Properties

Label 9240.2
Level 9240
Weight 2
Dimension 803896
Nonzero newspaces 144
Sturm bound 8847360

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Defining parameters

Level: \( N \) = \( 9240 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(8847360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9240))\).

Total New Old
Modular forms 2234880 808216 1426664
Cusp forms 2188801 803896 1384905
Eisenstein series 46079 4320 41759

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9240))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9240.2.a \(\chi_{9240}(1, \cdot)\) 9240.2.a.a 1 1
9240.2.a.b 1
9240.2.a.c 1
9240.2.a.d 1
9240.2.a.e 1
9240.2.a.f 1
9240.2.a.g 1
9240.2.a.h 1
9240.2.a.i 1
9240.2.a.j 1
9240.2.a.k 1
9240.2.a.l 1
9240.2.a.m 1
9240.2.a.n 1
9240.2.a.o 1
9240.2.a.p 1
9240.2.a.q 1
9240.2.a.r 1
9240.2.a.s 1
9240.2.a.t 1
9240.2.a.u 1
9240.2.a.v 1
9240.2.a.w 1
9240.2.a.x 1
9240.2.a.y 1
9240.2.a.z 1
9240.2.a.ba 1
9240.2.a.bb 1
9240.2.a.bc 1
9240.2.a.bd 1
9240.2.a.be 1
9240.2.a.bf 1
9240.2.a.bg 1
9240.2.a.bh 1
9240.2.a.bi 1
9240.2.a.bj 1
9240.2.a.bk 2
9240.2.a.bl 2
9240.2.a.bm 2
9240.2.a.bn 2
9240.2.a.bo 2
9240.2.a.bp 2
9240.2.a.bq 2
9240.2.a.br 2
9240.2.a.bs 2
9240.2.a.bt 2
9240.2.a.bu 2
9240.2.a.bv 2
9240.2.a.bw 2
9240.2.a.bx 3
9240.2.a.by 3
9240.2.a.bz 3
9240.2.a.ca 4
9240.2.a.cb 4
9240.2.a.cc 4
9240.2.a.cd 4
9240.2.a.ce 4
9240.2.a.cf 4
9240.2.a.cg 4
9240.2.a.ch 5
9240.2.a.ci 5
9240.2.a.cj 5
9240.2.a.ck 6
9240.2.j \(\chi_{9240}(769, \cdot)\) n/a 288 1
9240.2.k \(\chi_{9240}(6511, \cdot)\) None 0 1
9240.2.l \(\chi_{9240}(1849, \cdot)\) n/a 176 1
9240.2.m \(\chi_{9240}(6271, \cdot)\) None 0 1
9240.2.n \(\chi_{9240}(2771, \cdot)\) n/a 1536 1
9240.2.o \(\chi_{9240}(7589, \cdot)\) n/a 1728 1
9240.2.p \(\chi_{9240}(3851, \cdot)\) n/a 960 1
9240.2.q \(\chi_{9240}(7349, \cdot)\) n/a 1920 1
9240.2.r \(\chi_{9240}(1079, \cdot)\) None 0 1
9240.2.s \(\chi_{9240}(881, \cdot)\) n/a 320 1
9240.2.t \(\chi_{9240}(9239, \cdot)\) None 0 1
9240.2.u \(\chi_{9240}(1121, \cdot)\) n/a 288 1
9240.2.v \(\chi_{9240}(4621, \cdot)\) n/a 480 1
9240.2.w \(\chi_{9240}(3499, \cdot)\) n/a 960 1
9240.2.x \(\chi_{9240}(3541, \cdot)\) n/a 768 1
