↑

Properties

Label 17550.2
Level 17550
Weight 2
Dimension 1958356
Nonzero newspaces 160
Sturm bound 32659200

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 17550 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 160 \)
Sturm bound: \(32659200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(17550))\).

Total New Old
Modular forms 8205120 1958356 6246764
Cusp forms 8124481 1958356 6166125
Eisenstein series 80639 0 80639

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(17550))\)

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
17550.2.a \(\chi_{17550}(1, \cdot)\) 17550.2.a.a 1 1
17550.2.a.b 1
17550.2.a.c 1
17550.2.a.d 1
17550.2.a.e 1
17550.2.a.f 1
17550.2.a.g 1
17550.2.a.h 1
17550.2.a.i 1
17550.2.a.j 1
17550.2.a.k 1
17550.2.a.l 1
17550.2.a.m 1
17550.2.a.n 1
17550.2.a.o 1
17550.2.a.p 1
17550.2.a.q 1
17550.2.a.r 1
17550.2.a.s 1
17550.2.a.t 1
17550.2.a.u 1
17550.2.a.v 1
17550.2.a.w 1
17550.2.a.x 1
17550.2.a.y 1
17550.2.a.z 1
17550.2.a.ba 1
17550.2.a.bb 1
17550.2.a.bc 1
17550.2.a.bd 1
17550.2.a.be 1
17550.2.a.bf 1
17550.2.a.bg 1
17550.2.a.bh 1
17550.2.a.bi 1
17550.2.a.bj 1
17550.2.a.bk 1
17550.2.a.bl 1
17550.2.a.bm 1
17550.2.a.bn 1
17550.2.a.bo 1
17550.2.a.bp 1
17550.2.a.bq 1
17550.2.a.br 1
17550.2.a.bs 1
17550.2.a.bt 1
17550.2.a.bu 1
17550.2.a.bv 1
17550.2.a.bw 1
17550.2.a.bx 1
17550.2.a.by 1
17550.2.a.bz 1
17550.2.a.ca 1
17550.2.a.cb 1
17550.2.a.cc 1
17550.2.a.cd 1
17550.2.a.ce 1
17550.2.a.cf 1
17550.2.a.cg 1
17550.2.a.ch 1
17550.2.a.ci 1
17550.2.a.cj 1
17550.2.a.ck 1
17550.2.a.cl 1
17550.2.a.cm 1
17550.2.a.cn 1
17550.2.a.co 1
17550.2.a.cp 1
17550.2.a.cq 1
17550.2.a.cr 1
17550.2.a.cs 1
17550.2.a.ct 1
17550.2.a.cu 1
17550.2.a.cv 1
17550.2.a.cw 1
17550.2.a.cx 1
17550.2.a.cy 1
17550.2.a.cz 1
17550.2.a.da 1
17550.2.a.db 1
17550.2.a.dc 1
17550.2.a.dd 1
17550.2.a.de 1
17550.2.a.df 1
17550.2.a.dg 1
17550.2.a.dh 1
17550.2.a.di 1
17550.2.a.dj 1
17550.2.a.dk 2
17550.2.a.dl 2
17550.2.a.dm 2
17550.2.a.dn 2
17550.2.a.do 2
17550.2.a.dp 2
17550.2.a.dq 2
17550.2.a.dr 2
17550.2.a.ds 2
17550.2.a.dt 2
17550.2.a.du 2
17550.2.a.dv 2
17550.2.a.dw 2
17550.2.a.dx 2
17550.2.a.dy 2
17550.2.a.dz 2
17550.2.a.ea 2
17550.2.a.eb 2
17550.2.a.ec 3
17550.2.a.ed 3
17550.2.a.ee 3
17550.2.a.ef 3
17550.2.a.eg 3
17550.2.a.eh 3
17550.2.a.ei 3
