# Properties

 Label 8008.2 Level 8008 Weight 2 Dimension 1.00972e+06 Nonzero newspaces 180 Sturm bound 7.74144e+06

## Defining parameters

 Level: $$N$$ = $$8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$180$$ Sturm bound: $$7741440$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8008))$$.

Total New Old
Modular forms 1952640 1017640 935000
Cusp forms 1918081 1009720 908361
Eisenstein series 34559 7920 26639

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8008))$$

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
8008.2.a $$\chi_{8008}(1, \cdot)$$ 8008.2.a.a 1 1
8008.2.a.b 1
8008.2.a.c 1
8008.2.a.d 1
8008.2.a.e 1
8008.2.a.f 2
8008.2.a.g 2
8008.2.a.h 2
8008.2.a.i 3
8008.2.a.j 5
8008.2.a.k 6
8008.2.a.l 8
8008.2.a.m 9
8008.2.a.n 9
8008.2.a.o 9
8008.2.a.p 9
8008.2.a.q 9
8008.2.a.r 9
8008.2.a.s 10
8008.2.a.t 10
8008.2.a.u 10
8008.2.a.v 11
8008.2.a.w 11
8008.2.a.x 12
8008.2.a.y 14
8008.2.a.z 15
8008.2.b $$\chi_{8008}(3431, \cdot)$$ None 0 1
8008.2.d $$\chi_{8008}(4731, \cdot)$$ n/a 1120 1
8008.2.g $$\chi_{8008}(4005, \cdot)$$ n/a 720 1
8008.2.i $$\chi_{8008}(3849, \cdot)$$ n/a 288 1
8008.2.j $$\chi_{8008}(6579, \cdot)$$ n/a 960 1
8008.2.l $$\chi_{8008}(5279, \cdot)$$ None 0 1
8008.2.o $$\chi_{8008}(2001, \cdot)$$ n/a 336 1
8008.2.q $$\chi_{8008}(2157, \cdot)$$ n/a 840 1
8008.2.r $$\chi_{8008}(1275, \cdot)$$ n/a 864 1
8008.2.t $$\chi_{8008}(2575, \cdot)$$ None 0 1
8008.2.w $$\chi_{8008}(6161, \cdot)$$ n/a 212 1
8008.2.y $$\chi_{8008}(6005, \cdot)$$ n/a 1336 1
8008.2.z $$\chi_{8008}(727, \cdot)$$ None 0 1
8008.2.bb $$\chi_{8008}(7435, \cdot)$$ n/a 1008 1
8008.2.be $$\chi_{8008}(7853, \cdot)$$ n/a 1152 1
8008.2.bg $$\chi_{8008}(529, \cdot)$$ n/a 560 2
8008.2.bh $$\chi_{8008}(1145, \cdot)$$ n/a 480 2
8008.2.bi $$\chi_{8008}(1849, \cdot)$$ n/a 416 2
8008.2.bj $$\chi_{8008}(2993, \cdot)$$ n/a 560 2
8008.2.bm $$\chi_{8008}(307, \cdot)$$ n/a 2672 2
8008.2.bn $$\chi_{8008}(463, \cdot)$$ None 0 2
8008.2.bo $$\chi_{8008}(5741, \cdot)$$ n/a 2016 2
8008.2.bp $$\chi_{8008}(265, \cdot)$$ n/a 560 2
8008.2.bu $$\chi_{8008}(4467, \cdot)$$ n/a 1680 2
8008.2.bv $$\chi_{8008}(4311, \cdot)$$ None 0 2
8008.2.bw $$\chi_{8008}(3037, \cdot)$$ n/a 2240 2
