Properties

Label 9920.2
Level 9920
Weight 2
Dimension 1513644
Nonzero newspaces 112
Sturm bound 11796480

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Defining parameters

Level: \( N \) = \( 9920 = 2^{6} \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(11796480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9920))\).

Total New Old
Modular forms 2966400 1521300 1445100
Cusp forms 2931841 1513644 1418197
Eisenstein series 34559 7656 26903

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9920))\)

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
9920.2.a \(\chi_{9920}(1, \cdot)\) 9920.2.a.a 1 1
9920.2.a.b 1
9920.2.a.c 1
9920.2.a.d 1
9920.2.a.e 1
9920.2.a.f 1
9920.2.a.g 1
9920.2.a.h 1
9920.2.a.i 1
9920.2.a.j 1
9920.2.a.k 1
9920.2.a.l 1
9920.2.a.m 1
9920.2.a.n 1
9920.2.a.o 1
9920.2.a.p 1
9920.2.a.q 1
9920.2.a.r 1
9920.2.a.s 1
9920.2.a.t 1
9920.2.a.u 1
9920.2.a.v 1
9920.2.a.w 1
9920.2.a.x 1
9920.2.a.y 1
9920.2.a.z 1
9920.2.a.ba 1
9920.2.a.bb 1
9920.2.a.bc 1
9920.2.a.bd 1
9920.2.a.be 1
9920.2.a.bf 1
9920.2.a.bg 1
9920.2.a.bh 1
9920.2.a.bi 1
9920.2.a.bj 1
9920.2.a.bk 2
9920.2.a.bl 2
9920.2.a.bm 2
9920.2.a.bn 2
9920.2.a.bo 2
9920.2.a.bp 2
9920.2.a.bq 2
9920.2.a.br 2
9920.2.a.bs 2
9920.2.a.bt 2
9920.2.a.bu 3
9920.2.a.bv 3
9920.2.a.bw 3
9920.2.a.bx 3
9920.2.a.by 3
9920.2.a.bz 3
9920.2.a.ca 4
9920.2.a.cb 4
9920.2.a.cc 4
9920.2.a.cd 4
9920.2.a.ce 4
9920.2.a.cf 4
9920.2.a.cg 4
9920.2.a.ch 4
9920.2.a.ci 4
9920.2.a.cj 4
9920.2.a.ck 6
9920.2.a.cl 6
9920.2.a.cm 6
9920.2.a.cn 6
9920.2.a.co 6
9920.2.a.cp 6
9920.2.a.cq 6
9920.2.a.cr 6
9920.2.a.cs 6
9920.2.a.ct 6
9920.2.a.cu 8
9920.2.a.cv 8
9920.2.a.cw 8
9920.2.a.cx 8
9920.2.a.cy 8
9920.2.a.cz 8
9920.2.a.da 9
9920.2.a.db 9
9920.2.b \(\chi_{9920}(991, \cdot)\) n/a 256 1
9920.2.d \(\chi_{9920}(3969, \cdot)\) n/a 360 1
9920.2.g \(\chi_{9920}(4961, \cdot)\) n/a 240 1
9920.2.i \(\chi_{9920}(9919, \cdot)\) n/a 380 1
9920.2.j \(\chi_{9920}(8929, \cdot)\) n/a 360 1
9920.2.l \(\chi_{9920}(5951, \cdot)\) n/a 256 1
9920.2.o \(\chi_{9920}(4959, \cdot)\) n/a 384 1
9920.2.q \(\chi_{9920}(6081, \cdot)\) n/a 512 2
9920.2.r \(\chi_{9920}(433, \cdot)\) n/a 760 2
9920.2.u \(\chi_{9920}(4527, \cdot)\) n/a 720 2
