Properties

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

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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

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