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Properties

Label 8880.2
Level 8880
Weight 2
Dimension 809516
Nonzero newspaces 156
Sturm bound 8404992

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Defining parameters

Level: \( N \) = \( 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 156 \)
Sturm bound: \(8404992\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8880))\).

Total New Old
Modular forms 2117376 813292 1304084
Cusp forms 2085121 809516 1275605
Eisenstein series 32255 3776 28479

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8880))\)

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
8880.2.a \(\chi_{8880}(1, \cdot)\) 8880.2.a.a 1 1
8880.2.a.b 1
8880.2.a.c 1
8880.2.a.d 1
8880.2.a.e 1
8880.2.a.f 1
8880.2.a.g 1
8880.2.a.h 1
8880.2.a.i 1
8880.2.a.j 1
8880.2.a.k 1
8880.2.a.l 1
8880.2.a.m 1
8880.2.a.n 1
8880.2.a.o 1
8880.2.a.p 1
8880.2.a.q 1
8880.2.a.r 1
8880.2.a.s 1
8880.2.a.t 1
8880.2.a.u 1
8880.2.a.v 1
8880.2.a.w 1
8880.2.a.x 1
8880.2.a.y 1
8880.2.a.z 1
8880.2.a.ba 1
8880.2.a.bb 1
8880.2.a.bc 1
8880.2.a.bd 2
8880.2.a.be 2
8880.2.a.bf 2
8880.2.a.bg 2
8880.2.a.bh 2
8880.2.a.bi 2
8880.2.a.bj 2
8880.2.a.bk 2
8880.2.a.bl 2
8880.2.a.bm 2
8880.2.a.bn 2
8880.2.a.bo 2
8880.2.a.bp 2
8880.2.a.bq 2
8880.2.a.br 2
8880.2.a.bs 2
8880.2.a.bt 2
8880.2.a.bu 3
8880.2.a.bv 3
8880.2.a.bw 3
8880.2.a.bx 3
8880.2.a.by 3
8880.2.a.bz 3
8880.2.a.ca 3
8880.2.a.cb 3
8880.2.a.cc 3
8880.2.a.cd 3
8880.2.a.ce 4
8880.2.a.cf 4
8880.2.a.cg 4
8880.2.a.ch 4
8880.2.a.ci 4
8880.2.a.cj 5
8880.2.a.ck 5
8880.2.a.cl 5
8880.2.a.cm 5
8880.2.a.cn 5
8880.2.a.co 6
8880.2.c \(\chi_{8880}(7031, \cdot)\) None 0 1
8880.2.e \(\chi_{8880}(1849, \cdot)\) None 0 1
8880.2.f \(\chi_{8880}(889, \cdot)\) None 0 1
8880.2.h \(\chi_{8880}(7991, \cdot)\) None 0 1
8880.2.k \(\chi_{8880}(5329, \cdot)\) n/a 216 1
8880.2.m \(\chi_{8880}(3551, \cdot)\) n/a 304 1
8880.2.n \(\chi_{8880}(2591, \cdot)\) n/a 288 1
8880.2.p \(\chi_{8880}(6289, \cdot)\) n/a 228 1
8880.2.r \(\chi_{8880}(4439, \cdot)\) None 0 1
8880.2.t \(\chi_{8880}(4441, \cdot)\) None 0 1
8880.2.w \(\chi_{8880}(5401, \cdot)\) None 0 1
8880.2.y \(\chi_{8880}(3479, \cdot)\) None 0 1
8880.2.z \(\chi_{8880}(961, \cdot)\) n/a 152 1
8880.2.bb \(\chi_{8880}(7919, \cdot)\) n/a 432 1
8880.2.be \(\chi_{8880}(8879, \cdot)\) n/a 456 1
8880.2.bg \(\chi_{8880}(4561, \cdot)\) n/a 304 2
8880.2.bh \(\chi_{8880}(4471, \cdot)\) None 0 2
8880.2.bj \(\chi_{8880}(1289, \cdot)\) None 0 2
