# Properties

 Label 6840.2 Level 6840 Weight 2 Dimension 503212 Nonzero newspaces 144 Sturm bound 4976640

## Defining parameters

 Level: $$N$$ = $$6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$144$$ Sturm bound: $$4976640$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6840))$$.

Total New Old
Modular forms 1257984 506884 751100
Cusp forms 1230337 503212 727125
Eisenstein series 27647 3672 23975

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6840))$$

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
6840.2.a $$\chi_{6840}(1, \cdot)$$ 6840.2.a.a 1 1
6840.2.a.b 1
6840.2.a.c 1
6840.2.a.d 1
6840.2.a.e 1
6840.2.a.f 1
6840.2.a.g 1
6840.2.a.h 1
6840.2.a.i 1
6840.2.a.j 1
6840.2.a.k 1
6840.2.a.l 1
6840.2.a.m 1
6840.2.a.n 1
6840.2.a.o 1
6840.2.a.p 1
6840.2.a.q 1
6840.2.a.r 1
6840.2.a.s 1
6840.2.a.t 1
6840.2.a.u 1
6840.2.a.v 2
6840.2.a.w 2
6840.2.a.x 2
6840.2.a.y 2
6840.2.a.z 2
6840.2.a.ba 2
6840.2.a.bb 2
6840.2.a.bc 2
6840.2.a.bd 2
6840.2.a.be 3
6840.2.a.bf 3
6840.2.a.bg 3
6840.2.a.bh 3
6840.2.a.bi 3
6840.2.a.bj 3
6840.2.a.bk 3
6840.2.a.bl 3
6840.2.a.bm 3
6840.2.a.bn 3
6840.2.a.bo 3
6840.2.a.bp 4
6840.2.a.bq 4
6840.2.a.br 5
6840.2.a.bs 5
6840.2.c $$\chi_{6840}(1331, \cdot)$$ n/a 288 1
6840.2.d $$\chi_{6840}(2431, \cdot)$$ None 0 1
6840.2.f $$\chi_{6840}(4789, \cdot)$$ n/a 540 1
6840.2.i $$\chi_{6840}(5129, \cdot)$$ n/a 120 1
6840.2.j $$\chi_{6840}(1369, \cdot)$$ n/a 134 1
6840.2.m $$\chi_{6840}(1709, \cdot)$$ n/a 480 1
6840.2.o $$\chi_{6840}(4751, \cdot)$$ None 0 1
6840.2.p $$\chi_{6840}(5851, \cdot)$$ n/a 400 1
6840.2.r $$\chi_{6840}(3761, \cdot)$$ 6840.2.r.a 40 1
6840.2.r.b 40
6840.2.u $$\chi_{6840}(3421, \cdot)$$ n/a 360 1
6840.2.w $$\chi_{6840}(3799, \cdot)$$ None 0 1
6840.2.x $$\chi_{6840}(2699, \cdot)$$ n/a 432 1
6840.2.ba $$\chi_{6840}(379, \cdot)$$ n/a 596 1
6840.2.bb $$\chi_{6840}(6119, \cdot)$$ None 0 1
6840.2.bd $$\chi_{6840}(341, \cdot)$$ n/a 320 1
6840.2.bg $$\chi_{6840}(121, \cdot)$$ n/a 480 2
6840.2.bh $$\chi_{6840}(2281, \cdot)$$ n/a 432 2
6840.2.bi $$\chi_{6840}(2401, \cdot)$$ n/a 480 2
6840.2.bj $$\chi_{6840}(3241, \cdot)$$ n/a 200 2
6840.2.bk $$\chi_{6840}(37, \cdot)$$ n/a 1192 2
6840.2.bn $$\chi_{6840}(343, \cdot)$$ None 0 2
