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Properties

Label 4368.2
Level 4368
Weight 2
Dimension 205184
Nonzero newspaces 140
Sturm bound 2064384

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Defining parameters

Level: \( N \) = \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(2064384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4368))\).

Total New Old
Modular forms 524160 207160 317000
Cusp forms 508033 205184 302849
Eisenstein series 16127 1976 14151

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4368))\)

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
4368.2.a \(\chi_{4368}(1, \cdot)\) 4368.2.a.a 1 1
4368.2.a.b 1
4368.2.a.c 1
4368.2.a.d 1
4368.2.a.e 1
4368.2.a.f 1
4368.2.a.g 1
4368.2.a.h 1
4368.2.a.i 1
4368.2.a.j 1
4368.2.a.k 1
4368.2.a.l 1
4368.2.a.m 1
4368.2.a.n 1
4368.2.a.o 1
4368.2.a.p 1
4368.2.a.q 1
4368.2.a.r 1
4368.2.a.s 1
4368.2.a.t 1
4368.2.a.u 1
4368.2.a.v 1
4368.2.a.w 1
4368.2.a.x 1
4368.2.a.y 1
4368.2.a.z 1
4368.2.a.ba 1
4368.2.a.bb 2
4368.2.a.bc 2
4368.2.a.bd 2
4368.2.a.be 2
4368.2.a.bf 2
4368.2.a.bg 2
4368.2.a.bh 2
4368.2.a.bi 2
4368.2.a.bj 2
4368.2.a.bk 2
4368.2.a.bl 2
4368.2.a.bm 3
4368.2.a.bn 3
4368.2.a.bo 3
4368.2.a.bp 3
4368.2.a.bq 3
4368.2.a.br 4
4368.2.a.bs 4
4368.2.b \(\chi_{4368}(727, \cdot)\) None 0 1
4368.2.e \(\chi_{4368}(2575, \cdot)\) 4368.2.e.a 16 1
4368.2.e.b 16
4368.2.e.c 32
4368.2.e.d 32
4368.2.g \(\chi_{4368}(2185, \cdot)\) None 0 1
4368.2.h \(\chi_{4368}(337, \cdot)\) 4368.2.h.a 2 1
4368.2.h.b 2
4368.2.h.c 2
4368.2.h.d 2
4368.2.h.e 2
4368.2.h.f 2
4368.2.h.g 2
4368.2.h.h 2
4368.2.h.i 2
4368.2.h.j 2
4368.2.h.k 2
4368.2.h.l 4
4368.2.h.m 4
4368.2.h.n 4
4368.2.h.o 6
4368.2.h.p 6
4368.2.h.q 8
4368.2.h.r 10
4368.2.h.s 10
4368.2.h.t 10
4368.2.j \(\chi_{4368}(911, \cdot)\) n/a 144 1
4368.2.m \(\chi_{4368}(3431, \cdot)\) None 0 1
4368.2.o \(\chi_{4368}(545, \cdot)\) n/a 220 1
4368.2.p \(\chi_{4368}(2393, \cdot)\) None 0 1
4368.2.s \(\chi_{4368}(1247, \cdot)\) n/a 168 1
4368.2.t \(\chi_{4368}(3095, \cdot)\) None 0 1
4368.2.v \(\chi_{4368}(209, \cdot)\) n/a 192 1
4368.2.y \(\chi_{4368}(2729, \cdot)\) None 0 1
4368.2.ba \(\chi_{4368}(391, \cdot)\) None 0 1
4368.2.bb \(\chi_{4368}(2911, \cdot)\) n/a 112 1
4368.2.bd \(\chi_{4368}(2521, \cdot)\) None 0 1
