# Properties

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

## 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

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