17550.2.a.ej 3
17550.2.a.ek 3
17550.2.a.el 3
17550.2.a.em 3
17550.2.a.en 3
17550.2.a.eo 3
17550.2.a.ep 3
17550.2.a.eq 3
17550.2.a.er 3
17550.2.a.es 3
17550.2.a.et 3
17550.2.a.eu 3
17550.2.a.ev 3
17550.2.a.ew 4
17550.2.a.ex 4
17550.2.a.ey 4
17550.2.a.ez 4
17550.2.a.fa 4
17550.2.a.fb 4
17550.2.a.fc 4
17550.2.a.fd 4
17550.2.a.fe 4
17550.2.a.ff 4
17550.2.a.fg 4
17550.2.a.fh 4
17550.2.a.fi 5
17550.2.a.fj 5
17550.2.a.fk 5
17550.2.a.fl 5
17550.2.a.fm 6
17550.2.a.fn 6
17550.2.a.fo 6
17550.2.a.fp 6
17550.2.a.fq 7
17550.2.a.fr 7
17550.2.a.fs 7
17550.2.a.ft 7
17550.2.b \(\chi_{17550}(1351, \cdot)\) n/a 356 1
17550.2.e \(\chi_{17550}(16849, \cdot)\) n/a 288 1
17550.2.f \(\chi_{17550}(649, \cdot)\) n/a 336 1
17550.2.i \(\chi_{17550}(12151, \cdot)\) n/a 708 2
17550.2.j \(\chi_{17550}(5851, \cdot)\) n/a 456 2
17550.2.k \(\chi_{17550}(4501, \cdot)\) n/a 532 2
17550.2.l \(\chi_{17550}(451, \cdot)\) n/a 532 2
17550.2.m \(\chi_{17550}(1243, \cdot)\) n/a 672 2
17550.2.o \(\chi_{17550}(1457, \cdot)\) n/a 576 2
17550.2.q \(\chi_{17550}(2699, \cdot)\) n/a 672 2
17550.2.s \(\chi_{17550}(3401, \cdot)\) n/a 712 2
17550.2.v \(\chi_{17550}(2807, \cdot)\) n/a 672 2
17550.2.w \(\chi_{17550}(6157, \cdot)\) n/a 672 2
17550.2.y \(\chi_{17550}(3511, \cdot)\) n/a 1920 4
17550.2.z \(\chi_{17550}(9649, \cdot)\) n/a 504 2
17550.2.bc \(\chi_{17550}(12601, \cdot)\) n/a 532 2
17550.2.be \(\chi_{17550}(199, \cdot)\) n/a 504 2
17550.2.bh \(\chi_{17550}(6499, \cdot)\) n/a 504 2
17550.2.bk \(\chi_{17550}(1999, \cdot)\) n/a 672 2
17550.2.bn \(\chi_{17550}(901, \cdot)\) n/a 532 2
17550.2.bp \(\chi_{17550}(5149, \cdot)\) n/a 432 2
17550.2.bq \(\chi_{17550}(11449, \cdot)\) n/a 672 2
17550.2.bt \(\chi_{17550}(2701, \cdot)\) n/a 708 2
17550.2.bu \(\chi_{17550}(7201, \cdot)\) n/a 532 2
17550.2.bw \(\chi_{17550}(3799, \cdot)\) n/a 504 2
17550.2.ca \(\chi_{17550}(11899, \cdot)\) n/a 504 2
17550.2.cb \(\chi_{17550}(1951, \cdot)\) n/a 4104 6
17550.2.cc \(\chi_{17550}(2401, \cdot)\) n/a 4788 6
17550.2.cd \(\chi_{17550}(601, \cdot)\) n/a 4788 6
17550.2.ce \(\chi_{17550}(2809, \cdot)\) n/a 1920 4
17550.2.ch \(\chi_{17550}(4861, \cdot)\) n/a 2240 4
17550.2.ck \(\chi_{17550}(4159, \cdot)\) n/a 2240 4
17550.2.cm \(\chi_{17550}(2143, \cdot)\) n/a 1008 4