4368.2.bg \(\chi_{4368}(625, \cdot)\) n/a 192 2
4368.2.bh \(\chi_{4368}(289, \cdot)\) n/a 224 2
4368.2.bi \(\chi_{4368}(1537, \cdot)\) n/a 224 2
4368.2.bj \(\chi_{4368}(3025, \cdot)\) n/a 168 2
4368.2.bk \(\chi_{4368}(3739, \cdot)\) n/a 672 2
4368.2.bn \(\chi_{4368}(3037, \cdot)\) n/a 896 2
4368.2.bo \(\chi_{4368}(83, \cdot)\) n/a 1776 2
4368.2.br \(\chi_{4368}(1373, \cdot)\) n/a 1344 2
4368.2.bs \(\chi_{4368}(671, \cdot)\) n/a 448 2
4368.2.bv \(\chi_{4368}(2003, \cdot)\) n/a 1152 2
4368.2.bw \(\chi_{4368}(155, \cdot)\) n/a 1344 2
4368.2.by \(\chi_{4368}(1175, \cdot)\) None 0 2
4368.2.ca \(\chi_{4368}(967, \cdot)\) None 0 2
4368.2.cc \(\chi_{4368}(1819, \cdot)\) n/a 896 2
4368.2.cf \(\chi_{4368}(1483, \cdot)\) n/a 768 2
4368.2.cg \(\chi_{4368}(463, \cdot)\) n/a 168 2
4368.2.cj \(\chi_{4368}(265, \cdot)\) None 0 2
4368.2.ck \(\chi_{4368}(1429, \cdot)\) n/a 672 2
4368.2.cn \(\chi_{4368}(1093, \cdot)\) n/a 576 2
4368.2.cp \(\chi_{4368}(2449, \cdot)\) n/a 224 2
4368.2.cr \(\chi_{4368}(785, \cdot)\) n/a 336 2
4368.2.ct \(\chi_{4368}(1301, \cdot)\) n/a 1536 2
4368.2.cu \(\chi_{4368}(1637, \cdot)\) n/a 1776 2
4368.2.cx \(\chi_{4368}(281, \cdot)\) None 0 2
4368.2.cz \(\chi_{4368}(1763, \cdot)\) n/a 1776 2
4368.2.da \(\chi_{4368}(3557, \cdot)\) n/a 1344 2
4368.2.dd \(\chi_{4368}(1555, \cdot)\) n/a 672 2
4368.2.de \(\chi_{4368}(853, \cdot)\) n/a 896 2
4368.2.dg \(\chi_{4368}(1049, \cdot)\) None 0 2
4368.2.dj \(\chi_{4368}(881, \cdot)\) n/a 440 2
4368.2.dl \(\chi_{4368}(407, \cdot)\) None 0 2
4368.2.dm \(\chi_{4368}(575, \cdot)\) n/a 336 2
4368.2.do \(\chi_{4368}(673, \cdot)\) n/a 168 2
4368.2.dr \(\chi_{4368}(841, \cdot)\) None 0 2
4368.2.dt \(\chi_{4368}(1231, \cdot)\) n/a 224 2
4368.2.du \(\chi_{4368}(1063, \cdot)\) None 0 2
4368.2.dw \(\chi_{4368}(1193, \cdot)\) None 0 2
4368.2.dz \(\chi_{4368}(2369, \cdot)\) n/a 440 2
4368.2.eb \(\chi_{4368}(263, \cdot)\) None 0 2
4368.2.ec \(\chi_{4368}(3215, \cdot)\) n/a 448 2
4368.2.ef \(\chi_{4368}(2383, \cdot)\) n/a 224 2
4368.2.eg \(\chi_{4368}(1543, \cdot)\) None 0 2
4368.2.ej \(\chi_{4368}(25, \cdot)\) None 0 2
4368.2.el \(\chi_{4368}(2887, \cdot)\) None 0 2
4368.2.eo \(\chi_{4368}(1039, \cdot)\) n/a 224 2
4368.2.er \(\chi_{4368}(1369, \cdot)\) None 0 2
4368.2.et \(\chi_{4368}(3383, \cdot)\) None 0 2