9240.2.y \(\chi_{9240}(3739, \cdot)\) n/a 864 1
9240.2.bh \(\chi_{9240}(1651, \cdot)\) n/a 640 1
9240.2.bi \(\chi_{9240}(6469, \cdot)\) n/a 720 1
9240.2.bj \(\chi_{9240}(1891, \cdot)\) n/a 576 1
9240.2.bk \(\chi_{9240}(5389, \cdot)\) n/a 1152 1
9240.2.bl \(\chi_{9240}(2729, \cdot)\) n/a 480 1
9240.2.bm \(\chi_{9240}(8471, \cdot)\) None 0 1
9240.2.bn \(\chi_{9240}(2969, \cdot)\) n/a 432 1
9240.2.bo \(\chi_{9240}(7391, \cdot)\) None 0 1
9240.2.cf \(\chi_{9240}(5741, \cdot)\) n/a 1152 1
9240.2.cg \(\chi_{9240}(4619, \cdot)\) n/a 2288 1
9240.2.ch \(\chi_{9240}(5501, \cdot)\) n/a 1280 1
9240.2.ci \(\chi_{9240}(5699, \cdot)\) n/a 1440 1
9240.2.cj \(\chi_{9240}(8359, \cdot)\) None 0 1
9240.2.ck \(\chi_{9240}(8161, \cdot)\) n/a 192 1
9240.2.cl \(\chi_{9240}(8119, \cdot)\) None 0 1
9240.2.cm \(\chi_{9240}(2641, \cdot)\) n/a 320 2
9240.2.cn \(\chi_{9240}(3233, \cdot)\) n/a 1152 2
9240.2.cp \(\chi_{9240}(1583, \cdot)\) None 0 2
9240.2.cs \(\chi_{9240}(3277, \cdot)\) n/a 1728 2
9240.2.cu \(\chi_{9240}(307, \cdot)\) n/a 2304 2
9240.2.cv \(\chi_{9240}(3037, \cdot)\) n/a 1920 2
9240.2.cx \(\chi_{9240}(1387, \cdot)\) n/a 1440 2
9240.2.da \(\chi_{9240}(617, \cdot)\) n/a 720 2
9240.2.dc \(\chi_{9240}(1343, \cdot)\) None 0 2
9240.2.de \(\chi_{9240}(2113, \cdot)\) n/a 480 2
9240.2.dg \(\chi_{9240}(463, \cdot)\) None 0 2
9240.2.dh \(\chi_{9240}(5237, \cdot)\) n/a 2880 2
9240.2.dj \(\chi_{9240}(2267, \cdot)\) n/a 3840 2
9240.2.dm \(\chi_{9240}(4157, \cdot)\) n/a 4576 2
9240.2.do \(\chi_{9240}(2507, \cdot)\) n/a 3456 2
9240.2.dp \(\chi_{9240}(2353, \cdot)\) n/a 432 2
9240.2.dr \(\chi_{9240}(4927, \cdot)\) None 0 2
9240.2.dt \(\chi_{9240}(841, \cdot)\) n/a 576 4
9240.2.ec \(\chi_{9240}(859, \cdot)\) n/a 1920 2
9240.2.ed \(\chi_{9240}(3301, \cdot)\) n/a 1280 2
9240.2.ee \(\chi_{9240}(2419, \cdot)\) n/a 2304 2
9240.2.ef \(\chi_{9240}(901, \cdot)\) n/a 1536 2
9240.2.eg \(\chi_{9240}(2201, \cdot)\) n/a 640 2
9240.2.eh \(\chi_{9240}(3719, \cdot)\) None 0 2
9240.2.ei \(\chi_{9240}(3761, \cdot)\) n/a 768 2
9240.2.ej \(\chi_{9240}(1319, \cdot)\) None 0 2
9240.2.ek \(\chi_{9240}(989, \cdot)\) n/a 4576 2
9240.2.el \(\chi_{9240}(131, \cdot)\) n/a 3072 2
