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Properties

Label 9840.2
Level 9840
Weight 2
Dimension 994628
Nonzero newspaces 152
Sturm bound 10321920

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Defining parameters

Level: \( N \) = \( 9840 = 2^{4} \cdot 3 \cdot 5 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 152 \)
Sturm bound: \(10321920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9840))\).

Total New Old
Modular forms 2598400 998836 1599564
Cusp forms 2562561 994628 1567933
Eisenstein series 35839 4208 31631

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9840))\)

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
9840.2.a \(\chi_{9840}(1, \cdot)\) 9840.2.a.a 1 1
9840.2.a.b 1
9840.2.a.c 1
9840.2.a.d 1
9840.2.a.e 1
9840.2.a.f 1
9840.2.a.g 1
9840.2.a.h 1
9840.2.a.i 1
9840.2.a.j 1
9840.2.a.k 1
9840.2.a.l 1
9840.2.a.m 1
9840.2.a.n 1
9840.2.a.o 1
9840.2.a.p 1
9840.2.a.q 1
9840.2.a.r 1
9840.2.a.s 1
9840.2.a.t 1
9840.2.a.u 1
9840.2.a.v 1
9840.2.a.w 1
9840.2.a.x 1
9840.2.a.y 1
9840.2.a.z 1
9840.2.a.ba 1
9840.2.a.bb 1
9840.2.a.bc 2
9840.2.a.bd 2
9840.2.a.be 2
9840.2.a.bf 2
9840.2.a.bg 2
9840.2.a.bh 2
9840.2.a.bi 2
9840.2.a.bj 2
9840.2.a.bk 2
9840.2.a.bl 2
9840.2.a.bm 2
9840.2.a.bn 2
9840.2.a.bo 2
9840.2.a.bp 2
9840.2.a.bq 3
9840.2.a.br 3
9840.2.a.bs 3
9840.2.a.bt 3
9840.2.a.bu 3
9840.2.a.bv 3
9840.2.a.bw 3
9840.2.a.bx 4
9840.2.a.by 4
9840.2.a.bz 4
9840.2.a.ca 4
9840.2.a.cb 4
9840.2.a.cc 4
9840.2.a.cd 4
9840.2.a.ce 4
9840.2.a.cf 4
9840.2.a.cg 4
9840.2.a.ch 5
9840.2.a.ci 5
9840.2.a.cj 6
9840.2.a.ck 6
9840.2.a.cl 6
9840.2.a.cm 7
9840.2.a.cn 8
9840.2.b \(\chi_{9840}(3361, \cdot)\) n/a 168 1
9840.2.c \(\chi_{9840}(9431, \cdot)\) None 0 1
9840.2.f \(\chi_{9840}(6889, \cdot)\) None 0 1
9840.2.g \(\chi_{9840}(9839, \cdot)\) n/a 504 1
9840.2.j \(\chi_{9840}(4919, \cdot)\) None 0 1
9840.2.k \(\chi_{9840}(1969, \cdot)\) n/a 240 1
9840.2.n \(\chi_{9840}(4511, \cdot)\) n/a 320 1
9840.2.o \(\chi_{9840}(8281, \cdot)\) None 0 1
9840.2.t \(\chi_{9840}(4921, \cdot)\) None 0 1
9840.2.u \(\chi_{9840}(7871, \cdot)\) n/a 336 1
9840.2.x \(\chi_{9840}(5329, \cdot)\) n/a 252 1
9840.2.y \(\chi_{9840}(1559, \cdot)\) None 0 1
9840.2.bb \(\chi_{9840}(6479, \cdot)\) n/a 480 1
9840.2.bc \(\chi_{9840}(409, \cdot)\) None 0 1
9840.2.bf \(\chi_{9840}(2951, \cdot)\) None 0 1
9840.2.bi \(\chi_{9840}(173, \cdot)\) n/a 4016 2
9840.2.bj \(\chi_{9840}(8683, \cdot)\) n/a 2016 2