17550.2.cn \(\chi_{17550}(1207, \cdot)\) n/a 1008 4
17550.2.cq \(\chi_{17550}(2593, \cdot)\) n/a 1344 4
17550.2.cr \(\chi_{17550}(307, \cdot)\) n/a 1008 4
17550.2.cu \(\chi_{17550}(1907, \cdot)\) n/a 1008 4
17550.2.cw \(\chi_{17550}(3293, \cdot)\) n/a 1344 4
17550.2.cx \(\chi_{17550}(2357, \cdot)\) n/a 1008 4
17550.2.da \(\chi_{17550}(3743, \cdot)\) n/a 1008 4
17550.2.dc \(\chi_{17550}(1799, \cdot)\) n/a 1008 4
17550.2.dd \(\chi_{17550}(1151, \cdot)\) n/a 1064 4
17550.2.df \(\chi_{17550}(4751, \cdot)\) n/a 1416 4
17550.2.di \(\chi_{17550}(7001, \cdot)\) n/a 1064 4
17550.2.dk \(\chi_{17550}(6299, \cdot)\) n/a 1008 4
17550.2.dl \(\chi_{17550}(449, \cdot)\) n/a 1008 4
17550.2.dn \(\chi_{17550}(4049, \cdot)\) n/a 1344 4
17550.2.dq \(\chi_{17550}(2501, \cdot)\) n/a 1064 4
17550.2.dr \(\chi_{17550}(2393, \cdot)\) n/a 864 4
17550.2.du \(\chi_{17550}(1043, \cdot)\) n/a 1008 4
17550.2.dv \(\chi_{17550}(107, \cdot)\) n/a 1344 4
17550.2.dx \(\chi_{17550}(9143, \cdot)\) n/a 1008 4
17550.2.dz \(\chi_{17550}(1657, \cdot)\) n/a 1008 4
17550.2.ec \(\chi_{17550}(5257, \cdot)\) n/a 1008 4
17550.2.ed \(\chi_{17550}(7507, \cdot)\) n/a 1344 4
17550.2.eg \(\chi_{17550}(3907, \cdot)\) n/a 1008 4
17550.2.eh \(\chi_{17550}(991, \cdot)\) n/a 3360 8
17550.2.ei \(\chi_{17550}(1171, \cdot)\) n/a 2880 8
17550.2.ej \(\chi_{17550}(1621, \cdot)\) n/a 4480 8
17550.2.ek \(\chi_{17550}(3331, \cdot)\) n/a 3360 8
17550.2.em \(\chi_{17550}(3649, \cdot)\) n/a 4536 6
17550.2.en \(\chi_{17550}(3949, \cdot)\) n/a 4536 6
17550.2.ep \(\chi_{17550}(751, \cdot)\) n/a 4788 6
17550.2.et \(\chi_{17550}(3301, \cdot)\) n/a 4788 6
17550.2.ew \(\chi_{17550}(49, \cdot)\) n/a 4536 6
17550.2.ey \(\chi_{17550}(1249, \cdot)\) n/a 3888 6
17550.2.ez \(\chi_{17550}(2599, \cdot)\) n/a 4536 6
17550.2.fb \(\chi_{17550}(1699, \cdot)\) n/a 4536 6
17550.2.ff \(\chi_{17550}(4651, \cdot)\) n/a 4788 6
17550.2.fh \(\chi_{17550}(2917, \cdot)\) n/a 4480 8
17550.2.fi \(\chi_{17550}(1403, \cdot)\) n/a 4480 8
17550.2.fl \(\chi_{17550}(161, \cdot)\) n/a 4480 8
17550.2.fn \(\chi_{17550}(2969, \cdot)\) n/a 4480 8
17550.2.fp \(\chi_{17550}(53, \cdot)\) n/a 3840 8
17550.2.fr \(\chi_{17550}(1513, \cdot)\) n/a 4480 8
17550.2.fs \(\chi_{17550}(361, \cdot)\) n/a 3360 8
17550.2.fv \(\chi_{17550}(2629, \cdot)\) n/a 3360 8