8880.2.bl \(\chi_{8880}(5741, \cdot)\) n/a 2432 2
8880.2.bm \(\chi_{8880}(1819, \cdot)\) n/a 1824 2
8880.2.bq \(\chi_{8880}(2219, \cdot)\) n/a 3632 2
8880.2.br \(\chi_{8880}(3181, \cdot)\) n/a 1216 2
8880.2.bu \(\chi_{8880}(2221, \cdot)\) n/a 1152 2
8880.2.bv \(\chi_{8880}(1259, \cdot)\) n/a 3456 2
8880.2.bz \(\chi_{8880}(1301, \cdot)\) n/a 2432 2
8880.2.ca \(\chi_{8880}(6259, \cdot)\) n/a 1824 2
8880.2.cc \(\chi_{8880}(31, \cdot)\) n/a 304 2
8880.2.ce \(\chi_{8880}(5729, \cdot)\) n/a 904 2
8880.2.cg \(\chi_{8880}(3743, \cdot)\) n/a 912 2
8880.2.ch \(\chi_{8880}(1153, \cdot)\) n/a 456 2
8880.2.cl \(\chi_{8880}(593, \cdot)\) n/a 864 2
8880.2.cm \(\chi_{8880}(1183, \cdot)\) n/a 456 2
8880.2.cn \(\chi_{8880}(1553, \cdot)\) n/a 904 2
8880.2.co \(\chi_{8880}(223, \cdot)\) n/a 432 2
8880.2.cr \(\chi_{8880}(6913, \cdot)\) n/a 456 2
8880.2.cu \(\chi_{8880}(623, \cdot)\) n/a 912 2
8880.2.cv \(\chi_{8880}(667, \cdot)\) n/a 1728 2
8880.2.cy \(\chi_{8880}(1997, \cdot)\) n/a 3632 2
8880.2.cz \(\chi_{8880}(3403, \cdot)\) n/a 1824 2
8880.2.dc \(\chi_{8880}(2813, \cdot)\) n/a 3456 2
8880.2.de \(\chi_{8880}(253, \cdot)\) n/a 1824 2
8880.2.dg \(\chi_{8880}(1067, \cdot)\) n/a 3632 2
8880.2.dh \(\chi_{8880}(1597, \cdot)\) n/a 1824 2
8880.2.dj \(\chi_{8880}(5507, \cdot)\) n/a 3632 2
8880.2.dm \(\chi_{8880}(2843, \cdot)\) n/a 3632 2
8880.2.do \(\chi_{8880}(7357, \cdot)\) n/a 1824 2
8880.2.dp \(\chi_{8880}(4187, \cdot)\) n/a 3632 2
8880.2.dr \(\chi_{8880}(2917, \cdot)\) n/a 1824 2
8880.2.du \(\chi_{8880}(2443, \cdot)\) n/a 1728 2
8880.2.dv \(\chi_{8880}(3773, \cdot)\) n/a 3632 2
8880.2.dy \(\chi_{8880}(1627, \cdot)\) n/a 1824 2
8880.2.dz \(\chi_{8880}(1037, \cdot)\) n/a 3456 2
8880.2.eb \(\chi_{8880}(2473, \cdot)\) None 0 2
8880.2.ee \(\chi_{8880}(5063, \cdot)\) None 0 2
8880.2.eh \(\chi_{8880}(4217, \cdot)\) None 0 2
8880.2.ei \(\chi_{8880}(2887, \cdot)\) None 0 2
8880.2.ej \(\chi_{8880}(3257, \cdot)\) None 0 2
8880.2.ek \(\chi_{8880}(3847, \cdot)\) None 0 2
8880.2.eo \(\chi_{8880}(3287, \cdot)\) None 0 2
8880.2.ep \(\chi_{8880}(697, \cdot)\) None 0 2
8880.2.es \(\chi_{8880}(919, \cdot)\) None 0 2
8880.2.eu \(\chi_{8880}(4841, \cdot)\) None 0 2
8880.2.ex \(\chi_{8880}(6629, \cdot)\) n/a 3632 2
8880.2.ey \(\chi_{8880}(931, \cdot)\) n/a 1216 2
8880.2.ez \(\chi_{8880}(371, \cdot)\) n/a 2304 2
8880.2.fc \(\chi_{8880}(3109, \cdot)\) n/a 1728 2
8880.2.fd \(\chi_{8880}(4069, \cdot)\) n/a 1824 2
8880.2.fg \(\chi_{8880}(1331, \cdot)\) n/a 2432 2