8008.2.bx $$\chi_{8008}(1737, \cdot)$$ n/a 504 2
8008.2.ca $$\chi_{8008}(729, \cdot)$$ n/a 864 4
8008.2.cb $$\chi_{8008}(4905, \cdot)$$ n/a 672 2
8008.2.cd $$\chi_{8008}(485, \cdot)$$ n/a 2240 2
8008.2.cg $$\chi_{8008}(243, \cdot)$$ n/a 2240 2
8008.2.ci $$\chi_{8008}(263, \cdot)$$ None 0 2
8008.2.cj $$\chi_{8008}(1101, \cdot)$$ n/a 2240 2
8008.2.cl $$\chi_{8008}(4553, \cdot)$$ n/a 672 2
8008.2.co $$\chi_{8008}(1759, \cdot)$$ None 0 2
8008.2.cq $$\chi_{8008}(1739, \cdot)$$ n/a 2240 2
8008.2.cr $$\chi_{8008}(4157, \cdot)$$ n/a 2672 2
8008.2.ct $$\chi_{8008}(4313, \cdot)$$ n/a 424 2
8008.2.cw $$\chi_{8008}(1959, \cdot)$$ None 0 2
8008.2.cy $$\chi_{8008}(659, \cdot)$$ n/a 2016 2
8008.2.cz $$\chi_{8008}(1187, \cdot)$$ n/a 2672 2
8008.2.db $$\chi_{8008}(199, \cdot)$$ None 0 2
8008.2.df $$\chi_{8008}(3981, \cdot)$$ n/a 2672 2
8008.2.dh $$\chi_{8008}(2133, \cdot)$$ n/a 2304 2
8008.2.dk $$\chi_{8008}(571, \cdot)$$ n/a 2672 2
8008.2.dm $$\chi_{8008}(3015, \cdot)$$ None 0 2
8008.2.dn $$\chi_{8008}(285, \cdot)$$ n/a 2672 2
8008.2.dp $$\chi_{8008}(3873, \cdot)$$ n/a 560 2
8008.2.ds $$\chi_{8008}(1431, \cdot)$$ None 0 2
8008.2.du $$\chi_{8008}(2419, \cdot)$$ n/a 2304 2
8008.2.dv $$\chi_{8008}(815, \cdot)$$ None 0 2
8008.2.dx $$\chi_{8008}(835, \cdot)$$ n/a 2672 2
8008.2.ea $$\chi_{8008}(5477, \cdot)$$ n/a 2672 2
8008.2.ec $$\chi_{8008}(2025, \cdot)$$ n/a 560 2
8008.2.ee $$\chi_{8008}(1693, \cdot)$$ n/a 2672 2
8008.2.eh $$\chi_{8008}(43, \cdot)$$ n/a 2016 2
8008.2.ej $$\chi_{8008}(1343, \cdot)$$ None 0 2
8008.2.ek $$\chi_{8008}(3233, \cdot)$$ n/a 672 2
8008.2.em $$\chi_{8008}(3389, \cdot)$$ n/a 1680 2
8008.2.ep $$\chi_{8008}(2883, \cdot)$$ n/a 2240 2
8008.2.er $$\chi_{8008}(1583, \cdot)$$ None 0 2
8008.2.es $$\chi_{8008}(3301, \cdot)$$ n/a 2240 2
8008.2.eu $$\chi_{8008}(857, \cdot)$$ n/a 672 2
8008.2.ex $$\chi_{8008}(2991, \cdot)$$ None 0 2
8008.2.ez $$\chi_{8008}(859, \cdot)$$ n/a 1920 2
8008.2.fa $$\chi_{8008}(4839, \cdot)$$ None 0 2
8008.2.fc $$\chi_{8008}(2707, \cdot)$$ n/a 2240 2
8008.2.ff $$\chi_{8008}(3917, \cdot)$$ n/a 2240 2
8008.2.fh $$\chi_{8008}(1473, \cdot)$$ n/a 672 2
8008.2.fi $$\chi_{8008}(4203, \cdot)$$ n/a 2240 2
