# Properties

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

## 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

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