# Properties

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

## 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

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