8880.2.fh \(\chi_{8880}(2189, \cdot)\) n/a 3632 2
8880.2.fi \(\chi_{8880}(5371, \cdot)\) n/a 1216 2
8880.2.fl \(\chi_{8880}(5359, \cdot)\) n/a 456 2
8880.2.fn \(\chi_{8880}(401, \cdot)\) n/a 608 2
8880.2.fq \(\chi_{8880}(359, \cdot)\) None 0 2
8880.2.fs \(\chi_{8880}(841, \cdot)\) None 0 2
8880.2.ft \(\chi_{8880}(121, \cdot)\) None 0 2
8880.2.fv \(\chi_{8880}(7559, \cdot)\) None 0 2
8880.2.fz \(\chi_{8880}(3119, \cdot)\) n/a 912 2
8880.2.ga \(\chi_{8880}(3599, \cdot)\) n/a 912 2
8880.2.gc \(\chi_{8880}(4081, \cdot)\) n/a 304 2
8880.2.ge \(\chi_{8880}(2231, \cdot)\) None 0 2
8880.2.gg \(\chi_{8880}(5449, \cdot)\) None 0 2
8880.2.gj \(\chi_{8880}(4969, \cdot)\) None 0 2
8880.2.gl \(\chi_{8880}(2711, \cdot)\) None 0 2
8880.2.gm \(\chi_{8880}(529, \cdot)\) n/a 456 2
8880.2.go \(\chi_{8880}(7151, \cdot)\) n/a 608 2
8880.2.gr \(\chi_{8880}(6671, \cdot)\) n/a 608 2
8880.2.gt \(\chi_{8880}(1009, \cdot)\) n/a 456 2
8880.2.gu \(\chi_{8880}(1681, \cdot)\) n/a 912 6
8880.2.gv \(\chi_{8880}(4121, \cdot)\) None 0 4
8880.2.gx \(\chi_{8880}(199, \cdot)\) None 0 4
8880.2.gz \(\chi_{8880}(4411, \cdot)\) n/a 2432 4
8880.2.ha \(\chi_{8880}(1229, \cdot)\) n/a 7264 4
8880.2.hd \(\chi_{8880}(2749, \cdot)\) n/a 3648 4
8880.2.hg \(\chi_{8880}(11, \cdot)\) n/a 4864 4
8880.2.hh \(\chi_{8880}(491, \cdot)\) n/a 4864 4
8880.2.hk \(\chi_{8880}(3229, \cdot)\) n/a 3648 4
8880.2.hn \(\chi_{8880}(1531, \cdot)\) n/a 2432 4
8880.2.ho \(\chi_{8880}(29, \cdot)\) n/a 7264 4
8880.2.hq \(\chi_{8880}(1361, \cdot)\) n/a 1216 4
8880.2.hs \(\chi_{8880}(319, \cdot)\) n/a 912 4
8880.2.ht \(\chi_{8880}(1007, \cdot)\) n/a 1824 4
8880.2.hw \(\chi_{8880}(97, \cdot)\) n/a 912 4
8880.2.hx \(\chi_{8880}(3007, \cdot)\) n/a 912 4
8880.2.hy \(\chi_{8880}(2897, \cdot)\) n/a 1808 4
8880.2.id \(\chi_{8880}(2527, \cdot)\) n/a 912 4
8880.2.ie \(\chi_{8880}(3377, \cdot)\) n/a 1808 4
8880.2.ig \(\chi_{8880}(193, \cdot)\) n/a 912 4
8880.2.ih \(\chi_{8880}(2783, \cdot)\) n/a 1824 4
8880.2.ij \(\chi_{8880}(677, \cdot)\) n/a 7264 4
8880.2.im \(\chi_{8880}(787, \cdot)\) n/a 3648 4
8880.2.in \(\chi_{8880}(2933, \cdot)\) n/a 7264 4
8880.2.iq \(\chi_{8880}(2083, \cdot)\) n/a 3648 4
8880.2.ir \(\chi_{8880}(3227, \cdot)\) n/a 7264 4
8880.2.it \(\chi_{8880}(2197, \cdot)\) n/a 3648 4
8880.2.iw \(\chi_{8880}(467, \cdot)\) n/a 7264 4
8880.2.iy \(\chi_{8880}(6637, \cdot)\) n/a 3648 4
8880.2.iz \(\chi_{8880}(637, \cdot)\) n/a 3648 4
8880.2.jb \(\chi_{8880}(4787, \cdot)\) n/a 7264 4