9840.2.bk \(\chi_{9840}(2287, \cdot)\) n/a 504 2
9840.2.bl \(\chi_{9840}(3353, \cdot)\) None 0 2
9840.2.bs \(\chi_{9840}(491, \cdot)\) n/a 2688 2
9840.2.bt \(\chi_{9840}(2461, \cdot)\) n/a 1280 2
9840.2.bu \(\chi_{9840}(4019, \cdot)\) n/a 3840 2
9840.2.bv \(\chi_{9840}(2869, \cdot)\) n/a 2016 2
9840.2.bw \(\chi_{9840}(583, \cdot)\) None 0 2
9840.2.bx \(\chi_{9840}(3617, \cdot)\) n/a 1000 2
9840.2.cc \(\chi_{9840}(3763, \cdot)\) n/a 2016 2
9840.2.cd \(\chi_{9840}(5093, \cdot)\) n/a 4016 2
9840.2.cf \(\chi_{9840}(1549, \cdot)\) n/a 2016 2
9840.2.cg \(\chi_{9840}(1139, \cdot)\) n/a 4016 2
9840.2.ck \(\chi_{9840}(5657, \cdot)\) None 0 2
9840.2.cl \(\chi_{9840}(1313, \cdot)\) n/a 960 2
9840.2.cm \(\chi_{9840}(3607, \cdot)\) None 0 2
9840.2.cn \(\chi_{9840}(5167, \cdot)\) n/a 480 2
9840.2.cr \(\chi_{9840}(3781, \cdot)\) n/a 1344 2
9840.2.cs \(\chi_{9840}(3371, \cdot)\) n/a 2688 2
9840.2.cv \(\chi_{9840}(6643, \cdot)\) n/a 1920 2
9840.2.cx \(\chi_{9840}(5083, \cdot)\) n/a 2016 2
9840.2.cy \(\chi_{9840}(3773, \cdot)\) n/a 3840 2
9840.2.da \(\chi_{9840}(2213, \cdot)\) n/a 4016 2
9840.2.dc \(\chi_{9840}(2879, \cdot)\) n/a 1008 2
9840.2.df \(\chi_{9840}(7799, \cdot)\) None 0 2
9840.2.dg \(\chi_{9840}(8209, \cdot)\) n/a 504 2
9840.2.dj \(\chi_{9840}(3289, \cdot)\) None 0 2
9840.2.dl \(\chi_{9840}(5831, \cdot)\) None 0 2
9840.2.dm \(\chi_{9840}(911, \cdot)\) n/a 672 2
9840.2.dp \(\chi_{9840}(1321, \cdot)\) None 0 2
9840.2.dq \(\chi_{9840}(6241, \cdot)\) n/a 336 2
9840.2.ds \(\chi_{9840}(163, \cdot)\) n/a 2016 2
9840.2.du \(\chi_{9840}(1723, \cdot)\) n/a 1920 2
9840.2.dx \(\chi_{9840}(7133, \cdot)\) n/a 4016 2
9840.2.dz \(\chi_{9840}(8693, \cdot)\) n/a 3840 2
9840.2.eb \(\chi_{9840}(4091, \cdot)\) n/a 2688 2
9840.2.ec \(\chi_{9840}(4501, \cdot)\) n/a 1344 2
9840.2.eg \(\chi_{9840}(247, \cdot)\) None 0 2
9840.2.eh \(\chi_{9840}(2623, \cdot)\) n/a 504 2
9840.2.ei \(\chi_{9840}(2297, \cdot)\) None 0 2
9840.2.ej \(\chi_{9840}(737, \cdot)\) n/a 1000 2
9840.2.en \(\chi_{9840}(419, \cdot)\) n/a 4016 2
9840.2.eo \(\chi_{9840}(829, \cdot)\) n/a 2016 2
9840.2.eq \(\chi_{9840}(5813, \cdot)\) n/a 4016 2
9840.2.er \(\chi_{9840}(3043, \cdot)\) n/a 2016 2
9840.2.ew \(\chi_{9840}(1303, \cdot)\) None 0 2
9840.2.ex \(\chi_{9840}(4337, \cdot)\) n/a 1000 2
9840.2.ey \(\chi_{9840}(2051, \cdot)\) n/a 2560 2
9840.2.ez \(\chi_{9840}(901, \cdot)\) n/a 1344 2
9840.2.fa \(\chi_{9840}(2459, \cdot)\) n/a 4016 2