9240.2.em \(\chi_{9240}(4709, \cdot)\) n/a 3840 2
9240.2.en \(\chi_{9240}(2531, \cdot)\) n/a 2560 2
9240.2.eo \(\chi_{9240}(5191, \cdot)\) None 0 2
9240.2.ep \(\chi_{9240}(2089, \cdot)\) n/a 576 2
9240.2.eq \(\chi_{9240}(3631, \cdot)\) None 0 2
9240.2.er \(\chi_{9240}(529, \cdot)\) n/a 480 2
9240.2.fa \(\chi_{9240}(241, \cdot)\) n/a 384 2
9240.2.fb \(\chi_{9240}(1759, \cdot)\) None 0 2
9240.2.fc \(\chi_{9240}(199, \cdot)\) None 0 2
9240.2.fd \(\chi_{9240}(1979, \cdot)\) n/a 4576 2
9240.2.fe \(\chi_{9240}(4421, \cdot)\) n/a 3072 2
9240.2.ff \(\chi_{9240}(4379, \cdot)\) n/a 3840 2
9240.2.fg \(\chi_{9240}(2861, \cdot)\) n/a 2560 2
9240.2.fx \(\chi_{9240}(1871, \cdot)\) None 0 2
9240.2.fy \(\chi_{9240}(89, \cdot)\) n/a 960 2
9240.2.fz \(\chi_{9240}(4751, \cdot)\) None 0 2
9240.2.ga \(\chi_{9240}(1649, \cdot)\) n/a 1152 2
9240.2.gb \(\chi_{9240}(5149, \cdot)\) n/a 1920 2
9240.2.gc \(\chi_{9240}(2971, \cdot)\) n/a 1280 2
9240.2.gd \(\chi_{9240}(2749, \cdot)\) n/a 2304 2
9240.2.ge \(\chi_{9240}(571, \cdot)\) n/a 1536 2
9240.2.gf \(\chi_{9240}(1499, \cdot)\) n/a 6912 4
9240.2.gg \(\chi_{9240}(1301, \cdot)\) n/a 6144 4
9240.2.gh \(\chi_{9240}(2939, \cdot)\) n/a 9152 4
9240.2.gi \(\chi_{9240}(701, \cdot)\) n/a 4608 4
9240.2.gj \(\chi_{9240}(559, \cdot)\) None 0 4
9240.2.gk \(\chi_{9240}(601, \cdot)\) n/a 768 4
9240.2.gl \(\chi_{9240}(799, \cdot)\) None 0 4
9240.2.hc \(\chi_{9240}(349, \cdot)\) n/a 4608 4
9240.2.hd \(\chi_{9240}(211, \cdot)\) n/a 2304 4
9240.2.he \(\chi_{9240}(2269, \cdot)\) n/a 3456 4
9240.2.hf \(\chi_{9240}(2491, \cdot)\) n/a 3072 4
9240.2.hg \(\chi_{9240}(2351, \cdot)\) None 0 4
9240.2.hh \(\chi_{9240}(1289, \cdot)\) n/a 1728 4
9240.2.hi \(\chi_{9240}(71, \cdot)\) None 0 4
9240.2.hj \(\chi_{9240}(1049, \cdot)\) n/a 2304 4
9240.2.hs \(\chi_{9240}(281, \cdot)\) n/a 1152 4
9240.2.ht \(\chi_{9240}(1679, \cdot)\) None 0 4
9240.2.hu \(\chi_{9240}(1721, \cdot)\) n/a 1536 4
9240.2.hv \(\chi_{9240}(1919, \cdot)\) None 0 4
9240.2.hw \(\chi_{9240}(2059, \cdot)\) n/a 3456 4
9240.2.hx \(\chi_{9240}(1861, \cdot)\) n/a 3072 4
9240.2.hy \(\chi_{9240}(1819, \cdot)\) n/a 4608 4
9240.2.hz \(\chi_{9240}(421, \cdot)\) n/a 2304 4
9240.2.ia \(\chi_{9240}(2071, \cdot)\) None 0 4
