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Properties

Label 4320.2
Level 4320
Weight 2
Dimension 201792
Nonzero newspaces 60
Sturm bound 1990656

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Defining parameters

Level: \( N \) = \( 4320 = 2^{5} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1990656\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4320))\).

Total New Old
Modular forms 505344 203712 301632
Cusp forms 489985 201792 288193
Eisenstein series 15359 1920 13439

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4320))\)

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
4320.2.a \(\chi_{4320}(1, \cdot)\) 4320.2.a.a 1 1
4320.2.a.b 1
4320.2.a.c 1
4320.2.a.d 1
4320.2.a.e 1
4320.2.a.f 1
4320.2.a.g 1
4320.2.a.h 1
4320.2.a.i 1
4320.2.a.j 1
4320.2.a.k 1
4320.2.a.l 1
4320.2.a.m 2
4320.2.a.n 2
4320.2.a.o 2
4320.2.a.p 2
4320.2.a.q 2
4320.2.a.r 2
4320.2.a.s 2
4320.2.a.t 2
4320.2.a.u 2
4320.2.a.v 2
4320.2.a.w 2
4320.2.a.x 2
4320.2.a.y 2
4320.2.a.z 2
4320.2.a.ba 2
4320.2.a.bb 2
4320.2.a.bc 2
4320.2.a.bd 2
4320.2.a.be 2
4320.2.a.bf 2
4320.2.a.bg 3
4320.2.a.bh 3
4320.2.a.bi 3
4320.2.a.bj 3
4320.2.b \(\chi_{4320}(431, \cdot)\) 4320.2.b.a 16 1
4320.2.b.b 16
4320.2.b.c 16
4320.2.b.d 16
4320.2.d \(\chi_{4320}(3889, \cdot)\) 4320.2.d.a 4 1
4320.2.d.b 4
4320.2.d.c 4
4320.2.d.d 4
4320.2.d.e 4
4320.2.d.f 4
4320.2.d.g 16
4320.2.d.h 16
4320.2.d.i 20
4320.2.d.j 20
4320.2.f \(\chi_{4320}(1729, \cdot)\) 4320.2.f.a 2 1
4320.2.f.b 2
4320.2.f.c 2
4320.2.f.d 2
4320.2.f.e 8
4320.2.f.f 8
4320.2.f.g 8
4320.2.f.h 12
4320.2.f.i 12
4320.2.f.j 12
4320.2.f.k 12
4320.2.f.l 16
4320.2.h \(\chi_{4320}(2591, \cdot)\) 4320.2.h.a 16 1
4320.2.h.b 16
4320.2.h.c 16
4320.2.h.d 16
4320.2.k \(\chi_{4320}(2161, \cdot)\) 4320.2.k.a 12 1
4320.2.k.b 16
4320.2.k.c 16
4320.2.k.d 20
4320.2.m \(\chi_{4320}(2159, \cdot)\) 4320.2.m.a 8 1
4320.2.m.b 40
4320.2.m.c 48
4320.2.o \(\chi_{4320}(4319, \cdot)\) 4320.2.o.a 48 1
4320.2.o.b 48
4320.2.q \(\chi_{4320}(1441, \cdot)\) 4320.2.q.a 2 2
4320.2.q.b 2
4320.2.q.c 2
4320.2.q.d 2
4320.2.q.e 2
4320.2.q.f 2
4320.2.q.g 2
4320.2.q.h 2
4320.2.q.i 8
4320.2.q.j 8
4320.2.q.k 8
4320.2.q.l 8
4320.2.q.m 8
4320.2.q.n 8
4320.2.q.o 10
4320.2.q.p 10
4320.2.q.q 12
4320.2.t \(\chi_{4320}(1081, \cdot)\) None 0 2
4320.2.u \(\chi_{4320}(1079, \cdot)\) None 0 2
4320.2.w \(\chi_{4320}(2753, \cdot)\) n/a 192 2
4320.2.x \(\chi_{4320}(703, \cdot)\) n/a 192 2
4320.2.z \(\chi_{4320}(487, \cdot)\) None 0 2
4320.2.bc \(\chi_{4320}(377, \cdot)\) None 0 2
4320.2.bd \(\chi_{4320}(2647, \cdot)\) None 0 2
4320.2.bg \(\chi_{4320}(2537, \cdot)\) None 0 2
4320.2.bi \(\chi_{4320}(2863, \cdot)\) n/a 192 2
4320.2.bj \(\chi_{4320}(593, \cdot)\) n/a 192 2
4320.2.bl \(\chi_{4320}(1511, \cdot)\) None 0 2
4320.2.bm \(\chi_{4320}(649, \cdot)\) None 0 2
4320.2.br \(\chi_{4320}(1439, \cdot)\) n/a 144 2
4320.2.bt \(\chi_{4320}(719, \cdot)\) n/a 136 2
4320.2.bv \(\chi_{4320}(721, \cdot)\) 4320.2.bv.a 4 2
4320.2.bv.b 92
4320.2.bw \(\chi_{4320}(1151, \cdot)\) 4320.2.bw.a 48 2
