Properties

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

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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

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