6840.2.bp $$\chi_{6840}(1673, \cdot)$$ n/a 216 2
6840.2.bq $$\chi_{6840}(683, \cdot)$$ n/a 960 2
6840.2.bs $$\chi_{6840}(2357, \cdot)$$ n/a 864 2
6840.2.bv $$\chi_{6840}(1367, \cdot)$$ None 0 2
6840.2.bx $$\chi_{6840}(3457, \cdot)$$ n/a 300 2
6840.2.by $$\chi_{6840}(1027, \cdot)$$ n/a 1080 2
6840.2.ca $$\chi_{6840}(449, \cdot)$$ n/a 240 2
6840.2.cd $$\chi_{6840}(1189, \cdot)$$ n/a 1192 2
6840.2.cf $$\chi_{6840}(4591, \cdot)$$ None 0 2
6840.2.cg $$\chi_{6840}(4571, \cdot)$$ n/a 640 2
6840.2.cj $$\chi_{6840}(1171, \cdot)$$ n/a 800 2
6840.2.ck $$\chi_{6840}(1151, \cdot)$$ None 0 2
6840.2.cm $$\chi_{6840}(3869, \cdot)$$ n/a 960 2
6840.2.cp $$\chi_{6840}(4609, \cdot)$$ n/a 300 2
6840.2.cq $$\chi_{6840}(239, \cdot)$$ None 0 2
6840.2.ct $$\chi_{6840}(259, \cdot)$$ n/a 2864 2
6840.2.cv $$\chi_{6840}(2621, \cdot)$$ n/a 1920 2
6840.2.cy $$\chi_{6840}(221, \cdot)$$ n/a 1920 2
6840.2.da $$\chi_{6840}(2659, \cdot)$$ n/a 2864 2
6840.2.dd $$\chi_{6840}(1679, \cdot)$$ None 0 2
6840.2.de $$\chi_{6840}(1699, \cdot)$$ n/a 2864 2
6840.2.dh $$\chi_{6840}(1559, \cdot)$$ None 0 2
6840.2.dj $$\chi_{6840}(1661, \cdot)$$ n/a 1920 2
6840.2.dm $$\chi_{6840}(2101, \cdot)$$ n/a 1920 2
6840.2.dn $$\chi_{6840}(1361, \cdot)$$ n/a 480 2
6840.2.dp $$\chi_{6840}(1519, \cdot)$$ None 0 2
6840.2.ds $$\chi_{6840}(1379, \cdot)$$ n/a 2864 2
6840.2.dt $$\chi_{6840}(1399, \cdot)$$ None 0 2
6840.2.dw $$\chi_{6840}(419, \cdot)$$ n/a 2592 2
6840.2.dy $$\chi_{6840}(1481, \cdot)$$ n/a 480 2
6840.2.dz $$\chi_{6840}(3541, \cdot)$$ n/a 1920 2
6840.2.ec $$\chi_{6840}(2801, \cdot)$$ n/a 480 2
6840.2.ed $$\chi_{6840}(1141, \cdot)$$ n/a 1728 2
6840.2.ef $$\chi_{6840}(2819, \cdot)$$ n/a 2864 2
6840.2.ei $$\chi_{6840}(2839, \cdot)$$ None 0 2
6840.2.ek $$\chi_{6840}(3029, \cdot)$$ n/a 2864 2
6840.2.el $$\chi_{6840}(49, \cdot)$$ n/a 720 2
6840.2.en $$\chi_{6840}(191, \cdot)$$ None 0 2
6840.2.eq $$\chi_{6840}(331, \cdot)$$ n/a 1920 2
6840.2.er $$\chi_{6840}(311, \cdot)$$ None 0 2
6840.2.eu $$\chi_{6840}(1291, \cdot)$$ n/a 1920 2
6840.2.ew $$\chi_{6840}(3649, \cdot)$$ n/a 648 2
6840.2.ex $$\chi_{6840}(749, \cdot)$$ n/a 2864 2
6840.2.fa $$\chi_{6840}(1489, \cdot)$$ n/a 720 2
6840.2.fb $$\chi_{6840}(3989, \cdot)$$ n/a 2864 2
6840.2.fd $$\chi_{6840}(4891, \cdot)$$ n/a 1920 2
