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Properties

Label 5760.2
Level 5760
Weight 2
Dimension 359856
Nonzero newspaces 72
Sturm bound 3538944

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Defining parameters

Level: \( N \) = \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(3538944\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5760))\).

Total New Old
Modular forms 894976 362448 532528
Cusp forms 874497 359856 514641
Eisenstein series 20479 2592 17887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5760))\)

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
5760.2.a \(\chi_{5760}(1, \cdot)\) 5760.2.a.a 1 1
5760.2.a.b 1
5760.2.a.c 1
5760.2.a.d 1
5760.2.a.e 1
5760.2.a.f 1
5760.2.a.g 1
5760.2.a.h 1
5760.2.a.i 1
5760.2.a.j 1
5760.2.a.k 1
5760.2.a.l 1
5760.2.a.m 1
5760.2.a.n 1
5760.2.a.o 1
5760.2.a.p 1
5760.2.a.q 1
5760.2.a.r 1
5760.2.a.s 1
5760.2.a.t 1
5760.2.a.u 1
5760.2.a.v 1
5760.2.a.w 1
5760.2.a.x 1
5760.2.a.y 1
5760.2.a.z 1
5760.2.a.ba 1
5760.2.a.bb 1
5760.2.a.bc 1
5760.2.a.bd 1
5760.2.a.be 1
5760.2.a.bf 1
5760.2.a.bg 1
5760.2.a.bh 1
5760.2.a.bi 1
5760.2.a.bj 1
5760.2.a.bk 1
5760.2.a.bl 1
5760.2.a.bm 1
5760.2.a.bn 1
5760.2.a.bo 1
5760.2.a.bp 1
5760.2.a.bq 1
5760.2.a.br 1
5760.2.a.bs 1
5760.2.a.bt 1
5760.2.a.bu 1
5760.2.a.bv 1
5760.2.a.bw 2
5760.2.a.bx 2
5760.2.a.by 2
5760.2.a.bz 2
5760.2.a.ca 2
5760.2.a.cb 2
5760.2.a.cc 2
5760.2.a.cd 2
5760.2.a.ce 2
5760.2.a.cf 2
5760.2.a.cg 2
5760.2.a.ch 2
5760.2.a.ci 2
5760.2.a.cj 2
5760.2.a.ck 2
5760.2.a.cl 2
5760.2.b \(\chi_{5760}(4031, \cdot)\) 5760.2.b.a 2 1
5760.2.b.b 2
5760.2.b.c 2
5760.2.b.d 2
5760.2.b.e 2
5760.2.b.f 2
5760.2.b.g 2
5760.2.b.h 2
5760.2.b.i 8
5760.2.b.j 8
5760.2.b.k 8
5760.2.b.l 8
5760.2.b.m 8
5760.2.b.n 8
5760.2.d \(\chi_{5760}(1729, \cdot)\) n/a 120 1
5760.2.f \(\chi_{5760}(4609, \cdot)\) n/a 120 1
5760.2.h \(\chi_{5760}(1151, \cdot)\) 5760.2.h.a 8 1
5760.2.h.b 8
5760.2.h.c 8
5760.2.h.d 8
5760.2.h.e 8
5760.2.h.f 8
5760.2.h.g 8
5760.2.h.h 8
5760.2.k \(\chi_{5760}(2881, \cdot)\) 5760.2.k.a 2 1
5760.2.k.b 2
5760.2.k.c 2
5760.2.k.d 2
5760.2.k.e 2
5760.2.k.f 2
5760.2.k.g 2
5760.2.k.h 2
5760.2.k.i 2
5760.2.k.j 2
5760.2.k.k 2
5760.2.k.l 2
5760.2.k.m 4
5760.2.k.n 4
5760.2.k.o 4
5760.2.k.p 4
5760.2.k.q 4