9920.2.x \(\chi_{9920}(2481, \cdot)\) n/a 480 2
9920.2.y \(\chi_{9920}(2479, \cdot)\) n/a 760 2
9920.2.z \(\chi_{9920}(7873, \cdot)\) n/a 760 2
9920.2.bc \(\chi_{9920}(63, \cdot)\) n/a 720 2
9920.2.bd \(\chi_{9920}(5023, \cdot)\) n/a 720 2
9920.2.bg \(\chi_{9920}(2913, \cdot)\) n/a 768 2
9920.2.bh \(\chi_{9920}(3471, \cdot)\) n/a 512 2
9920.2.bi \(\chi_{9920}(1489, \cdot)\) n/a 720 2
9920.2.bl \(\chi_{9920}(2543, \cdot)\) n/a 720 2
9920.2.bo \(\chi_{9920}(2417, \cdot)\) n/a 760 2
9920.2.bp \(\chi_{9920}(3201, \cdot)\) n/a 1024 4
9920.2.br \(\chi_{9920}(8159, \cdot)\) n/a 768 2
9920.2.bu \(\chi_{9920}(9151, \cdot)\) n/a 512 2
9920.2.bw \(\chi_{9920}(5089, \cdot)\) n/a 768 2
9920.2.bx \(\chi_{9920}(3199, \cdot)\) n/a 760 2
9920.2.bz \(\chi_{9920}(1121, \cdot)\) n/a 512 2
9920.2.cc \(\chi_{9920}(129, \cdot)\) n/a 760 2
9920.2.ce \(\chi_{9920}(4191, \cdot)\) n/a 512 2
9920.2.cg \(\chi_{9920}(3287, \cdot)\) None 0 4
9920.2.ci \(\chi_{9920}(1177, \cdot)\) None 0 4
9920.2.cj \(\chi_{9920}(1239, \cdot)\) None 0 4
9920.2.cl \(\chi_{9920}(1241, \cdot)\) None 0 4
9920.2.co \(\chi_{9920}(249, \cdot)\) None 0 4
9920.2.cq \(\chi_{9920}(2231, \cdot)\) None 0 4
9920.2.cr \(\chi_{9920}(3657, \cdot)\) None 0 4
9920.2.ct \(\chi_{9920}(807, \cdot)\) None 0 4
9920.2.cw \(\chi_{9920}(1759, \cdot)\) n/a 1536 4
9920.2.cz \(\chi_{9920}(511, \cdot)\) n/a 1024 4
9920.2.db \(\chi_{9920}(2209, \cdot)\) n/a 1536 4
9920.2.dc \(\chi_{9920}(959, \cdot)\) n/a 1520 4
9920.2.de \(\chi_{9920}(481, \cdot)\) n/a 1024 4
9920.2.dh \(\chi_{9920}(1089, \cdot)\) n/a 1520 4
9920.2.dj \(\chi_{9920}(1951, \cdot)\) n/a 1024 4
9920.2.dk \(\chi_{9920}(5617, \cdot)\) n/a 1520 4
9920.2.dn \(\chi_{9920}(5647, \cdot)\) n/a 1520 4
9920.2.dq \(\chi_{9920}(1711, \cdot)\) n/a 1024 4
9920.2.dr \(\chi_{9920}(2609, \cdot)\) n/a 1520 4
9920.2.ds \(\chi_{9920}(6113, \cdot)\) n/a 1536 4
9920.2.dv \(\chi_{9920}(1183, \cdot)\) n/a 1536 4
9920.2.dw \(\chi_{9920}(6143, \cdot)\) n/a 1520 4
9920.2.dz \(\chi_{9920}(1153, \cdot)\) n/a 1520 4
9920.2.ea \(\chi_{9920}(3601, \cdot)\) n/a 1024 4
9920.2.eb \(\chi_{9920}(719, \cdot)\) n/a 1520 4
9920.2.ee \(\chi_{9920}(687, \cdot)\) n/a 1520 4
9920.2.eh \(\chi_{9920}(657, \cdot)\) n/a 1520 4