6840.2.fg $$\chi_{6840}(4871, \cdot)$$ None 0 2
6840.2.fh $$\chi_{6840}(1471, \cdot)$$ None 0 2
6840.2.fk $$\chi_{6840}(1451, \cdot)$$ n/a 1920 2
6840.2.fm $$\chi_{6840}(229, \cdot)$$ n/a 2592 2
6840.2.fn $$\chi_{6840}(4169, \cdot)$$ n/a 720 2
6840.2.fq $$\chi_{6840}(4909, \cdot)$$ n/a 2864 2
6840.2.fr $$\chi_{6840}(569, \cdot)$$ n/a 720 2
6840.2.ft $$\chi_{6840}(3611, \cdot)$$ n/a 1728 2
6840.2.fw $$\chi_{6840}(31, \cdot)$$ None 0 2
6840.2.fx $$\chi_{6840}(11, \cdot)$$ n/a 1920 2
6840.2.ga $$\chi_{6840}(151, \cdot)$$ None 0 2
6840.2.gc $$\chi_{6840}(2729, \cdot)$$ n/a 720 2
6840.2.gd $$\chi_{6840}(349, \cdot)$$ n/a 2864 2
6840.2.gg $$\chi_{6840}(539, \cdot)$$ n/a 960 2
6840.2.gh $$\chi_{6840}(559, \cdot)$$ None 0 2
6840.2.gj $$\chi_{6840}(1261, \cdot)$$ n/a 800 2
6840.2.gm $$\chi_{6840}(521, \cdot)$$ n/a 160 2
6840.2.gp $$\chi_{6840}(2501, \cdot)$$ n/a 640 2
6840.2.gr $$\chi_{6840}(2519, \cdot)$$ None 0 2
6840.2.gs $$\chi_{6840}(2539, \cdot)$$ n/a 1192 2
6840.2.gu $$\chi_{6840}(1081, \cdot)$$ n/a 600 6
6840.2.gv $$\chi_{6840}(841, \cdot)$$ n/a 1440 6
6840.2.gw $$\chi_{6840}(481, \cdot)$$ n/a 1440 6
6840.2.gy $$\chi_{6840}(107, \cdot)$$ n/a 1920 4
6840.2.gz $$\chi_{6840}(2177, \cdot)$$ n/a 480 4
6840.2.hb $$\chi_{6840}(847, \cdot)$$ None 0 4
6840.2.he $$\chi_{6840}(2197, \cdot)$$ n/a 2384 4
6840.2.hf $$\chi_{6840}(653, \cdot)$$ n/a 5728 4
6840.2.hi $$\chi_{6840}(407, \cdot)$$ None 0 4
6840.2.hl $$\chi_{6840}(1483, \cdot)$$ n/a 5184 4
6840.2.hm $$\chi_{6840}(2443, \cdot)$$ n/a 5728 4
6840.2.hn $$\chi_{6840}(1177, \cdot)$$ n/a 1440 4
6840.2.ho $$\chi_{6840}(2497, \cdot)$$ n/a 1440 4
6840.2.hr $$\chi_{6840}(1823, \cdot)$$ None 0 4
6840.2.hs $$\chi_{6840}(1703, \cdot)$$ None 0 4
6840.2.hx $$\chi_{6840}(77, \cdot)$$ n/a 5184 4
6840.2.hy $$\chi_{6840}(2477, \cdot)$$ n/a 5728 4
6840.2.ia $$\chi_{6840}(673, \cdot)$$ n/a 1440 4
6840.2.ib $$\chi_{6840}(1147, \cdot)$$ n/a 5728 4
6840.2.id $$\chi_{6840}(373, \cdot)$$ n/a 5728 4
6840.2.ig $$\chi_{6840}(463, \cdot)$$ None 0 4
6840.2.ij $$\chi_{6840}(227, \cdot)$$ n/a 5728 4
6840.2.ik $$\chi_{6840}(2003, \cdot)$$ n/a 5728 4
6840.2.il $$\chi_{6840}(1217, \cdot)$$ n/a 1296 4
6840.2.im $$\chi_{6840}(1793, \cdot)$$ n/a 1440 4
6840.2.ip $$\chi_{6840}(2167, \cdot)$$ None 0 4