8008.2.fk $$\chi_{8008}(5191, \cdot)$$ None 0 2
8008.2.fn $$\chi_{8008}(2089, \cdot)$$ n/a 672 2
8008.2.fp $$\chi_{8008}(3565, \cdot)$$ n/a 2240 2
8008.2.fq $$\chi_{8008}(2705, \cdot)$$ n/a 576 2
8008.2.fs $$\chi_{8008}(1717, \cdot)$$ n/a 1920 2
8008.2.fv $$\chi_{8008}(3587, \cdot)$$ n/a 2240 2
8008.2.fx $$\chi_{8008}(1143, \cdot)$$ None 0 2
8008.2.fy $$\chi_{8008}(309, \cdot)$$ n/a 1680 2
8008.2.ga $$\chi_{8008}(153, \cdot)$$ n/a 672 2
8008.2.gd $$\chi_{8008}(4663, \cdot)$$ None 0 2
8008.2.gf $$\chi_{8008}(419, \cdot)$$ n/a 2240 2
8008.2.gg $$\chi_{8008}(549, \cdot)$$ n/a 2672 2
8008.2.gk $$\chi_{8008}(3631, \cdot)$$ None 0 2
8008.2.gm $$\chi_{8008}(5763, \cdot)$$ n/a 2672 2
8008.2.gn $$\chi_{8008}(4489, \cdot)$$ n/a 560 2
8008.2.gp $$\chi_{8008}(901, \cdot)$$ n/a 2672 2
8008.2.gs $$\chi_{8008}(4267, \cdot)$$ n/a 2672 2
8008.2.gu $$\chi_{8008}(3279, \cdot)$$ None 0 2
8008.2.gx $$\chi_{8008}(2757, \cdot)$$ n/a 4608 4
8008.2.gy $$\chi_{8008}(2339, \cdot)$$ n/a 4032 4
8008.2.ha $$\chi_{8008}(1455, \cdot)$$ None 0 4
8008.2.hd $$\chi_{8008}(909, \cdot)$$ n/a 5344 4
8008.2.hf $$\chi_{8008}(1065, \cdot)$$ n/a 1008 4
8008.2.hg $$\chi_{8008}(3303, \cdot)$$ None 0 4
8008.2.hi $$\chi_{8008}(547, \cdot)$$ n/a 3456 4
8008.2.hl $$\chi_{8008}(2885, \cdot)$$ n/a 4032 4
8008.2.hn $$\chi_{8008}(545, \cdot)$$ n/a 1344 4
8008.2.ho $$\chi_{8008}(183, \cdot)$$ None 0 4
8008.2.hq $$\chi_{8008}(27, \cdot)$$ n/a 4608 4
8008.2.ht $$\chi_{8008}(937, \cdot)$$ n/a 1152 4
8008.2.hv $$\chi_{8008}(1093, \cdot)$$ n/a 3456 4
8008.2.hw $$\chi_{8008}(1819, \cdot)$$ n/a 5344 4
8008.2.hy $$\chi_{8008}(519, \cdot)$$ None 0 4
8008.2.ic $$\chi_{8008}(353, \cdot)$$ n/a 1120 4
8008.2.id $$\chi_{8008}(1341, \cdot)$$ n/a 5344 4
8008.2.ie $$\chi_{8008}(375, \cdot)$$ None 0 4
8008.2.if $$\chi_{8008}(747, \cdot)$$ n/a 5344 4
8008.2.ik $$\chi_{8008}(1055, \cdot)$$ None 0 4
8008.2.il $$\chi_{8008}(683, \cdot)$$ n/a 4480 4
8008.2.iq $$\chi_{8008}(1189, \cdot)$$ n/a 4480 4
8008.2.ir $$\chi_{8008}(505, \cdot)$$ n/a 1008 4
8008.2.is $$\chi_{8008}(681, \cdot)$$ n/a 1344 4
8008.2.it $$\chi_{8008}(1893, \cdot)$$ n/a 4480 4
8008.2.iu $$\chi_{8008}(2619, \cdot)$$ n/a 3360 4
8008.2.iv $$\chi_{8008}(2463, \cdot)$$ None 0 4