5760.2.k.r 4
5760.2.k.s 4
5760.2.k.t 4
5760.2.k.u 4
5760.2.k.v 4
5760.2.k.w 4
5760.2.k.x 4
5760.2.k.y 8
5760.2.m \(\chi_{5760}(2879, \cdot)\) 5760.2.m.a 4 1
5760.2.m.b 4
5760.2.m.c 4
5760.2.m.d 4
5760.2.m.e 4
5760.2.m.f 4
5760.2.m.g 4
5760.2.m.h 4
5760.2.m.i 4
5760.2.m.j 4
5760.2.m.k 4
5760.2.m.l 4
5760.2.m.m 4
5760.2.m.n 4
5760.2.m.o 4
5760.2.m.p 4
5760.2.m.q 4
5760.2.m.r 4
5760.2.m.s 4
5760.2.m.t 4
5760.2.m.u 8
5760.2.m.v 8
5760.2.o \(\chi_{5760}(5759, \cdot)\) 5760.2.o.a 24 1
5760.2.o.b 24
5760.2.o.c 24
5760.2.o.d 24
5760.2.q \(\chi_{5760}(1921, \cdot)\) n/a 384 2
5760.2.t \(\chi_{5760}(1441, \cdot)\) n/a 160 2
5760.2.u \(\chi_{5760}(1439, \cdot)\) n/a 192 2
5760.2.w \(\chi_{5760}(2177, \cdot)\) n/a 192 2
5760.2.x \(\chi_{5760}(127, \cdot)\) n/a 240 2
5760.2.z \(\chi_{5760}(1567, \cdot)\) n/a 232 2
5760.2.bc \(\chi_{5760}(737, \cdot)\) n/a 192 2
5760.2.bd \(\chi_{5760}(4447, \cdot)\) n/a 232 2
5760.2.bg \(\chi_{5760}(3617, \cdot)\) n/a 192 2
5760.2.bi \(\chi_{5760}(703, \cdot)\) n/a 240 2
5760.2.bj \(\chi_{5760}(2753, \cdot)\) n/a 192 2
5760.2.bl \(\chi_{5760}(2591, \cdot)\) n/a 128 2
5760.2.bm \(\chi_{5760}(289, \cdot)\) n/a 232 2
5760.2.br \(\chi_{5760}(1919, \cdot)\) n/a 576 2
5760.2.bt \(\chi_{5760}(959, \cdot)\) n/a 576 2
5760.2.bv \(\chi_{5760}(961, \cdot)\) n/a 384 2
5760.2.bw \(\chi_{5760}(3071, \cdot)\) n/a 384 2
5760.2.by \(\chi_{5760}(769, \cdot)\) n/a 576 2
5760.2.ca \(\chi_{5760}(3649, \cdot)\) n/a 576 2
5760.2.cc \(\chi_{5760}(191, \cdot)\) n/a 384 2
5760.2.ce \(\chi_{5760}(1423, \cdot)\) n/a 472 4
5760.2.ch \(\chi_{5760}(593, \cdot)\) n/a 384 4
5760.2.ci \(\chi_{5760}(719, \cdot)\) n/a 384 4
5760.2.cl \(\chi_{5760}(721, \cdot)\) n/a 320 4
5760.2.cn \(\chi_{5760}(431, \cdot)\) n/a 256 4
5760.2.co \(\chi_{5760}(1009, \cdot)\) n/a 472 4
5760.2.cr \(\chi_{5760}(17, \cdot)\) n/a 384 4
5760.2.cs \(\chi_{5760}(847, \cdot)\) n/a 472 4
5760.2.cu \(\chi_{5760}(1249, \cdot)\) n/a 1120 4
5760.2.cv \(\chi_{5760}(671, \cdot)\) n/a 768 4
5760.2.cy \(\chi_{5760}(1087, \cdot)\) n/a 1152 4
5760.2.db \(\chi_{5760}(833, \cdot)\) n/a 1152 4
5760.2.dc \(\chi_{5760}(353, \cdot)\) n/a 1120 4
5760.2.df \(\chi_{5760}(607, \cdot)\) n/a 1120 4
5760.2.dg \(\chi_{5760}(2657, \cdot)\) n/a 1120 4
5760.2.dj \(\chi_{5760}(223, \cdot)\) n/a 1120 4