4368.2.eu \(\chi_{4368}(95, \cdot)\) n/a 448 2
4368.2.ex \(\chi_{4368}(2705, \cdot)\) n/a 384 2
4368.2.ey \(\chi_{4368}(857, \cdot)\) None 0 2
4368.2.fa \(\chi_{4368}(1871, \cdot)\) n/a 448 2
4368.2.fd \(\chi_{4368}(599, \cdot)\) None 0 2
4368.2.fe \(\chi_{4368}(2201, \cdot)\) None 0 2
4368.2.fh \(\chi_{4368}(1361, \cdot)\) n/a 440 2
4368.2.fk \(\chi_{4368}(121, \cdot)\) None 0 2
4368.2.fm \(\chi_{4368}(1375, \cdot)\) n/a 224 2
4368.2.fn \(\chi_{4368}(2551, \cdot)\) None 0 2
4368.2.fq \(\chi_{4368}(2305, \cdot)\) n/a 224 2
4368.2.fr \(\chi_{4368}(1465, \cdot)\) None 0 2
4368.2.ft \(\chi_{4368}(367, \cdot)\) n/a 224 2
4368.2.fw \(\chi_{4368}(1447, \cdot)\) None 0 2
4368.2.fx \(\chi_{4368}(23, \cdot)\) None 0 2
4368.2.ga \(\chi_{4368}(1199, \cdot)\) n/a 448 2
4368.2.gb \(\chi_{4368}(3041, \cdot)\) n/a 440 2
4368.2.ge \(\chi_{4368}(521, \cdot)\) None 0 2
4368.2.gg \(\chi_{4368}(1535, \cdot)\) n/a 384 2
4368.2.gh \(\chi_{4368}(935, \cdot)\) None 0 2
4368.2.gk \(\chi_{4368}(1433, \cdot)\) None 0 2
4368.2.gl \(\chi_{4368}(17, \cdot)\) n/a 440 2
4368.2.gn \(\chi_{4368}(1615, \cdot)\) n/a 224 2
4368.2.gq \(\chi_{4368}(199, \cdot)\) None 0 2
4368.2.gr \(\chi_{4368}(2809, \cdot)\) None 0 2
4368.2.gu \(\chi_{4368}(961, \cdot)\) n/a 224 2
4368.2.gw \(\chi_{4368}(103, \cdot)\) None 0 2
4368.2.gx \(\chi_{4368}(703, \cdot)\) n/a 192 2
4368.2.ha \(\chi_{4368}(1297, \cdot)\) n/a 224 2
4368.2.hb \(\chi_{4368}(2473, \cdot)\) None 0 2
4368.2.he \(\chi_{4368}(185, \cdot)\) None 0 2
4368.2.hf \(\chi_{4368}(1265, \cdot)\) n/a 440 2
4368.2.hh \(\chi_{4368}(1031, \cdot)\) None 0 2
4368.2.hk \(\chi_{4368}(191, \cdot)\) n/a 448 2
4368.2.hm \(\chi_{4368}(2857, \cdot)\) None 0 2
4368.2.ho \(\chi_{4368}(3247, \cdot)\) n/a 224 2
4368.2.hr \(\chi_{4368}(55, \cdot)\) None 0 2
4368.2.ht \(\chi_{4368}(3065, \cdot)\) None 0 2
4368.2.hu \(\chi_{4368}(3233, \cdot)\) n/a 440 2
4368.2.hw \(\chi_{4368}(1751, \cdot)\) None 0 2
4368.2.hz \(\chi_{4368}(1583, \cdot)\) n/a 336 2
4368.2.ia \(\chi_{4368}(197, \cdot)\) n/a 2688 4
4368.2.id \(\chi_{4368}(1259, \cdot)\) n/a 3552 4
4368.2.ie \(\chi_{4368}(349, \cdot)\) n/a 1792 4
4368.2.ih \(\chi_{4368}(1051, \cdot)\) n/a 1344 4
4368.2.ij \(\chi_{4368}(2165, \cdot)\) n/a 3552 4
4368.2.ik \(\chi_{4368}(1571, \cdot)\) n/a 3552 4