8008.2.iw $$\chi_{8008}(3167, \cdot)$$ None 0 4
8008.2.ix $$\chi_{8008}(2179, \cdot)$$ n/a 4480 4
8008.2.jc $$\chi_{8008}(1033, \cdot)$$ n/a 1344 4
8008.2.jd $$\chi_{8008}(45, \cdot)$$ n/a 4480 4
8008.2.ji $$\chi_{8008}(639, \cdot)$$ None 0 4
8008.2.jj $$\chi_{8008}(1363, \cdot)$$ n/a 5344 4
8008.2.jo $$\chi_{8008}(197, \cdot)$$ n/a 4032 4
8008.2.jp $$\chi_{8008}(1497, \cdot)$$ n/a 1120 4
8008.2.jq $$\chi_{8008}(1321, \cdot)$$ n/a 1120 4
8008.2.jr $$\chi_{8008}(109, \cdot)$$ n/a 5344 4
8008.2.js $$\chi_{8008}(2771, \cdot)$$ n/a 5344 4
8008.2.jt $$\chi_{8008}(2927, \cdot)$$ None 0 4
8008.2.ju $$\chi_{8008}(1607, \cdot)$$ None 0 4
8008.2.jv $$\chi_{8008}(395, \cdot)$$ n/a 5344 4
8008.2.ka $$\chi_{8008}(89, \cdot)$$ n/a 1120 4
8008.2.kb $$\chi_{8008}(1957, \cdot)$$ n/a 5344 4
8008.2.kg $$\chi_{8008}(1649, \cdot)$$ n/a 1344 4
8008.2.kh $$\chi_{8008}(397, \cdot)$$ n/a 4480 4
8008.2.ki $$\chi_{8008}(1671, \cdot)$$ None 0 4
8008.2.kj $$\chi_{8008}(67, \cdot)$$ n/a 4480 4
8008.2.km $$\chi_{8008}(9, \cdot)$$ n/a 2688 8
8008.2.kn $$\chi_{8008}(113, \cdot)$$ n/a 2016 8
8008.2.ko $$\chi_{8008}(625, \cdot)$$ n/a 2304 8
8008.2.kp $$\chi_{8008}(289, \cdot)$$ n/a 2688 8
8008.2.kq $$\chi_{8008}(57, \cdot)$$ n/a 2016 8
8008.2.kr $$\chi_{8008}(125, \cdot)$$ n/a 10688 8
8008.2.kw $$\chi_{8008}(447, \cdot)$$ None 0 8
8008.2.kx $$\chi_{8008}(603, \cdot)$$ n/a 8064 8
8008.2.ky $$\chi_{8008}(489, \cdot)$$ n/a 2688 8
8008.2.kz $$\chi_{8008}(645, \cdot)$$ n/a 8064 8
8008.2.le $$\chi_{8008}(1191, \cdot)$$ None 0 8
8008.2.lf $$\chi_{8008}(83, \cdot)$$ n/a 10688 8
8008.2.lh $$\chi_{8008}(367, \cdot)$$ None 0 8
8008.2.lj $$\chi_{8008}(1283, \cdot)$$ n/a 10688 8
8008.2.lk $$\chi_{8008}(101, \cdot)$$ n/a 10688 8
8008.2.lm $$\chi_{8008}(361, \cdot)$$ n/a 2688 8
8008.2.lp $$\chi_{8008}(667, \cdot)$$ n/a 10688 8
8008.2.lr $$\chi_{8008}(647, \cdot)$$ None 0 8
8008.2.lt $$\chi_{8008}(61, \cdot)$$ n/a 10688 8
8008.2.lw $$\chi_{8008}(867, \cdot)$$ n/a 10688 8
8008.2.ly $$\chi_{8008}(1751, \cdot)$$ None 0 8
8008.2.lz $$\chi_{8008}(1161, \cdot)$$ n/a 2688 8
8008.2.mb $$\chi_{8008}(1037, \cdot)$$ n/a 8064 8
8008.2.me $$\chi_{8008}(415, \cdot)$$ None 0 8