4320.2.bw.b 48
4320.2.by \(\chi_{4320}(289, \cdot)\) n/a 144 2
4320.2.ca \(\chi_{4320}(1009, \cdot)\) n/a 136 2
4320.2.cc \(\chi_{4320}(1871, \cdot)\) 4320.2.cc.a 48 2
4320.2.cc.b 48
4320.2.ce \(\chi_{4320}(1027, \cdot)\) n/a 1536 4
4320.2.ch \(\chi_{4320}(917, \cdot)\) n/a 1536 4
4320.2.ci \(\chi_{4320}(539, \cdot)\) n/a 1536 4
4320.2.cl \(\chi_{4320}(541, \cdot)\) n/a 1024 4
4320.2.cn \(\chi_{4320}(971, \cdot)\) n/a 1024 4
4320.2.co \(\chi_{4320}(109, \cdot)\) n/a 1536 4
4320.2.cr \(\chi_{4320}(53, \cdot)\) n/a 1536 4
4320.2.cs \(\chi_{4320}(163, \cdot)\) n/a 1536 4
4320.2.cu \(\chi_{4320}(481, \cdot)\) n/a 864 6
4320.2.cv \(\chi_{4320}(1369, \cdot)\) None 0 4
4320.2.cw \(\chi_{4320}(71, \cdot)\) None 0 4
4320.2.cz \(\chi_{4320}(847, \cdot)\) n/a 272 4
4320.2.dc \(\chi_{4320}(17, \cdot)\) n/a 272 4
4320.2.dd \(\chi_{4320}(953, \cdot)\) None 0 4
4320.2.dg \(\chi_{4320}(1063, \cdot)\) None 0 4
4320.2.dh \(\chi_{4320}(233, \cdot)\) None 0 4
4320.2.dk \(\chi_{4320}(343, \cdot)\) None 0 4
4320.2.dl \(\chi_{4320}(737, \cdot)\) n/a 288 4
4320.2.do \(\chi_{4320}(127, \cdot)\) n/a 288 4
4320.2.dr \(\chi_{4320}(359, \cdot)\) None 0 4
4320.2.ds \(\chi_{4320}(361, \cdot)\) None 0 4
4320.2.dt \(\chi_{4320}(239, \cdot)\) n/a 1272 6
4320.2.dy \(\chi_{4320}(241, \cdot)\) n/a 864 6
4320.2.dz \(\chi_{4320}(479, \cdot)\) n/a 1296 6
4320.2.ec \(\chi_{4320}(769, \cdot)\) n/a 1296 6
4320.2.ed \(\chi_{4320}(911, \cdot)\) n/a 864 6
4320.2.ee \(\chi_{4320}(191, \cdot)\) n/a 864 6
4320.2.ef \(\chi_{4320}(49, \cdot)\) n/a 1272 6
4320.2.ej \(\chi_{4320}(667, \cdot)\) n/a 2272 8
4320.2.ek \(\chi_{4320}(557, \cdot)\) n/a 2272 8
4320.2.em \(\chi_{4320}(181, \cdot)\) n/a 1536 8
4320.2.ep \(\chi_{4320}(179, \cdot)\) n/a 2272 8
4320.2.er \(\chi_{4320}(469, \cdot)\) n/a 2272 8
4320.2.es \(\chi_{4320}(251, \cdot)\) n/a 1536 8
4320.2.eu \(\chi_{4320}(197, \cdot)\) n/a 2272 8
4320.2.ex \(\chi_{4320}(307, \cdot)\) n/a 2272 8
4320.2.fa \(\chi_{4320}(119, \cdot)\) None 0 12
4320.2.fb \(\chi_{4320}(121, \cdot)\) None 0 12
4320.2.fe \(\chi_{4320}(113, \cdot)\) n/a 2544 12
4320.2.ff \(\chi_{4320}(223, \cdot)\) n/a 2592 12
4320.2.fg \(\chi_{4320}(103, \cdot)\) None 0 12
4320.2.fi \(\chi_{4320}(137, \cdot)\) None 0 12
4320.2.fk \(\chi_{4320}(713, \cdot)\) None 0 12
4320.2.fm \(\chi_{4320}(7, \cdot)\) None 0 12
4320.2.fq \(\chi_{4320}(257, \cdot)\) n/a 2592 12
4320.2.fr \(\chi_{4320}(367, \cdot)\) n/a 2544 12
4320.2.fu \(\chi_{4320}(169, \cdot)\) None 0 12
4320.2.fv \(\chi_{4320}(311, \cdot)\) None 0 12
4320.2.fy \(\chi_{4320}(229, \cdot)\) n/a 20640 24
4320.2.fz \(\chi_{4320}(11, \cdot)\) n/a 13824 24
4320.2.ga \(\chi_{4320}(77, \cdot)\) n/a 20640 24
4320.2.gd \(\chi_{4320}(43, \cdot)\) n/a 20640 24
4320.2.ge \(\chi_{4320}(173, \cdot)\) n/a 20640 24
4320.2.gh \(\chi_{4320}(187, \cdot)\) n/a 20640 24
4320.2.gi \(\chi_{4320}(59, \cdot)\) n/a 20640 24
4320.2.gj \(\chi_{4320}(61, \cdot)\) n/a 13824 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2160))\)\(^{\oplus 2}\)