4368.2.in \(\chi_{4368}(1003, \cdot)\) n/a 1792 4
4368.2.ip \(\chi_{4368}(229, \cdot)\) n/a 1792 4
4368.2.iq \(\chi_{4368}(2179, \cdot)\) n/a 1792 4
4368.2.is \(\chi_{4368}(1333, \cdot)\) n/a 1792 4
4368.2.iv \(\chi_{4368}(2243, \cdot)\) n/a 3552 4
4368.2.ix \(\chi_{4368}(317, \cdot)\) n/a 3552 4
4368.2.iy \(\chi_{4368}(395, \cdot)\) n/a 3552 4
4368.2.ja \(\chi_{4368}(1493, \cdot)\) n/a 3552 4
4368.2.jd \(\chi_{4368}(661, \cdot)\) n/a 1792 4
4368.2.je \(\chi_{4368}(163, \cdot)\) n/a 1792 4
4368.2.jh \(\chi_{4368}(1319, \cdot)\) None 0 4
4368.2.jj \(\chi_{4368}(1115, \cdot)\) n/a 3552 4
4368.2.jk \(\chi_{4368}(107, \cdot)\) n/a 3552 4
4368.2.jn \(\chi_{4368}(1055, \cdot)\) n/a 896 4
4368.2.jp \(\chi_{4368}(319, \cdot)\) n/a 448 4
4368.2.jq \(\chi_{4368}(451, \cdot)\) n/a 1792 4
4368.2.jt \(\chi_{4368}(1291, \cdot)\) n/a 1792 4
4368.2.jv \(\chi_{4368}(487, \cdot)\) None 0 4
4368.2.jx \(\chi_{4368}(617, \cdot)\) None 0 4
4368.2.jz \(\chi_{4368}(965, \cdot)\) n/a 3552 4
4368.2.ka \(\chi_{4368}(797, \cdot)\) n/a 3552 4
4368.2.kd \(\chi_{4368}(449, \cdot)\) n/a 672 4
4368.2.ke \(\chi_{4368}(1409, \cdot)\) n/a 880 4
4368.2.kg \(\chi_{4368}(1241, \cdot)\) None 0 4
4368.2.kj \(\chi_{4368}(101, \cdot)\) n/a 3552 4
4368.2.kl \(\chi_{4368}(1013, \cdot)\) n/a 3552 4
4368.2.km \(\chi_{4368}(677, \cdot)\) n/a 3072 4
4368.2.ko \(\chi_{4368}(1277, \cdot)\) n/a 3552 4
4368.2.kq \(\chi_{4368}(977, \cdot)\) n/a 880 4
4368.2.ks \(\chi_{4368}(473, \cdot)\) None 0 4
4368.2.kv \(\chi_{4368}(97, \cdot)\) n/a 448 4
4368.2.kw \(\chi_{4368}(589, \cdot)\) n/a 1344 4
4368.2.kz \(\chi_{4368}(757, \cdot)\) n/a 1344 4
4368.2.lb \(\chi_{4368}(2281, \cdot)\) None 0 4
4368.2.lc \(\chi_{4368}(73, \cdot)\) None 0 4
4368.2.le \(\chi_{4368}(1489, \cdot)\) n/a 448 4
4368.2.lg \(\chi_{4368}(781, \cdot)\) n/a 1536 4
4368.2.li \(\chi_{4368}(373, \cdot)\) n/a 1792 4
4368.2.ll \(\chi_{4368}(1213, \cdot)\) n/a 1792 4
4368.2.ln \(\chi_{4368}(1117, \cdot)\) n/a 1792 4
4368.2.lo \(\chi_{4368}(1081, \cdot)\) None 0 4
4368.2.lq \(\chi_{4368}(577, \cdot)\) n/a 448 4
4368.2.ls \(\chi_{4368}(799, \cdot)\) n/a 336 4
4368.2.lu \(\chi_{4368}(979, \cdot)\) n/a 1792 4
4368.2.lx \(\chi_{4368}(139, \cdot)\) n/a 1792 4
4368.2.ly \(\chi_{4368}(631, \cdot)\) None 0 4