17550.2.fx \(\chi_{17550}(2539, \cdot)\) n/a 4480 8
17550.2.ga \(\chi_{17550}(1819, \cdot)\) n/a 3360 8
17550.2.gd \(\chi_{17550}(829, \cdot)\) n/a 3360 8
17550.2.gg \(\chi_{17550}(289, \cdot)\) n/a 3360 8
17550.2.gi \(\chi_{17550}(181, \cdot)\) n/a 3360 8
17550.2.gj \(\chi_{17550}(3241, \cdot)\) n/a 4480 8
17550.2.gm \(\chi_{17550}(919, \cdot)\) n/a 4480 8
17550.2.gn \(\chi_{17550}(469, \cdot)\) n/a 2880 8
17550.2.gp \(\chi_{17550}(1531, \cdot)\) n/a 3360 8
17550.2.gr \(\chi_{17550}(1369, \cdot)\) n/a 3360 8
17550.2.gv \(\chi_{17550}(149, \cdot)\) n/a 9072 12
17550.2.gx \(\chi_{17550}(551, \cdot)\) n/a 9576 12
17550.2.gz \(\chi_{17550}(401, \cdot)\) n/a 9576 12
17550.2.hb \(\chi_{17550}(893, \cdot)\) n/a 9072 12
17550.2.hd \(\chi_{17550}(857, \cdot)\) n/a 9072 12
17550.2.hf \(\chi_{17550}(2207, \cdot)\) n/a 9072 12
17550.2.hh \(\chi_{17550}(193, \cdot)\) n/a 9072 12
17550.2.hi \(\chi_{17550}(2257, \cdot)\) n/a 9072 12
17550.2.hk \(\chi_{17550}(643, \cdot)\) n/a 9072 12
17550.2.hm \(\chi_{17550}(457, \cdot)\) n/a 9072 12
17550.2.ho \(\chi_{17550}(1357, \cdot)\) n/a 9072 12
17550.2.hr \(\chi_{17550}(7, \cdot)\) n/a 9072 12
17550.2.hs \(\chi_{17550}(3857, \cdot)\) n/a 9072 12
17550.2.hu \(\chi_{17550}(443, \cdot)\) n/a 7776 12
17550.2.hw \(\chi_{17550}(257, \cdot)\) n/a 9072 12
17550.2.hy \(\chi_{17550}(2099, \cdot)\) n/a 9072 12
17550.2.ia \(\chi_{17550}(749, \cdot)\) n/a 9072 12
17550.2.ic \(\chi_{17550}(851, \cdot)\) n/a 9576 12
17550.2.ie \(\chi_{17550}(841, \cdot)\) n/a 30240 24
17550.2.if \(\chi_{17550}(61, \cdot)\) n/a 30240 24
17550.2.ig \(\chi_{17550}(391, \cdot)\) n/a 25920 24
17550.2.ih \(\chi_{17550}(847, \cdot)\) n/a 6720 16
17550.2.ik \(\chi_{17550}(1477, \cdot)\) n/a 6720 16
17550.2.il \(\chi_{17550}(1567, \cdot)\) n/a 8960 16
17550.2.io \(\chi_{17550}(253, \cdot)\) n/a 6720 16
17550.2.iq \(\chi_{17550}(17, \cdot)\) n/a 6720 16
17550.2.is \(\chi_{17550}(1673, \cdot)\) n/a 8960 16
17550.2.it \(\chi_{17550}(737, \cdot)\) n/a 6720 16
17550.2.iw \(\chi_{17550}(287, \cdot)\) n/a 5760 16
17550.2.ix \(\chi_{17550}(1061, \cdot)\) n/a 6720 16
17550.2.ja \(\chi_{17550}(539, \cdot)\) n/a 8960 16
17550.2.jc \(\chi_{17550}(89, \cdot)\) n/a 6720 16
17550.2.jd \(\chi_{17550}(1259, \cdot)\) n/a 6720 16
17550.2.jf \(\chi_{17550}(1961, \cdot)\) n/a 6720 16