5760.2.dk \(\chi_{5760}(257, \cdot)\) n/a 1152 4
5760.2.dn \(\chi_{5760}(1663, \cdot)\) n/a 1152 4
5760.2.dq \(\chi_{5760}(479, \cdot)\) n/a 1120 4
5760.2.dr \(\chi_{5760}(481, \cdot)\) n/a 768 4
5760.2.dt \(\chi_{5760}(233, \cdot)\) None 0 8
5760.2.du \(\chi_{5760}(1063, \cdot)\) None 0 8
5760.2.dw \(\chi_{5760}(361, \cdot)\) None 0 8
5760.2.dy \(\chi_{5760}(649, \cdot)\) None 0 8
5760.2.eb \(\chi_{5760}(71, \cdot)\) None 0 8
5760.2.ed \(\chi_{5760}(359, \cdot)\) None 0 8
5760.2.ef \(\chi_{5760}(953, \cdot)\) None 0 8
5760.2.eg \(\chi_{5760}(343, \cdot)\) None 0 8
5760.2.ej \(\chi_{5760}(943, \cdot)\) n/a 2272 8
5760.2.ek \(\chi_{5760}(113, \cdot)\) n/a 2272 8
5760.2.em \(\chi_{5760}(241, \cdot)\) n/a 1536 8
5760.2.ep \(\chi_{5760}(239, \cdot)\) n/a 2272 8
5760.2.er \(\chi_{5760}(49, \cdot)\) n/a 2272 8
5760.2.es \(\chi_{5760}(911, \cdot)\) n/a 1536 8
5760.2.eu \(\chi_{5760}(497, \cdot)\) n/a 2272 8
5760.2.ex \(\chi_{5760}(367, \cdot)\) n/a 2272 8
5760.2.fa \(\chi_{5760}(197, \cdot)\) n/a 6144 16
5760.2.fb \(\chi_{5760}(163, \cdot)\) n/a 7648 16
5760.2.fc \(\chi_{5760}(251, \cdot)\) n/a 4096 16
5760.2.fd \(\chi_{5760}(109, \cdot)\) n/a 7648 16
5760.2.fg \(\chi_{5760}(181, \cdot)\) n/a 5120 16
5760.2.fh \(\chi_{5760}(179, \cdot)\) n/a 6144 16
5760.2.fm \(\chi_{5760}(307, \cdot)\) n/a 7648 16
5760.2.fn \(\chi_{5760}(53, \cdot)\) n/a 6144 16
5760.2.fo \(\chi_{5760}(103, \cdot)\) None 0 16
5760.2.fr \(\chi_{5760}(713, \cdot)\) None 0 16
5760.2.ft \(\chi_{5760}(119, \cdot)\) None 0 16
5760.2.fv \(\chi_{5760}(311, \cdot)\) None 0 16
5760.2.fw \(\chi_{5760}(169, \cdot)\) None 0 16
5760.2.fy \(\chi_{5760}(121, \cdot)\) None 0 16
5760.2.ga \(\chi_{5760}(7, \cdot)\) None 0 16
5760.2.gd \(\chi_{5760}(137, \cdot)\) None 0 16
5760.2.ge \(\chi_{5760}(77, \cdot)\) n/a 36736 32
5760.2.gf \(\chi_{5760}(43, \cdot)\) n/a 36736 32
5760.2.gk \(\chi_{5760}(229, \cdot)\) n/a 36736 32
5760.2.gl \(\chi_{5760}(11, \cdot)\) n/a 24576 32
5760.2.go \(\chi_{5760}(59, \cdot)\) n/a 36736 32
5760.2.gp \(\chi_{5760}(61, \cdot)\) n/a 24576 32
5760.2.gq \(\chi_{5760}(187, \cdot)\) n/a 36736 32
5760.2.gr \(\chi_{5760}(173, \cdot)\) n/a 36736 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2880))\)\(^{\oplus 2}\)