Properties

 Label 8568.2 Level 8568 Weight 2 Dimension 840928 Nonzero newspaces 150 Sturm bound 7962624

Defining parameters

 Level: $$N$$ = $$8568 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$150$$ Sturm bound: $$7962624$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8568))$$.

Total New Old
Modular forms 2009088 846328 1162760
Cusp forms 1972225 840928 1131297
Eisenstein series 36863 5400 31463

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8568))$$

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
8568.2.a $$\chi_{8568}(1, \cdot)$$ 8568.2.a.a 1 1
8568.2.a.b 1
8568.2.a.c 1
8568.2.a.d 1
8568.2.a.e 1
8568.2.a.f 1
8568.2.a.g 1
8568.2.a.h 1
8568.2.a.i 1
8568.2.a.j 1
8568.2.a.k 1
8568.2.a.l 1
8568.2.a.m 2
8568.2.a.n 2
8568.2.a.o 2
8568.2.a.p 2
8568.2.a.q 2
8568.2.a.r 2
8568.2.a.s 2
8568.2.a.t 2
8568.2.a.u 2
8568.2.a.v 2
8568.2.a.w 3
8568.2.a.x 3
8568.2.a.y 3
8568.2.a.z 3
8568.2.a.ba 3
8568.2.a.bb 3
8568.2.a.bc 3
8568.2.a.bd 3
8568.2.a.be 3
8568.2.a.bf 4
8568.2.a.bg 4
8568.2.a.bh 4
8568.2.a.bi 4
8568.2.a.bj 4
8568.2.a.bk 4
8568.2.a.bl 4
8568.2.a.bm 5
8568.2.a.bn 7
8568.2.a.bo 7
8568.2.a.bp 7
8568.2.a.bq 7
8568.2.c $$\chi_{8568}(4285, \cdot)$$ n/a 480 1
8568.2.e $$\chi_{8568}(4591, \cdot)$$ None 0 1
8568.2.f $$\chi_{8568}(3331, \cdot)$$ n/a 716 1
8568.2.h $$\chi_{8568}(3025, \cdot)$$ n/a 136 1
8568.2.k $$\chi_{8568}(6425, \cdot)$$ n/a 144 1
8568.2.m $$\chi_{8568}(1835, \cdot)$$ n/a 432 1
8568.2.n $$\chi_{8568}(3095, \cdot)$$ None 0 1
8568.2.p $$\chi_{8568}(7685, \cdot)$$ n/a 512 1
8568.2.r $$\chi_{8568}(3401, \cdot)$$ n/a 128 1
8568.2.t $$\chi_{8568}(7379, \cdot)$$ n/a 384 1
8568.2.w $$\chi_{8568}(6119, \cdot)$$ None 0 1
8568.2.y $$\chi_{8568}(2141, \cdot)$$ n/a 576 1
8568.2.z $$\chi_{8568}(7309, \cdot)$$ n/a 540 1
8568.2.bb $$\chi_{8568}(7615, \cdot)$$ None 0 1
8568.2.be $$\chi_{8568}(307, \cdot)$$ n/a 640 1
8568.2.bg $$\chi_{8568}(1633, \cdot)$$ n/a 768 2
8568.2.bh $$\chi_{8568}(2857, \cdot)$$ n/a 576 2
8568.2.bi $$\chi_{8568}(4897, \cdot)$$ n/a 320 2
8568.2.bj $$\chi_{8568}(4489, \cdot)$$ n/a 768 2
8568.2.bl $$\chi_{8568}(2843, \cdot)$$ n/a 864 2
8568.2.bn $$\chi_{8568}(55, \cdot)$$ None 0 2
8568.2.bp $$\chi_{8568}(2393, \cdot)$$ n/a 288 2
8568.2.br $$\chi_{8568}(3277, \cdot)$$ n/a 1080 2
8568.2.bt $$\chi_{8568}(4033, \cdot)$$ n/a 272 2
8568.2.bv $$\chi_{8568}(3149, \cdot)$$ n/a 1152 2