6840.2.iq $$\chi_{6840}(7, \cdot)$$ None 0 4
6840.2.iv $$\chi_{6840}(493, \cdot)$$ n/a 5728 4
6840.2.iw $$\chi_{6840}(1813, \cdot)$$ n/a 5728 4
6840.2.iy $$\chi_{6840}(353, \cdot)$$ n/a 1440 4
6840.2.iz $$\chi_{6840}(563, \cdot)$$ n/a 5728 4
6840.2.jc $$\chi_{6840}(163, \cdot)$$ n/a 2384 4
6840.2.jd $$\chi_{6840}(217, \cdot)$$ n/a 600 4
6840.2.jf $$\chi_{6840}(863, \cdot)$$ None 0 4
6840.2.ji $$\chi_{6840}(197, \cdot)$$ n/a 1920 4
6840.2.jj $$\chi_{6840}(169, \cdot)$$ n/a 2160 6
6840.2.jm $$\chi_{6840}(2131, \cdot)$$ n/a 5760 6
6840.2.jn $$\chi_{6840}(509, \cdot)$$ n/a 8592 6
6840.2.jq $$\chi_{6840}(671, \cdot)$$ None 0 6
6840.2.jr $$\chi_{6840}(751, \cdot)$$ None 0 6
6840.2.ju $$\chi_{6840}(1069, \cdot)$$ n/a 8592 6
6840.2.jv $$\chi_{6840}(2171, \cdot)$$ n/a 5760 6
6840.2.jy $$\chi_{6840}(2009, \cdot)$$ n/a 2160 6
6840.2.ka $$\chi_{6840}(41, \cdot)$$ n/a 1440 6
6840.2.kb $$\chi_{6840}(1499, \cdot)$$ n/a 8592 6
6840.2.ke $$\chi_{6840}(61, \cdot)$$ n/a 5760 6
6840.2.kf $$\chi_{6840}(679, \cdot)$$ None 0 6
6840.2.ki $$\chi_{6840}(1459, \cdot)$$ n/a 3576 6
6840.2.kl $$\chi_{6840}(359, \cdot)$$ None 0 6
6840.2.km $$\chi_{6840}(1421, \cdot)$$ n/a 1920 6
6840.2.kp $$\chi_{6840}(541, \cdot)$$ n/a 2400 6
6840.2.kq $$\chi_{6840}(2359, \cdot)$$ None 0 6
6840.2.kt $$\chi_{6840}(2321, \cdot)$$ n/a 480 6
6840.2.ku $$\chi_{6840}(899, \cdot)$$ n/a 2880 6
6840.2.kx $$\chi_{6840}(479, \cdot)$$ None 0 6
6840.2.ky $$\chi_{6840}(3461, \cdot)$$ n/a 5760 6
6840.2.lb $$\chi_{6840}(979, \cdot)$$ n/a 8592 6
6840.2.le $$\chi_{6840}(131, \cdot)$$ n/a 5760 6
6840.2.lf $$\chi_{6840}(1409, \cdot)$$ n/a 2160 6
6840.2.li $$\chi_{6840}(1231, \cdot)$$ None 0 6
6840.2.lj $$\chi_{6840}(709, \cdot)$$ n/a 8592 6
6840.2.lm $$\chi_{6840}(289, \cdot)$$ n/a 900 6
6840.2.ln $$\chi_{6840}(91, \cdot)$$ n/a 2400 6
6840.2.lq $$\chi_{6840}(269, \cdot)$$ n/a 2880 6
6840.2.lr $$\chi_{6840}(1871, \cdot)$$ None 0 6
6840.2.lu $$\chi_{6840}(991, \cdot)$$ None 0 6
6840.2.lv $$\chi_{6840}(1909, \cdot)$$ n/a 3576 6
6840.2.ly $$\chi_{6840}(251, \cdot)$$ n/a 1920 6
6840.2.lz $$\chi_{6840}(89, \cdot)$$ n/a 720 6
6840.2.mc $$\chi_{6840}(29, \cdot)$$ n/a 8592 6
6840.2.md $$\chi_{6840}(1031, \cdot)$$ None 0 6