9840.2.fb \(\chi_{9840}(4429, \cdot)\) n/a 1920 2
9840.2.fi \(\chi_{9840}(1567, \cdot)\) n/a 504 2
9840.2.fj \(\chi_{9840}(2633, \cdot)\) None 0 2
9840.2.fk \(\chi_{9840}(7963, \cdot)\) n/a 2016 2
9840.2.fl \(\chi_{9840}(893, \cdot)\) n/a 4016 2
9840.2.fo \(\chi_{9840}(961, \cdot)\) n/a 672 4
9840.2.fq \(\chi_{9840}(929, \cdot)\) n/a 2000 4
9840.2.fs \(\chi_{9840}(2381, \cdot)\) n/a 5376 4
9840.2.ft \(\chi_{9840}(1421, \cdot)\) n/a 5376 4
9840.2.fv \(\chi_{9840}(5849, \cdot)\) None 0 4
9840.2.fy \(\chi_{9840}(79, \cdot)\) n/a 1008 4
9840.2.fz \(\chi_{9840}(331, \cdot)\) n/a 2688 4
9840.2.gc \(\chi_{9840}(1531, \cdot)\) n/a 2688 4
9840.2.gd \(\chi_{9840}(3799, \cdot)\) None 0 4
9840.2.gf \(\chi_{9840}(6013, \cdot)\) n/a 4032 4
9840.2.gh \(\chi_{9840}(6973, \cdot)\) n/a 4032 4
9840.2.gj \(\chi_{9840}(577, \cdot)\) n/a 1008 4
9840.2.gm \(\chi_{9840}(4537, \cdot)\) None 0 4
9840.2.go \(\chi_{9840}(1777, \cdot)\) n/a 1008 4
9840.2.gp \(\chi_{9840}(793, \cdot)\) None 0 4
9840.2.gs \(\chi_{9840}(2053, \cdot)\) n/a 4032 4
9840.2.gu \(\chi_{9840}(1093, \cdot)\) n/a 4032 4
9840.2.gv \(\chi_{9840}(5603, \cdot)\) n/a 8032 4
9840.2.gx \(\chi_{9840}(6563, \cdot)\) n/a 8032 4
9840.2.ha \(\chi_{9840}(4127, \cdot)\) n/a 2016 4
9840.2.hb \(\chi_{9840}(167, \cdot)\) None 0 4
9840.2.hd \(\chi_{9840}(383, \cdot)\) n/a 2016 4
9840.2.hg \(\chi_{9840}(1367, \cdot)\) None 0 4
9840.2.hi \(\chi_{9840}(1643, \cdot)\) n/a 8032 4
9840.2.hk \(\chi_{9840}(683, \cdot)\) n/a 8032 4
9840.2.hm \(\chi_{9840}(3881, \cdot)\) None 0 4
9840.2.hn \(\chi_{9840}(3389, \cdot)\) n/a 8032 4
9840.2.hq \(\chi_{9840}(629, \cdot)\) n/a 8032 4
9840.2.hr \(\chi_{9840}(161, \cdot)\) n/a 1344 4
9840.2.hu \(\chi_{9840}(1831, \cdot)\) None 0 4
9840.2.hw \(\chi_{9840}(1339, \cdot)\) n/a 4032 4
9840.2.hx \(\chi_{9840}(2299, \cdot)\) n/a 4032 4
9840.2.hz \(\chi_{9840}(6751, \cdot)\) n/a 672 4
9840.2.ib \(\chi_{9840}(1991, \cdot)\) None 0 4
9840.2.ie \(\chi_{9840}(1849, \cdot)\) None 0 4
9840.2.if \(\chi_{9840}(959, \cdot)\) n/a 2016 4
9840.2.ii \(\chi_{9840}(119, \cdot)\) None 0 4
9840.2.ij \(\chi_{9840}(769, \cdot)\) n/a 1008 4
9840.2.im \(\chi_{9840}(3311, \cdot)\) n/a 1344 4
9840.2.in \(\chi_{9840}(3481, \cdot)\) None 0 4
9840.2.is \(\chi_{9840}(3721, \cdot)\) None 0 4
9840.2.it \(\chi_{9840}(3071, \cdot)\) n/a 1344 4
9840.2.iw \(\chi_{9840}(529, \cdot)\) n/a 1008 4
9840.2.ix \(\chi_{9840}(359, \cdot)\) None 0 4