8008.2.mg $$\chi_{8008}(467, \cdot)$$ n/a 10688 8
8008.2.mh $$\chi_{8008}(53, \cdot)$$ n/a 9216 8
8008.2.mj $$\chi_{8008}(1041, \cdot)$$ n/a 2304 8
8008.2.mm $$\chi_{8008}(653, \cdot)$$ n/a 10688 8
8008.2.mo $$\chi_{8008}(633, \cdot)$$ n/a 2688 8
8008.2.mp $$\chi_{8008}(95, \cdot)$$ None 0 8
8008.2.mr $$\chi_{8008}(75, \cdot)$$ n/a 10688 8
8008.2.mu $$\chi_{8008}(17, \cdot)$$ n/a 2688 8
8008.2.mw $$\chi_{8008}(933, \cdot)$$ n/a 10688 8
8008.2.mx $$\chi_{8008}(1907, \cdot)$$ n/a 10688 8
8008.2.mz $$\chi_{8008}(711, \cdot)$$ None 0 8
8008.2.nc $$\chi_{8008}(339, \cdot)$$ n/a 9216 8
8008.2.ne $$\chi_{8008}(79, \cdot)$$ None 0 8
8008.2.nf $$\chi_{8008}(129, \cdot)$$ n/a 2688 8
8008.2.nh $$\chi_{8008}(389, \cdot)$$ n/a 10688 8
8008.2.nk $$\chi_{8008}(127, \cdot)$$ None 0 8
8008.2.nm $$\chi_{8008}(251, \cdot)$$ n/a 10688 8
8008.2.nn $$\chi_{8008}(477, \cdot)$$ n/a 8064 8
8008.2.np $$\chi_{8008}(321, \cdot)$$ n/a 2688 8
8008.2.ns $$\chi_{8008}(335, \cdot)$$ None 0 8
8008.2.nu $$\chi_{8008}(491, \cdot)$$ n/a 8064 8
8008.2.nv $$\chi_{8008}(237, \cdot)$$ n/a 10688 8
8008.2.nz $$\chi_{8008}(641, \cdot)$$ n/a 2688 8
8008.2.ob $$\chi_{8008}(381, \cdot)$$ n/a 10688 8
8008.2.oc $$\chi_{8008}(107, \cdot)$$ n/a 10688 8
8008.2.oe $$\chi_{8008}(159, \cdot)$$ None 0 8
8008.2.oh $$\chi_{8008}(963, \cdot)$$ n/a 9216 8
8008.2.oj $$\chi_{8008}(1951, \cdot)$$ None 0 8
8008.2.ok $$\chi_{8008}(25, \cdot)$$ n/a 2688 8
8008.2.om $$\chi_{8008}(1949, \cdot)$$ n/a 10688 8
8008.2.op $$\chi_{8008}(103, \cdot)$$ None 0 8
8008.2.or $$\chi_{8008}(51, \cdot)$$ n/a 10688 8
8008.2.os $$\chi_{8008}(677, \cdot)$$ n/a 9216 8
8008.2.ow $$\chi_{8008}(997, \cdot)$$ n/a 10688 8
8008.2.oy $$\chi_{8008}(927, \cdot)$$ None 0 8
8008.2.pa $$\chi_{8008}(387, \cdot)$$ n/a 10688 8
8008.2.pd $$\chi_{8008}(211, \cdot)$$ n/a 8064 8
8008.2.pf $$\chi_{8008}(1511, \cdot)$$ None 0 8
8008.2.pg $$\chi_{8008}(225, \cdot)$$ n/a 2016 8
8008.2.pi $$\chi_{8008}(1245, \cdot)$$ n/a 10688 8
8008.2.pl $$\chi_{8008}(355, \cdot)$$ n/a 10688 8
8008.2.pn $$\chi_{8008}(303, \cdot)$$ None 0 8
8008.2.po $$\chi_{8008}(425, \cdot)$$ n/a 2688 8
8008.2.pq $$\chi_{8008}(445, \cdot)$$ n/a 10688 8
8008.2.pt $$\chi_{8008}(919, \cdot)$$ None 0 8