8880.2.je \(\chi_{8880}(1213, \cdot)\) n/a 3648 4
8880.2.jg \(\chi_{8880}(347, \cdot)\) n/a 7264 4
8880.2.ji \(\chi_{8880}(2453, \cdot)\) n/a 7264 4
8880.2.jj \(\chi_{8880}(2563, \cdot)\) n/a 3648 4
8880.2.jm \(\chi_{8880}(1157, \cdot)\) n/a 7264 4
8880.2.jn \(\chi_{8880}(307, \cdot)\) n/a 3648 4
8880.2.jq \(\chi_{8880}(1657, \cdot)\) None 0 4
8880.2.jr \(\chi_{8880}(23, \cdot)\) None 0 4
8880.2.jt \(\chi_{8880}(1063, \cdot)\) None 0 4
8880.2.ju \(\chi_{8880}(137, \cdot)\) None 0 4
8880.2.jz \(\chi_{8880}(343, \cdot)\) None 0 4
8880.2.ka \(\chi_{8880}(233, \cdot)\) None 0 4
8880.2.kb \(\chi_{8880}(4343, \cdot)\) None 0 4
8880.2.ke \(\chi_{8880}(1753, \cdot)\) None 0 4
8880.2.kg \(\chi_{8880}(569, \cdot)\) None 0 4
8880.2.ki \(\chi_{8880}(3751, \cdot)\) None 0 4
8880.2.kl \(\chi_{8880}(5299, \cdot)\) n/a 3648 4
8880.2.km \(\chi_{8880}(341, \cdot)\) n/a 4864 4
8880.2.ko \(\chi_{8880}(2341, \cdot)\) n/a 2432 4
8880.2.kp \(\chi_{8880}(1379, \cdot)\) n/a 7264 4
8880.2.ks \(\chi_{8880}(899, \cdot)\) n/a 7264 4
8880.2.kt \(\chi_{8880}(1861, \cdot)\) n/a 2432 4
8880.2.kv \(\chi_{8880}(859, \cdot)\) n/a 3648 4
8880.2.kw \(\chi_{8880}(4781, \cdot)\) n/a 4864 4
8880.2.kz \(\chi_{8880}(689, \cdot)\) n/a 1808 4
8880.2.lb \(\chi_{8880}(991, \cdot)\) n/a 608 4
8880.2.ld \(\chi_{8880}(2879, \cdot)\) n/a 2736 6
8880.2.lh \(\chi_{8880}(4271, \cdot)\) n/a 1824 6
8880.2.li \(\chi_{8880}(289, \cdot)\) n/a 1368 6
8880.2.lk \(\chi_{8880}(49, \cdot)\) n/a 1368 6
8880.2.ln \(\chi_{8880}(1151, \cdot)\) n/a 1824 6
8880.2.lp \(\chi_{8880}(3841, \cdot)\) n/a 912 6
8880.2.lq \(\chi_{8880}(719, \cdot)\) n/a 2736 6
8880.2.ls \(\chi_{8880}(169, \cdot)\) None 0 6
8880.2.lv \(\chi_{8880}(71, \cdot)\) None 0 6
8880.2.lx \(\chi_{8880}(601, \cdot)\) None 0 6
8880.2.ly \(\chi_{8880}(839, \cdot)\) None 0 6
8880.2.ma \(\chi_{8880}(599, \cdot)\) None 0 6
8880.2.md \(\chi_{8880}(361, \cdot)\) None 0 6
8880.2.mf \(\chi_{8880}(1991, \cdot)\) None 0 6
8880.2.mg \(\chi_{8880}(2569, \cdot)\) None 0 6
8880.2.mj \(\chi_{8880}(457, \cdot)\) None 0 12
8880.2.ml \(\chi_{8880}(167, \cdot)\) None 0 12
8880.2.mn \(\chi_{8880}(617, \cdot)\) None 0 12
8880.2.mo \(\chi_{8880}(7, \cdot)\) None 0 12
8880.2.ms \(\chi_{8880}(209, \cdot)\) n/a 5424 12
8880.2.mt \(\chi_{8880}(79, \cdot)\) n/a 2736 12
8880.2.mu \(\chi_{8880}(161, \cdot)\) n/a 3648 12
8880.2.mv \(\chi_{8880}(3391, \cdot)\) n/a 1824 12
8880.2.my \(\chi_{8880}(377, \cdot)\) None 0 12