9840.2.ja \(\chi_{9840}(1439, \cdot)\) n/a 2016 4
9840.2.jb \(\chi_{9840}(1369, \cdot)\) None 0 4
9840.2.je \(\chi_{9840}(551, \cdot)\) None 0 4
9840.2.jf \(\chi_{9840}(2401, \cdot)\) n/a 672 4
9840.2.ji \(\chi_{9840}(677, \cdot)\) n/a 16064 8
9840.2.jj \(\chi_{9840}(307, \cdot)\) n/a 8064 8
9840.2.jk \(\chi_{9840}(617, \cdot)\) None 0 8
9840.2.jl \(\chi_{9840}(367, \cdot)\) n/a 2016 8
9840.2.js \(\chi_{9840}(469, \cdot)\) n/a 8064 8
9840.2.jt \(\chi_{9840}(1499, \cdot)\) n/a 16064 8
9840.2.ju \(\chi_{9840}(1261, \cdot)\) n/a 5376 8
9840.2.jv \(\chi_{9840}(611, \cdot)\) n/a 10752 8
9840.2.jw \(\chi_{9840}(2657, \cdot)\) n/a 4000 8
9840.2.jx \(\chi_{9840}(1783, \cdot)\) None 0 8
9840.2.kc \(\chi_{9840}(1843, \cdot)\) n/a 8064 8
9840.2.kd \(\chi_{9840}(2957, \cdot)\) n/a 16064 8
9840.2.kf \(\chi_{9840}(349, \cdot)\) n/a 8064 8
9840.2.kg \(\chi_{9840}(2099, \cdot)\) n/a 16064 8
9840.2.kk \(\chi_{9840}(113, \cdot)\) n/a 4000 8
9840.2.kl \(\chi_{9840}(713, \cdot)\) None 0 8
9840.2.km \(\chi_{9840}(127, \cdot)\) n/a 2016 8
9840.2.kn \(\chi_{9840}(1207, \cdot)\) None 0 8
9840.2.kr \(\chi_{9840}(541, \cdot)\) n/a 5376 8
9840.2.ks \(\chi_{9840}(131, \cdot)\) n/a 10752 8
9840.2.ku \(\chi_{9840}(797, \cdot)\) n/a 16064 8
9840.2.kw \(\chi_{9840}(2573, \cdot)\) n/a 16064 8
9840.2.kz \(\chi_{9840}(283, \cdot)\) n/a 8064 8
9840.2.lb \(\chi_{9840}(187, \cdot)\) n/a 8064 8
9840.2.ld \(\chi_{9840}(241, \cdot)\) n/a 1344 8
9840.2.le \(\chi_{9840}(121, \cdot)\) None 0 8
9840.2.lh \(\chi_{9840}(431, \cdot)\) n/a 2688 8
9840.2.li \(\chi_{9840}(2711, \cdot)\) None 0 8
9840.2.lk \(\chi_{9840}(169, \cdot)\) None 0 8
9840.2.ln \(\chi_{9840}(49, \cdot)\) n/a 2016 8
9840.2.lo \(\chi_{9840}(1799, \cdot)\) None 0 8
9840.2.lr \(\chi_{9840}(1679, \cdot)\) n/a 4032 8
9840.2.lt \(\chi_{9840}(1253, \cdot)\) n/a 16064 8
9840.2.lv \(\chi_{9840}(2333, \cdot)\) n/a 16064 8
9840.2.lw \(\chi_{9840}(523, \cdot)\) n/a 8064 8
9840.2.ly \(\chi_{9840}(1123, \cdot)\) n/a 8064 8
9840.2.mb \(\chi_{9840}(251, \cdot)\) n/a 10752 8
9840.2.mc \(\chi_{9840}(61, \cdot)\) n/a 5376 8
9840.2.mg \(\chi_{9840}(223, \cdot)\) n/a 2016 8
9840.2.mh \(\chi_{9840}(2647, \cdot)\) None 0 8
9840.2.mi \(\chi_{9840}(1697, \cdot)\) n/a 4000 8
9840.2.mj \(\chi_{9840}(1097, \cdot)\) None 0 8
9840.2.mn \(\chi_{9840}(1619, \cdot)\) n/a 16064 8
9840.2.mo \(\chi_{9840}(2029, \cdot)\) n/a 8064 8
9840.2.mq \(\chi_{9840}(77, \cdot)\) n/a 16064 8