9240.2.ib \(\chi_{9240}(169, \cdot)\) n/a 864 4
9240.2.ic \(\chi_{9240}(1471, \cdot)\) None 0 4
9240.2.id \(\chi_{9240}(2449, \cdot)\) n/a 1152 4
9240.2.ie \(\chi_{9240}(3149, \cdot)\) n/a 9152 4
9240.2.if \(\chi_{9240}(2171, \cdot)\) n/a 4608 4
9240.2.ig \(\chi_{9240}(29, \cdot)\) n/a 6912 4
9240.2.ih \(\chi_{9240}(1091, \cdot)\) n/a 6144 4
9240.2.ir \(\chi_{9240}(2333, \cdot)\) n/a 7680 4
9240.2.it \(\chi_{9240}(3323, \cdot)\) n/a 7680 4
9240.2.iu \(\chi_{9240}(3433, \cdot)\) n/a 960 4
9240.2.iw \(\chi_{9240}(3103, \cdot)\) None 0 4
9240.2.iz \(\chi_{9240}(1033, \cdot)\) n/a 1152 4
9240.2.jb \(\chi_{9240}(703, \cdot)\) None 0 4
9240.2.jc \(\chi_{9240}(1517, \cdot)\) n/a 9152 4
9240.2.je \(\chi_{9240}(1187, \cdot)\) n/a 9152 4
9240.2.jg \(\chi_{9240}(373, \cdot)\) n/a 4608 4
9240.2.ji \(\chi_{9240}(1363, \cdot)\) n/a 4608 4
9240.2.jl \(\chi_{9240}(593, \cdot)\) n/a 2304 4
9240.2.jn \(\chi_{9240}(263, \cdot)\) None 0 4
9240.2.jo \(\chi_{9240}(2993, \cdot)\) n/a 1920 4
9240.2.jq \(\chi_{9240}(2663, \cdot)\) None 0 4
9240.2.jt \(\chi_{9240}(397, \cdot)\) n/a 3840 4
9240.2.jv \(\chi_{9240}(67, \cdot)\) n/a 3840 4
9240.2.jw \(\chi_{9240}(361, \cdot)\) n/a 1536 8
9240.2.jy \(\chi_{9240}(1063, \cdot)\) None 0 8
9240.2.ka \(\chi_{9240}(337, \cdot)\) n/a 1728 8
9240.2.kb \(\chi_{9240}(827, \cdot)\) n/a 13824 8
9240.2.kd \(\chi_{9240}(293, \cdot)\) n/a 18304 8
9240.2.kg \(\chi_{9240}(587, \cdot)\) n/a 18304 8
9240.2.ki \(\chi_{9240}(533, \cdot)\) n/a 13824 8
9240.2.kj \(\chi_{9240}(1303, \cdot)\) None 0 8
9240.2.kl \(\chi_{9240}(97, \cdot)\) n/a 2304 8
9240.2.kn \(\chi_{9240}(2183, \cdot)\) None 0 8
9240.2.kp \(\chi_{9240}(113, \cdot)\) n/a 3456 8
9240.2.ks \(\chi_{9240}(883, \cdot)\) n/a 6912 8
9240.2.ku \(\chi_{9240}(1357, \cdot)\) n/a 9216 8
9240.2.kv \(\chi_{9240}(1987, \cdot)\) n/a 9216 8
9240.2.kx \(\chi_{9240}(1597, \cdot)\) n/a 6912 8
9240.2.la \(\chi_{9240}(743, \cdot)\) None 0 8
9240.2.lc \(\chi_{9240}(1217, \cdot)\) n/a 4608 8
9240.2.ld \(\chi_{9240}(569, \cdot)\) n/a 4608 8
9240.2.le \(\chi_{9240}(1151, \cdot)\) None 0 8
9240.2.lf \(\chi_{9240}(929, \cdot)\) n/a 4608 8
9240.2.lg \(\chi_{9240}(191, \cdot)\) None 0 8