8880.2.nb \(\chi_{8880}(247, \cdot)\) None 0 12
8880.2.nc \(\chi_{8880}(503, \cdot)\) None 0 12
8880.2.ne \(\chi_{8880}(217, \cdot)\) None 0 12
8880.2.ng \(\chi_{8880}(587, \cdot)\) n/a 21792 12
8880.2.nh \(\chi_{8880}(133, \cdot)\) n/a 10944 12
8880.2.nk \(\chi_{8880}(781, \cdot)\) n/a 7296 12
8880.2.nn \(\chi_{8880}(419, \cdot)\) n/a 21792 12
8880.2.no \(\chi_{8880}(731, \cdot)\) n/a 14592 12
8880.2.nr \(\chi_{8880}(229, \cdot)\) n/a 10944 12
8880.2.ns \(\chi_{8880}(683, \cdot)\) n/a 21792 12
8880.2.nt \(\chi_{8880}(13, \cdot)\) n/a 10944 12
8880.2.ny \(\chi_{8880}(1421, \cdot)\) n/a 14592 12
8880.2.nz \(\chi_{8880}(1051, \cdot)\) n/a 7296 12
8880.2.oa \(\chi_{8880}(19, \cdot)\) n/a 10944 12
8880.2.ob \(\chi_{8880}(389, \cdot)\) n/a 21792 12
8880.2.of \(\chi_{8880}(173, \cdot)\) n/a 21792 12
8880.2.og \(\chi_{8880}(403, \cdot)\) n/a 10944 12
8880.2.oi \(\chi_{8880}(77, \cdot)\) n/a 21792 12
8880.2.ol \(\chi_{8880}(1267, \cdot)\) n/a 10944 12
8880.2.om \(\chi_{8880}(67, \cdot)\) n/a 10944 12
8880.2.op \(\chi_{8880}(53, \cdot)\) n/a 21792 12
8880.2.or \(\chi_{8880}(1843, \cdot)\) n/a 10944 12
8880.2.os \(\chi_{8880}(197, \cdot)\) n/a 21792 12
8880.2.ou \(\chi_{8880}(499, \cdot)\) n/a 10944 12
8880.2.ov \(\chi_{8880}(869, \cdot)\) n/a 21792 12
8880.2.pa \(\chi_{8880}(461, \cdot)\) n/a 14592 12
8880.2.pb \(\chi_{8880}(91, \cdot)\) n/a 7296 12
8880.2.pe \(\chi_{8880}(757, \cdot)\) n/a 10944 12
8880.2.pf \(\chi_{8880}(203, \cdot)\) n/a 21792 12
8880.2.pg \(\chi_{8880}(971, \cdot)\) n/a 14592 12
8880.2.pj \(\chi_{8880}(469, \cdot)\) n/a 10944 12
8880.2.pk \(\chi_{8880}(181, \cdot)\) n/a 7296 12
8880.2.pn \(\chi_{8880}(299, \cdot)\) n/a 21792 12
8880.2.pq \(\chi_{8880}(853, \cdot)\) n/a 10944 12
8880.2.pr \(\chi_{8880}(827, \cdot)\) n/a 21792 12
8880.2.pt \(\chi_{8880}(143, \cdot)\) n/a 5472 12
8880.2.pv \(\chi_{8880}(577, \cdot)\) n/a 2736 12
8880.2.px \(\chi_{8880}(2287, \cdot)\) n/a 2736 12
8880.2.py \(\chi_{8880}(497, \cdot)\) n/a 5424 12
8880.2.qc \(\chi_{8880}(439, \cdot)\) None 0 12
8880.2.qd \(\chi_{8880}(89, \cdot)\) None 0 12
8880.2.qe \(\chi_{8880}(631, \cdot)\) None 0 12
8880.2.qf \(\chi_{8880}(281, \cdot)\) None 0 12
8880.2.qi \(\chi_{8880}(127, \cdot)\) n/a 2736 12
8880.2.ql \(\chi_{8880}(2657, \cdot)\) n/a 5424 12
8880.2.qm \(\chi_{8880}(1297, \cdot)\) n/a 2736 12
8880.2.qo \(\chi_{8880}(383, \cdot)\) n/a 5472 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4440))\)\(^{\oplus 2}\)