8008.2.pv $$\chi_{8008}(3, \cdot)$$ n/a 10688 8
8008.2.pw $$\chi_{8008}(1213, \cdot)$$ n/a 10688 8
8008.2.py $$\chi_{8008}(1921, \cdot)$$ n/a 2688 8
8008.2.qa $$\chi_{8008}(163, \cdot)$$ n/a 21376 16
8008.2.qb $$\chi_{8008}(215, \cdot)$$ None 0 16
8008.2.qg $$\chi_{8008}(565, \cdot)$$ n/a 21376 16
8008.2.qh $$\chi_{8008}(193, \cdot)$$ n/a 5376 16
8008.2.qi $$\chi_{8008}(501, \cdot)$$ n/a 21376 16
8008.2.qj $$\chi_{8008}(817, \cdot)$$ n/a 5376 16
8008.2.qm $$\chi_{8008}(915, \cdot)$$ n/a 21376 16
8008.2.qn $$\chi_{8008}(135, \cdot)$$ None 0 16
8008.2.qo $$\chi_{8008}(15, \cdot)$$ None 0 16
8008.2.qp $$\chi_{8008}(475, \cdot)$$ n/a 21376 16
8008.2.qy $$\chi_{8008}(541, \cdot)$$ n/a 21376 16
8008.2.qz $$\chi_{8008}(577, \cdot)$$ n/a 5376 16
8008.2.ra $$\chi_{8008}(97, \cdot)$$ n/a 5376 16
8008.2.rb $$\chi_{8008}(85, \cdot)$$ n/a 16128 16
8008.2.re $$\chi_{8008}(227, \cdot)$$ n/a 21376 16
8008.2.rf $$\chi_{8008}(487, \cdot)$$ None 0 16
8008.2.rg $$\chi_{8008}(509, \cdot)$$ n/a 21376 16
8008.2.rh $$\chi_{8008}(305, \cdot)$$ n/a 5376 16
8008.2.rk $$\chi_{8008}(291, \cdot)$$ n/a 21376 16
8008.2.rl $$\chi_{8008}(255, \cdot)$$ None 0 16
8008.2.rm $$\chi_{8008}(167, \cdot)$$ None 0 16
8008.2.rn $$\chi_{8008}(267, \cdot)$$ n/a 16128 16
8008.2.rw $$\chi_{8008}(5, \cdot)$$ n/a 21376 16
8008.2.rx $$\chi_{8008}(1201, \cdot)$$ n/a 5376 16
8008.2.ry $$\chi_{8008}(1289, \cdot)$$ n/a 4032 16
8008.2.rz $$\chi_{8008}(405, \cdot)$$ n/a 21376 16
8008.2.sc $$\chi_{8008}(851, \cdot)$$ n/a 21376 16
8008.2.sd $$\chi_{8008}(271, \cdot)$$ None 0 16
8008.2.se $$\chi_{8008}(19, \cdot)$$ n/a 21376 16
8008.2.sf $$\chi_{8008}(1103, \cdot)$$ None 0 16
8008.2.sk $$\chi_{8008}(149, \cdot)$$ n/a 21376 16
8008.2.sl $$\chi_{8008}(201, \cdot)$$ n/a 5376 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8008))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8008)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(286))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(572))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1001))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2002))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4004))$$$$^{\oplus 2}$$