9240.2.lh \(\chi_{9240}(2251, \cdot)\) n/a 6144 8
9240.2.li \(\chi_{9240}(1069, \cdot)\) n/a 9216 8
9240.2.lj \(\chi_{9240}(691, \cdot)\) n/a 6144 8
9240.2.lk \(\chi_{9240}(709, \cdot)\) n/a 9216 8
9240.2.mb \(\chi_{9240}(1039, \cdot)\) None 0 8
9240.2.mc \(\chi_{9240}(79, \cdot)\) None 0 8
9240.2.md \(\chi_{9240}(481, \cdot)\) n/a 1536 8
9240.2.me \(\chi_{9240}(1181, \cdot)\) n/a 12288 8
9240.2.mf \(\chi_{9240}(179, \cdot)\) n/a 18304 8
9240.2.mg \(\chi_{9240}(821, \cdot)\) n/a 12288 8
9240.2.mh \(\chi_{9240}(299, \cdot)\) n/a 18304 8
9240.2.mq \(\chi_{9240}(851, \cdot)\) n/a 12288 8
9240.2.mr \(\chi_{9240}(269, \cdot)\) n/a 18304 8
9240.2.ms \(\chi_{9240}(1811, \cdot)\) n/a 12288 8
9240.2.mt \(\chi_{9240}(149, \cdot)\) n/a 18304 8
9240.2.mu \(\chi_{9240}(289, \cdot)\) n/a 2304 8
9240.2.mv \(\chi_{9240}(31, \cdot)\) None 0 8
9240.2.mw \(\chi_{9240}(409, \cdot)\) n/a 2304 8
9240.2.mx \(\chi_{9240}(151, \cdot)\) None 0 8
9240.2.my \(\chi_{9240}(61, \cdot)\) n/a 6144 8
9240.2.mz \(\chi_{9240}(739, \cdot)\) n/a 9216 8
9240.2.na \(\chi_{9240}(1621, \cdot)\) n/a 6144 8
9240.2.nb \(\chi_{9240}(619, \cdot)\) n/a 9216 8
9240.2.nc \(\chi_{9240}(479, \cdot)\) None 0 8
9240.2.nd \(\chi_{9240}(1481, \cdot)\) n/a 3072 8
9240.2.ne \(\chi_{9240}(599, \cdot)\) None 0 8
9240.2.nf \(\chi_{9240}(521, \cdot)\) n/a 3072 8
9240.2.no \(\chi_{9240}(163, \cdot)\) n/a 18432 16
9240.2.nq \(\chi_{9240}(157, \cdot)\) n/a 18432 16
9240.2.nt \(\chi_{9240}(47, \cdot)\) None 0 16
9240.2.nv \(\chi_{9240}(137, \cdot)\) n/a 9216 16
9240.2.nw \(\chi_{9240}(767, \cdot)\) None 0 16
9240.2.ny \(\chi_{9240}(17, \cdot)\) n/a 9216 16
9240.2.ob \(\chi_{9240}(283, \cdot)\) n/a 18432 16
9240.2.od \(\chi_{9240}(277, \cdot)\) n/a 18432 16
9240.2.of \(\chi_{9240}(107, \cdot)\) n/a 36608 16
9240.2.oh \(\chi_{9240}(173, \cdot)\) n/a 36608 16
9240.2.oi \(\chi_{9240}(607, \cdot)\) None 0 16
9240.2.ok \(\chi_{9240}(193, \cdot)\) n/a 4608 16
9240.2.on \(\chi_{9240}(247, \cdot)\) None 0 16
9240.2.op \(\chi_{9240}(313, \cdot)\) n/a 4608 16
9240.2.oq \(\chi_{9240}(467, \cdot)\) n/a 36608 16
9240.2.os \(\chi_{9240}(53, \cdot)\) n/a 36608 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4620))\)\(^{\oplus 2}\)