Properties

Label 8008.2
Level 8008
Weight 2
Dimension 1009720
Nonzero newspaces 180
Sturm bound 7741440

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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

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