8568.2.bx $$\chi_{8568}(4339, \cdot)$$ n/a 1432 2
8568.2.bz $$\chi_{8568}(2087, \cdot)$$ None 0 2
8568.2.cb $$\chi_{8568}(2209, \cdot)$$ n/a 864 2
8568.2.cd $$\chi_{8568}(1291, \cdot)$$ n/a 3440 2
8568.2.ce $$\chi_{8568}(2551, \cdot)$$ None 0 2
8568.2.cg $$\chi_{8568}(205, \cdot)$$ n/a 3072 2
8568.2.cj $$\chi_{8568}(3197, \cdot)$$ n/a 3072 2
8568.2.cl $$\chi_{8568}(4727, \cdot)$$ None 0 2
8568.2.cm $$\chi_{8568}(3467, \cdot)$$ n/a 3440 2
8568.2.co $$\chi_{8568}(1937, \cdot)$$ n/a 864 2
8568.2.cr $$\chi_{8568}(271, \cdot)$$ None 0 2
8568.2.ct $$\chi_{8568}(3637, \cdot)$$ n/a 1432 2
8568.2.cu $$\chi_{8568}(3163, \cdot)$$ n/a 3072 2
8568.2.cy $$\chi_{8568}(1123, \cdot)$$ n/a 3072 2
8568.2.db $$\chi_{8568}(1597, \cdot)$$ n/a 2592 2
8568.2.dc $$\chi_{8568}(3127, \cdot)$$ None 0 2
8568.2.de $$\chi_{8568}(373, \cdot)$$ n/a 3440 2
8568.2.dh $$\chi_{8568}(1903, \cdot)$$ None 0 2
8568.2.dj $$\chi_{8568}(1531, \cdot)$$ n/a 1280 2
8568.2.dm $$\chi_{8568}(3707, \cdot)$$ n/a 1024 2
8568.2.do $$\chi_{8568}(4625, \cdot)$$ n/a 256 2
8568.2.dp $$\chi_{8568}(407, \cdot)$$ None 0 2
8568.2.ds $$\chi_{8568}(101, \cdot)$$ n/a 3440 2
8568.2.du $$\chi_{8568}(2039, \cdot)$$ None 0 2
8568.2.dv $$\chi_{8568}(4997, \cdot)$$ n/a 3440 2
8568.2.dy $$\chi_{8568}(545, \cdot)$$ n/a 768 2
8568.2.dz $$\chi_{8568}(3299, \cdot)$$ n/a 3072 2
8568.2.eb $$\chi_{8568}(1361, \cdot)$$ n/a 768 2
8568.2.ee $$\chi_{8568}(1667, \cdot)$$ n/a 2304 2
8568.2.ef $$\chi_{8568}(3365, \cdot)$$ n/a 1152 2
8568.2.eh $$\chi_{8568}(2447, \cdot)$$ None 0 2
8568.2.ej $$\chi_{8568}(611, \cdot)$$ n/a 1152 2
8568.2.el $$\chi_{8568}(1529, \cdot)$$ n/a 288 2
8568.2.eo $$\chi_{8568}(239, \cdot)$$ None 0 2
8568.2.ep $$\chi_{8568}(5645, \cdot)$$ n/a 3072 2
8568.2.er $$\chi_{8568}(2279, \cdot)$$ None 0 2
8568.2.eu $$\chi_{8568}(1973, \cdot)$$ n/a 3072 2
8568.2.ev $$\chi_{8568}(713, \cdot)$$ n/a 864 2
8568.2.ey $$\chi_{8568}(1019, \cdot)$$ n/a 3440 2
8568.2.fa $$\chi_{8568}(4385, \cdot)$$ n/a 864 2
8568.2.fb $$\chi_{8568}(4691, \cdot)$$ n/a 2592 2
8568.2.fe $$\chi_{8568}(341, \cdot)$$ n/a 1024 2
8568.2.fg $$\chi_{8568}(1871, \cdot)$$ None 0 2
8568.2.fh $$\chi_{8568}(5815, \cdot)$$ None 0 2
8568.2.fj $$\chi_{8568}(613, \cdot)$$ n/a 1280 2
8568.2.fm $$\chi_{8568}(475, \cdot)$$ n/a 3440 2
8568.2.fn $$\chi_{8568}(4657, \cdot)$$ n/a 864 2
8568.2.fp $$\chi_{8568}(4147, \cdot)$$ n/a 3440 2