6840.2.mg $$\chi_{6840}(2209, \cdot)$$ n/a 2160 6
6840.2.mh $$\chi_{6840}(211, \cdot)$$ n/a 5760 6
6840.2.mj $$\chi_{6840}(3499, \cdot)$$ n/a 8592 6
6840.2.mm $$\chi_{6840}(119, \cdot)$$ None 0 6
6840.2.mp $$\chi_{6840}(941, \cdot)$$ n/a 5760 6
6840.2.mq $$\chi_{6840}(2221, \cdot)$$ n/a 5760 6
6840.2.mt $$\chi_{6840}(79, \cdot)$$ None 0 6
6840.2.mu $$\chi_{6840}(641, \cdot)$$ n/a 1440 6
6840.2.mx $$\chi_{6840}(3539, \cdot)$$ n/a 8592 6
6840.2.mz $$\chi_{6840}(367, \cdot)$$ None 0 12
6840.2.na $$\chi_{6840}(637, \cdot)$$ n/a 17184 12
6840.2.nd $$\chi_{6840}(137, \cdot)$$ n/a 4320 12
6840.2.ne $$\chi_{6840}(1067, \cdot)$$ n/a 17184 12
6840.2.ng $$\chi_{6840}(167, \cdot)$$ None 0 12
6840.2.nj $$\chi_{6840}(1013, \cdot)$$ n/a 17184 12
6840.2.nl $$\chi_{6840}(143, \cdot)$$ None 0 12
6840.2.nm $$\chi_{6840}(557, \cdot)$$ n/a 5760 12
6840.2.no $$\chi_{6840}(97, \cdot)$$ n/a 4320 12
6840.2.nr $$\chi_{6840}(43, \cdot)$$ n/a 17184 12
6840.2.nt $$\chi_{6840}(433, \cdot)$$ n/a 1800 12
6840.2.nu $$\chi_{6840}(883, \cdot)$$ n/a 7152 12
6840.2.nx $$\chi_{6840}(617, \cdot)$$ n/a 4320 12
6840.2.ny $$\chi_{6840}(203, \cdot)$$ n/a 17184 12
6840.2.oa $$\chi_{6840}(17, \cdot)$$ n/a 1440 12
6840.2.od $$\chi_{6840}(827, \cdot)$$ n/a 5760 12
6840.2.of $$\chi_{6840}(727, \cdot)$$ None 0 12
6840.2.og $$\chi_{6840}(13, \cdot)$$ n/a 17184 12
6840.2.oi $$\chi_{6840}(1423, \cdot)$$ None 0 12
6840.2.ol $$\chi_{6840}(1117, \cdot)$$ n/a 7152 12
6840.2.om $$\chi_{6840}(193, \cdot)$$ n/a 4320 12
6840.2.op $$\chi_{6840}(283, \cdot)$$ n/a 17184 12
6840.2.oq $$\chi_{6840}(383, \cdot)$$ None 0 12
6840.2.ot $$\chi_{6840}(1157, \cdot)$$ n/a 17184 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6840))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6840)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(684))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(855))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1140))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1368))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1710))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2280))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3420))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6840))$$$$^{\oplus 1}$$