4368.2.mb \(\chi_{4368}(151, \cdot)\) None 0 4
4368.2.md \(\chi_{4368}(1423, \cdot)\) n/a 448 4
4368.2.me \(\chi_{4368}(1459, \cdot)\) n/a 1792 4
4368.2.mg \(\chi_{4368}(859, \cdot)\) n/a 1536 4
4368.2.mj \(\chi_{4368}(1195, \cdot)\) n/a 1792 4
4368.2.ml \(\chi_{4368}(283, \cdot)\) n/a 1792 4
4368.2.mn \(\chi_{4368}(1159, \cdot)\) None 0 4
4368.2.mp \(\chi_{4368}(655, \cdot)\) n/a 448 4
4368.2.mq \(\chi_{4368}(167, \cdot)\) None 0 4
4368.2.mt \(\chi_{4368}(659, \cdot)\) n/a 2688 4
4368.2.mu \(\chi_{4368}(491, \cdot)\) n/a 2688 4
4368.2.mw \(\chi_{4368}(1007, \cdot)\) n/a 896 4
4368.2.mz \(\chi_{4368}(47, \cdot)\) n/a 896 4
4368.2.nb \(\chi_{4368}(215, \cdot)\) None 0 4
4368.2.nd \(\chi_{4368}(779, \cdot)\) n/a 3552 4
4368.2.nf \(\chi_{4368}(179, \cdot)\) n/a 3552 4
4368.2.ng \(\chi_{4368}(1283, \cdot)\) n/a 3552 4
4368.2.ni \(\chi_{4368}(443, \cdot)\) n/a 3072 4
4368.2.nl \(\chi_{4368}(383, \cdot)\) n/a 896 4
4368.2.nn \(\chi_{4368}(551, \cdot)\) None 0 4
4368.2.no \(\chi_{4368}(145, \cdot)\) n/a 448 4
4368.2.nq \(\chi_{4368}(1381, \cdot)\) n/a 1792 4
4368.2.nt \(\chi_{4368}(205, \cdot)\) n/a 1792 4
4368.2.nu \(\chi_{4368}(409, \cdot)\) None 0 4
4368.2.nw \(\chi_{4368}(137, \cdot)\) None 0 4
4368.2.nz \(\chi_{4368}(1109, \cdot)\) n/a 3552 4
4368.2.oa \(\chi_{4368}(269, \cdot)\) n/a 3552 4
4368.2.oc \(\chi_{4368}(305, \cdot)\) n/a 880 4
4368.2.oe \(\chi_{4368}(397, \cdot)\) n/a 1792 4
4368.2.oh \(\chi_{4368}(67, \cdot)\) n/a 1792 4
4368.2.oi \(\chi_{4368}(59, \cdot)\) n/a 3552 4
4368.2.ok \(\chi_{4368}(1997, \cdot)\) n/a 3552 4
4368.2.on \(\chi_{4368}(2075, \cdot)\) n/a 3552 4
4368.2.op \(\chi_{4368}(821, \cdot)\) n/a 3552 4
4368.2.oq \(\chi_{4368}(1675, \cdot)\) n/a 1792 4
4368.2.os \(\chi_{4368}(1165, \cdot)\) n/a 1792 4
4368.2.ov \(\chi_{4368}(499, \cdot)\) n/a 1792 4
4368.2.ox \(\chi_{4368}(1237, \cdot)\) n/a 1792 4
4368.2.oy \(\chi_{4368}(149, \cdot)\) n/a 3552 4
4368.2.pb \(\chi_{4368}(899, \cdot)\) n/a 3552 4
4368.2.pd \(\chi_{4368}(2533, \cdot)\) n/a 1792 4
4368.2.pe \(\chi_{4368}(379, \cdot)\) n/a 1344 4
4368.2.ph \(\chi_{4368}(869, \cdot)\) n/a 2688 4
4368.2.pi \(\chi_{4368}(587, \cdot)\) n/a 3552 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1092))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4368))\)\(^{\oplus 1}\)