950}(529, \cdot)$$ n/a 2400 8
4950.2.fo $$\chi_{4950}(113, \cdot)$$ n/a 5760 16
4950.2.fv $$\chi_{4950}(277, \cdot)$$ n/a 5760 16
4950.2.fw $$\chi_{4950}(7, \cdot)$$ n/a 3456 16
4950.2.fx $$\chi_{4950}(337, \cdot)$$ n/a 5760 16
4950.2.fy $$\chi_{4950}(13, \cdot)$$ n/a 5760 16
4950.2.fz $$\chi_{4950}(373, \cdot)$$ n/a 5760 16
4950.2.gf $$\chi_{4950}(137, \cdot)$$ n/a 5760 16
4950.2.gg $$\chi_{4950}(47, \cdot)$$ n/a 5760 16
4950.2.gh $$\chi_{4950}(533, \cdot)$$ n/a 5760 16
4950.2.gi $$\chi_{4950}(257, \cdot)$$ n/a 3456 16
4950.2.gj $$\chi_{4950}(23, \cdot)$$ n/a 4800 16
4950.2.gk $$\chi_{4950}(853, \cdot)$$ n/a 5760 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4950))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4950)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(495))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(550))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(825))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(990))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1650))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2475))$$$$^{\oplus 2}$$