8568.2.fs $$\chi_{8568}(169, \cdot)$$ n/a 648 2
8568.2.ft $$\chi_{8568}(1429, \cdot)$$ n/a 2304 2
8568.2.fw $$\chi_{8568}(103, \cdot)$$ None 0 2
8568.2.fy $$\chi_{8568}(5917, \cdot)$$ n/a 3072 2
8568.2.fz $$\chi_{8568}(1735, \cdot)$$ None 0 2
8568.2.gc $$\chi_{8568}(1801, \cdot)$$ n/a 360 2
8568.2.ge $$\chi_{8568}(4555, \cdot)$$ n/a 1432 2
8568.2.gf $$\chi_{8568}(2957, \cdot)$$ n/a 3440 2
8568.2.gh $$\chi_{8568}(7751, \cdot)$$ None 0 2
8568.2.gk $$\chi_{8568}(443, \cdot)$$ n/a 3072 2
8568.2.gm $$\chi_{8568}(4217, \cdot)$$ n/a 768 2
8568.2.go $$\chi_{8568}(6835, \cdot)$$ n/a 3072 2
8568.2.gr $$\chi_{8568}(5575, \cdot)$$ None 0 2
8568.2.gt $$\chi_{8568}(3229, \cdot)$$ n/a 3440 2
8568.2.gu $$\chi_{8568}(4537, \cdot)$$ n/a 536 4
8568.2.gv $$\chi_{8568}(4843, \cdot)$$ n/a 2864 4
8568.2.gw $$\chi_{8568}(3653, \cdot)$$ n/a 2304 4
8568.2.gx $$\chi_{8568}(1079, \cdot)$$ None 0 4
8568.2.hc $$\chi_{8568}(253, \cdot)$$ n/a 2160 4
8568.2.hd $$\chi_{8568}(559, \cdot)$$ None 0 4
8568.2.he $$\chi_{8568}(1385, \cdot)$$ n/a 576 4
8568.2.hf $$\chi_{8568}(3347, \cdot)$$ n/a 1728 4
8568.2.hk $$\chi_{8568}(89, \cdot)$$ n/a 576 4
8568.2.hm $$\chi_{8568}(2053, \cdot)$$ n/a 2864 4
8568.2.ho $$\chi_{8568}(1619, \cdot)$$ n/a 2304 4
8568.2.hq $$\chi_{8568}(1279, \cdot)$$ None 0 4
8568.2.hs $$\chi_{8568}(293, \cdot)$$ n/a 6880 4
8568.2.hu $$\chi_{8568}(1177, \cdot)$$ n/a 1296 4
8568.2.hw $$\chi_{8568}(191, \cdot)$$ None 0 4
8568.2.hy $$\chi_{8568}(2299, \cdot)$$ n/a 6880 4
8568.2.ib $$\chi_{8568}(1271, \cdot)$$ None 0 4
8568.2.id $$\chi_{8568}(115, \cdot)$$ n/a 6880 4
8568.2.ie $$\chi_{8568}(2189, \cdot)$$ n/a 6880 4
8568.2.ig $$\chi_{8568}(3217, \cdot)$$ n/a 1728 4
8568.2.ij $$\chi_{8568}(1109, \cdot)$$ n/a 6880 4
8568.2.il $$\chi_{8568}(625, \cdot)$$ n/a 1728 4
8568.2.im $$\chi_{8568}(1415, \cdot)$$ None 0 4
8568.2.io $$\chi_{8568}(1483, \cdot)$$ n/a 6880 4
8568.2.iq $$\chi_{8568}(727, \cdot)$$ None 0 4
8568.2.is $$\chi_{8568}(659, \cdot)$$ n/a 5184 4
8568.2.iu $$\chi_{8568}(2461, \cdot)$$ n/a 6880 4
8568.2.iw $$\chi_{8568}(2945, \cdot)$$ n/a 1728 4
8568.2.iz $$\chi_{8568}(1381, \cdot)$$ n/a 6880 4
8568.2.jb $$\chi_{8568}(353, \cdot)$$ n/a 1728 4
8568.2.jc $$\chi_{8568}(1543, \cdot)$$ None 0 4
8568.2.je $$\chi_{8568}(4475, \cdot)$$ n/a 6880 4
8568.2.jh $$\chi_{8568}(871, \cdot)$$ None 0 4
8568.2.jj $$\chi_{8568}(2027, \cdot)$$ n/a 6880 4