9920.2.ei \(\chi_{9920}(1281, \cdot)\) n/a 2048 8
9920.2.el \(\chi_{9920}(683, \cdot)\) n/a 11520 8
9920.2.em \(\chi_{9920}(1053, \cdot)\) n/a 12256 8
9920.2.eo \(\chi_{9920}(371, \cdot)\) n/a 8192 8
9920.2.eq \(\chi_{9920}(621, \cdot)\) n/a 7680 8
9920.2.er \(\chi_{9920}(869, \cdot)\) n/a 11520 8
9920.2.et \(\chi_{9920}(619, \cdot)\) n/a 12256 8
9920.2.ev \(\chi_{9920}(557, \cdot)\) n/a 12256 8
9920.2.ew \(\chi_{9920}(187, \cdot)\) n/a 11520 8
9920.2.fa \(\chi_{9920}(2193, \cdot)\) n/a 3040 8
9920.2.fb \(\chi_{9920}(1583, \cdot)\) n/a 3040 8
9920.2.ff \(\chi_{9920}(529, \cdot)\) n/a 3040 8
9920.2.fg \(\chi_{9920}(271, \cdot)\) n/a 2048 8
9920.2.fh \(\chi_{9920}(1697, \cdot)\) n/a 3072 8
9920.2.fk \(\chi_{9920}(287, \cdot)\) n/a 3072 8
9920.2.fl \(\chi_{9920}(1087, \cdot)\) n/a 3040 8
9920.2.fo \(\chi_{9920}(833, \cdot)\) n/a 3040 8
9920.2.fp \(\chi_{9920}(399, \cdot)\) n/a 3040 8
9920.2.fq \(\chi_{9920}(721, \cdot)\) n/a 2048 8
9920.2.fu \(\chi_{9920}(47, \cdot)\) n/a 3040 8
9920.2.fv \(\chi_{9920}(337, \cdot)\) n/a 3040 8
9920.2.fy \(\chi_{9920}(1897, \cdot)\) None 0 8
9920.2.ga \(\chi_{9920}(1927, \cdot)\) None 0 8
9920.2.gc \(\chi_{9920}(1369, \cdot)\) None 0 8
9920.2.ge \(\chi_{9920}(471, \cdot)\) None 0 8
9920.2.gf \(\chi_{9920}(119, \cdot)\) None 0 8
9920.2.gh \(\chi_{9920}(521, \cdot)\) None 0 8
9920.2.gj \(\chi_{9920}(87, \cdot)\) None 0 8
9920.2.gl \(\chi_{9920}(57, \cdot)\) None 0 8
9920.2.gn \(\chi_{9920}(3551, \cdot)\) n/a 2048 8
9920.2.gp \(\chi_{9920}(1409, \cdot)\) n/a 3040 8
9920.2.gs \(\chi_{9920}(2401, \cdot)\) n/a 2048 8
9920.2.gu \(\chi_{9920}(2559, \cdot)\) n/a 3040 8
9920.2.gv \(\chi_{9920}(289, \cdot)\) n/a 3072 8
9920.2.gx \(\chi_{9920}(1791, \cdot)\) n/a 2048 8
9920.2.ha \(\chi_{9920}(799, \cdot)\) n/a 3072 8
9920.2.hc \(\chi_{9920}(343, \cdot)\) None 0 16
9920.2.he \(\chi_{9920}(153, \cdot)\) None 0 16
9920.2.hg \(\chi_{9920}(151, \cdot)\) None 0 16
9920.2.hi \(\chi_{9920}(729, \cdot)\) None 0 16
9920.2.hl \(\chi_{9920}(281, \cdot)\) None 0 16
9920.2.hn \(\chi_{9920}(519, \cdot)\) None 0 16
9920.2.hp \(\chi_{9920}(697, \cdot)\) None 0 16
9920.2.hr \(\chi_{9920}(407, \cdot)\) None 0 16
9920.2.hs \(\chi_{9920}(563, \cdot)\) n/a 24512 16