9840.2.mr \(\chi_{9840}(907, \cdot)\) n/a 8064 8
9840.2.mw \(\chi_{9840}(497, \cdot)\) n/a 4000 8
9840.2.mx \(\chi_{9840}(103, \cdot)\) None 0 8
9840.2.my \(\chi_{9840}(1909, \cdot)\) n/a 8064 8
9840.2.mz \(\chi_{9840}(59, \cdot)\) n/a 16064 8
9840.2.na \(\chi_{9840}(1021, \cdot)\) n/a 5376 8
9840.2.nb \(\chi_{9840}(851, \cdot)\) n/a 10752 8
9840.2.ni \(\chi_{9840}(377, \cdot)\) None 0 8
9840.2.nj \(\chi_{9840}(607, \cdot)\) n/a 2016 8
9840.2.nk \(\chi_{9840}(43, \cdot)\) n/a 8064 8
9840.2.nl \(\chi_{9840}(197, \cdot)\) n/a 16064 8
9840.2.no \(\chi_{9840}(511, \cdot)\) n/a 2688 16
9840.2.nr \(\chi_{9840}(19, \cdot)\) n/a 16128 16
9840.2.ns \(\chi_{9840}(259, \cdot)\) n/a 16128 16
9840.2.nv \(\chi_{9840}(151, \cdot)\) None 0 16
9840.2.nw \(\chi_{9840}(641, \cdot)\) n/a 5376 16
9840.2.ny \(\chi_{9840}(29, \cdot)\) n/a 32128 16
9840.2.ob \(\chi_{9840}(509, \cdot)\) n/a 32128 16
9840.2.od \(\chi_{9840}(281, \cdot)\) None 0 16
9840.2.of \(\chi_{9840}(1163, \cdot)\) n/a 32128 16
9840.2.oh \(\chi_{9840}(227, \cdot)\) n/a 32128 16
9840.2.oj \(\chi_{9840}(503, \cdot)\) None 0 16
9840.2.ok \(\chi_{9840}(767, \cdot)\) n/a 8064 16
9840.2.om \(\chi_{9840}(263, \cdot)\) None 0 16
9840.2.op \(\chi_{9840}(47, \cdot)\) n/a 8064 16
9840.2.oq \(\chi_{9840}(347, \cdot)\) n/a 32128 16
9840.2.os \(\chi_{9840}(587, \cdot)\) n/a 32128 16
9840.2.ov \(\chi_{9840}(157, \cdot)\) n/a 16128 16
9840.2.ox \(\chi_{9840}(637, \cdot)\) n/a 16128 16
9840.2.oy \(\chi_{9840}(217, \cdot)\) None 0 16
9840.2.pb \(\chi_{9840}(97, \cdot)\) n/a 4032 16
9840.2.pd \(\chi_{9840}(457, \cdot)\) None 0 16
9840.2.pe \(\chi_{9840}(673, \cdot)\) n/a 4032 16
9840.2.pg \(\chi_{9840}(13, \cdot)\) n/a 16128 16
9840.2.pi \(\chi_{9840}(997, \cdot)\) n/a 16128 16
9840.2.pk \(\chi_{9840}(199, \cdot)\) None 0 16
9840.2.pm \(\chi_{9840}(931, \cdot)\) n/a 10752 16
9840.2.pp \(\chi_{9840}(211, \cdot)\) n/a 10752 16
9840.2.pr \(\chi_{9840}(559, \cdot)\) n/a 4032 16
9840.2.ps \(\chi_{9840}(89, \cdot)\) None 0 16
9840.2.pv \(\chi_{9840}(341, \cdot)\) n/a 21504 16
9840.2.pw \(\chi_{9840}(101, \cdot)\) n/a 21504 16
9840.2.pz \(\chi_{9840}(1409, \cdot)\) n/a 8000 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(410))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(615))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(820))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4920))\)\(^{\oplus 2}\)