8568.2.jk $$\chi_{8568}(421, \cdot)$$ n/a 5184 4
8568.2.jm $$\chi_{8568}(1721, \cdot)$$ n/a 1728 4
8568.2.jo $$\chi_{8568}(523, \cdot)$$ n/a 2864 4
8568.2.jq $$\chi_{8568}(863, \cdot)$$ None 0 4
8568.2.js $$\chi_{8568}(361, \cdot)$$ n/a 720 4
8568.2.ju $$\chi_{8568}(1781, \cdot)$$ n/a 2304 4
8568.2.ka $$\chi_{8568}(379, \cdot)$$ n/a 4320 8
8568.2.kb $$\chi_{8568}(1945, \cdot)$$ n/a 1440 8
8568.2.kc $$\chi_{8568}(755, \cdot)$$ n/a 4608 8
8568.2.kd $$\chi_{8568}(449, \cdot)$$ n/a 864 8
8568.2.ke $$\chi_{8568}(181, \cdot)$$ n/a 5728 8
8568.2.kf $$\chi_{8568}(1639, \cdot)$$ None 0 8
8568.2.kg $$\chi_{8568}(197, \cdot)$$ n/a 3456 8
8568.2.kh $$\chi_{8568}(503, \cdot)$$ None 0 8
8568.2.kq $$\chi_{8568}(19, \cdot)$$ n/a 5728 8
8568.2.kr $$\chi_{8568}(865, \cdot)$$ n/a 1440 8
8568.2.ks $$\chi_{8568}(359, \cdot)$$ None 0 8
8568.2.kt $$\chi_{8568}(773, \cdot)$$ n/a 4608 8
8568.2.ku $$\chi_{8568}(1375, \cdot)$$ None 0 8
8568.2.kv $$\chi_{8568}(1885, \cdot)$$ n/a 13760 8
8568.2.kw $$\chi_{8568}(1283, \cdot)$$ n/a 13760 8
8568.2.kx $$\chi_{8568}(257, \cdot)$$ n/a 3456 8
8568.2.lg $$\chi_{8568}(3109, \cdot)$$ n/a 10368 8
8568.2.lh $$\chi_{8568}(535, \cdot)$$ None 0 8
8568.2.li $$\chi_{8568}(1453, \cdot)$$ n/a 13760 8
8568.2.lj $$\chi_{8568}(223, \cdot)$$ None 0 8
8568.2.lk $$\chi_{8568}(2225, \cdot)$$ n/a 3456 8
8568.2.ll $$\chi_{8568}(4979, \cdot)$$ n/a 13760 8
8568.2.lm $$\chi_{8568}(185, \cdot)$$ n/a 3456 8
8568.2.ln $$\chi_{8568}(155, \cdot)$$ n/a 10368 8
8568.2.ls $$\chi_{8568}(355, \cdot)$$ n/a 13760 8
8568.2.lt $$\chi_{8568}(25, \cdot)$$ n/a 3456 8
8568.2.lu $$\chi_{8568}(263, \cdot)$$ None 0 8
8568.2.lv $$\chi_{8568}(1613, \cdot)$$ n/a 13760 8
8568.2.me $$\chi_{8568}(841, \cdot)$$ n/a 2592 8
8568.2.mf $$\chi_{8568}(2803, \cdot)$$ n/a 13760 8
8568.2.mg $$\chi_{8568}(457, \cdot)$$ n/a 3456 8
8568.2.mh $$\chi_{8568}(1147, \cdot)$$ n/a 13760 8
8568.2.mi $$\chi_{8568}(461, \cdot)$$ n/a 13760 8
8568.2.mj $$\chi_{8568}(695, \cdot)$$ None 0 8
8568.2.mk $$\chi_{8568}(1181, \cdot)$$ n/a 13760 8
8568.2.ml $$\chi_{8568}(1919, \cdot)$$ None 0 8
8568.2.mu $$\chi_{8568}(1783, \cdot)$$ None 0 8
8568.2.mv $$\chi_{8568}(1045, \cdot)$$ n/a 5728 8
8568.2.mw $$\chi_{8568}(179, \cdot)$$ n/a 4608 8
8568.2.mx $$\chi_{8568}(593, \cdot)$$ n/a 1152 8
8568.2.my $$\chi_{8568}(131, \cdot)$$ n/a 27520 16
8568.2.mz $$\chi_{8568}(401, \cdot)$$ n/a 6912 16