17550.2.ji \(\chi_{17550}(431, \cdot)\) n/a 8960 16
17550.2.jk \(\chi_{17550}(71, \cdot)\) n/a 6720 16
17550.2.jl \(\chi_{17550}(359, \cdot)\) n/a 6720 16
17550.2.jn \(\chi_{17550}(233, \cdot)\) n/a 6720 16
17550.2.jq \(\chi_{17550}(953, \cdot)\) n/a 6720 16
17550.2.jr \(\chi_{17550}(647, \cdot)\) n/a 8960 16
17550.2.jt \(\chi_{17550}(503, \cdot)\) n/a 6720 16
17550.2.jw \(\chi_{17550}(163, \cdot)\) n/a 8960 16
17550.2.jx \(\chi_{17550}(73, \cdot)\) n/a 6720 16
17550.2.ka \(\chi_{17550}(1333, \cdot)\) n/a 6720 16
17550.2.kb \(\chi_{17550}(37, \cdot)\) n/a 6720 16
17550.2.kd \(\chi_{17550}(121, \cdot)\) n/a 30240 24
17550.2.kh \(\chi_{17550}(529, \cdot)\) n/a 30240 24
17550.2.kj \(\chi_{17550}(259, \cdot)\) n/a 30240 24
17550.2.kk \(\chi_{17550}(79, \cdot)\) n/a 25920 24
17550.2.km \(\chi_{17550}(979, \cdot)\) n/a 30240 24
17550.2.kp \(\chi_{17550}(571, \cdot)\) n/a 30240 24
17550.2.kt \(\chi_{17550}(511, \cdot)\) n/a 30240 24
17550.2.kv \(\chi_{17550}(439, \cdot)\) n/a 30240 24
17550.2.kw \(\chi_{17550}(139, \cdot)\) n/a 30240 24
17550.2.kz \(\chi_{17550}(11, \cdot)\) n/a 60480 48
17550.2.lb \(\chi_{17550}(509, \cdot)\) n/a 60480 48
17550.2.ld \(\chi_{17550}(239, \cdot)\) n/a 60480 48
17550.2.lf \(\chi_{17550}(23, \cdot)\) n/a 60480 48
17550.2.lh \(\chi_{17550}(677, \cdot)\) n/a 51840 48
17550.2.lj \(\chi_{17550}(113, \cdot)\) n/a 60480 48
17550.2.lk \(\chi_{17550}(427, \cdot)\) n/a 60480 48
17550.2.ln \(\chi_{17550}(187, \cdot)\) n/a 60480 48
17550.2.lp \(\chi_{17550}(553, \cdot)\) n/a 60480 48
17550.2.lr \(\chi_{17550}(223, \cdot)\) n/a 60480 48
17550.2.lt \(\chi_{17550}(697, \cdot)\) n/a 60480 48
17550.2.lu \(\chi_{17550}(67, \cdot)\) n/a 60480 48
17550.2.lw \(\chi_{17550}(563, \cdot)\) n/a 60480 48
17550.2.ly \(\chi_{17550}(77, \cdot)\) n/a 60480 48
17550.2.ma \(\chi_{17550}(653, \cdot)\) n/a 60480 48
17550.2.mc \(\chi_{17550}(281, \cdot)\) n/a 60480 48
17550.2.me \(\chi_{17550}(41, \cdot)\) n/a 60480 48
17550.2.mg \(\chi_{17550}(59, \cdot)\) n/a 60480 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(17550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(17550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2925))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8775))\)\(^{\oplus 2}\)