9920.2.ht \(\chi_{9920}(533, \cdot)\) n/a 24512 16
9920.2.hw \(\chi_{9920}(491, \cdot)\) n/a 16384 16
9920.2.hy \(\chi_{9920}(501, \cdot)\) n/a 16384 16
9920.2.ib \(\chi_{9920}(149, \cdot)\) n/a 24512 16
9920.2.id \(\chi_{9920}(99, \cdot)\) n/a 24512 16
9920.2.ig \(\chi_{9920}(37, \cdot)\) n/a 24512 16
9920.2.ih \(\chi_{9920}(67, \cdot)\) n/a 24512 16
9920.2.ij \(\chi_{9920}(17, \cdot)\) n/a 6080 16
9920.2.ik \(\chi_{9920}(143, \cdot)\) n/a 6080 16
9920.2.io \(\chi_{9920}(79, \cdot)\) n/a 6080 16
9920.2.ip \(\chi_{9920}(81, \cdot)\) n/a 4096 16
9920.2.iq \(\chi_{9920}(513, \cdot)\) n/a 6080 16
9920.2.it \(\chi_{9920}(1343, \cdot)\) n/a 6080 16
9920.2.iu \(\chi_{9920}(607, \cdot)\) n/a 6144 16
9920.2.ix \(\chi_{9920}(353, \cdot)\) n/a 6144 16
9920.2.iy \(\chi_{9920}(49, \cdot)\) n/a 6080 16
9920.2.iz \(\chi_{9920}(911, \cdot)\) n/a 4096 16
9920.2.jd \(\chi_{9920}(847, \cdot)\) n/a 6080 16
9920.2.je \(\chi_{9920}(177, \cdot)\) n/a 6080 16
9920.2.ji \(\chi_{9920}(163, \cdot)\) n/a 49024 32
9920.2.jj \(\chi_{9920}(77, \cdot)\) n/a 49024 32
9920.2.jl \(\chi_{9920}(109, \cdot)\) n/a 49024 32
9920.2.jn \(\chi_{9920}(139, \cdot)\) n/a 49024 32
9920.2.jo \(\chi_{9920}(91, \cdot)\) n/a 32768 32
9920.2.jq \(\chi_{9920}(101, \cdot)\) n/a 32768 32
9920.2.js \(\chi_{9920}(277, \cdot)\) n/a 49024 32
9920.2.jt \(\chi_{9920}(283, \cdot)\) n/a 49024 32
9920.2.jw \(\chi_{9920}(73, \cdot)\) None 0 32
9920.2.jy \(\chi_{9920}(103, \cdot)\) None 0 32
9920.2.kb \(\chi_{9920}(41, \cdot)\) None 0 32
9920.2.kd \(\chi_{9920}(199, \cdot)\) None 0 32
9920.2.ke \(\chi_{9920}(551, \cdot)\) None 0 32
9920.2.kg \(\chi_{9920}(9, \cdot)\) None 0 32
9920.2.kj \(\chi_{9920}(7, \cdot)\) None 0 32
9920.2.kl \(\chi_{9920}(137, \cdot)\) None 0 32
9920.2.km \(\chi_{9920}(227, \cdot)\) n/a 98048 64
9920.2.kn \(\chi_{9920}(13, \cdot)\) n/a 98048 64
9920.2.kq \(\chi_{9920}(69, \cdot)\) n/a 98048 64
9920.2.ks \(\chi_{9920}(179, \cdot)\) n/a 98048 64
9920.2.kv \(\chi_{9920}(11, \cdot)\) n/a 65536 64
9920.2.kx \(\chi_{9920}(381, \cdot)\) n/a 65536 64
9920.2.la \(\chi_{9920}(53, \cdot)\) n/a 98048 64
9920.2.lb \(\chi_{9920}(107, \cdot)\) n/a 98048 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9920))\)\(^{\oplus 1}\)