8568.2.na $$\chi_{8568}(403, \cdot)$$ n/a 27520 16
8568.2.nb $$\chi_{8568}(241, \cdot)$$ n/a 6912 16
8568.2.ng $$\chi_{8568}(79, \cdot)$$ None 0 16
8568.2.nh $$\chi_{8568}(61, \cdot)$$ n/a 27520 16
8568.2.ni $$\chi_{8568}(311, \cdot)$$ None 0 16
8568.2.nj $$\chi_{8568}(317, \cdot)$$ n/a 27520 16
8568.2.ns $$\chi_{8568}(143, \cdot)$$ None 0 16
8568.2.nt $$\chi_{8568}(989, \cdot)$$ n/a 9216 16
8568.2.nu $$\chi_{8568}(167, \cdot)$$ None 0 16
8568.2.nv $$\chi_{8568}(29, \cdot)$$ n/a 20736 16
8568.2.nw $$\chi_{8568}(415, \cdot)$$ None 0 16
8568.2.nx $$\chi_{8568}(397, \cdot)$$ n/a 11456 16
8568.2.ny $$\chi_{8568}(295, \cdot)$$ None 0 16
8568.2.nz $$\chi_{8568}(517, \cdot)$$ n/a 27520 16
8568.2.oi $$\chi_{8568}(233, \cdot)$$ n/a 2304 16
8568.2.oj $$\chi_{8568}(1907, \cdot)$$ n/a 9216 16
8568.2.ok $$\chi_{8568}(113, \cdot)$$ n/a 5184 16
8568.2.ol $$\chi_{8568}(419, \cdot)$$ n/a 27520 16
8568.2.om $$\chi_{8568}(73, \cdot)$$ n/a 2880 16
8568.2.on $$\chi_{8568}(163, \cdot)$$ n/a 11456 16
8568.2.oo $$\chi_{8568}(97, \cdot)$$ n/a 6912 16
8568.2.op $$\chi_{8568}(211, \cdot)$$ n/a 20736 16
8568.2.oy $$\chi_{8568}(313, \cdot)$$ n/a 6912 16
8568.2.oz $$\chi_{8568}(571, \cdot)$$ n/a 27520 16
8568.2.pa $$\chi_{8568}(65, \cdot)$$ n/a 6912 16
8568.2.pb $$\chi_{8568}(299, \cdot)$$ n/a 27520 16
8568.2.pg $$\chi_{8568}(653, \cdot)$$ n/a 27520 16
8568.2.ph $$\chi_{8568}(479, \cdot)$$ None 0 16
8568.2.pi $$\chi_{8568}(997, \cdot)$$ n/a 27520 16
8568.2.pj $$\chi_{8568}(751, \cdot)$$ None 0 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8568))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8568)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(306))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(408))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(612))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(714))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(952))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1071))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1224))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1428))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2142))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2856))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4284))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8568))$$$$^{\oplus 1}$$