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Properties

Label 5040.2
Level 5040
Weight 2
Dimension 258362
Nonzero newspaces 140
Sturm bound 2654208

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Defining parameters

Level: \( N \) = \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 140 \)
Sturm bound: \(2654208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5040))\).

Total New Old
Modular forms 674304 260794 413510
Cusp forms 652801 258362 394439
Eisenstein series 21503 2432 19071

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5040))\)

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
5040.2.a \(\chi_{5040}(1, \cdot)\) 5040.2.a.a 1 1
5040.2.a.b 1
5040.2.a.c 1
5040.2.a.d 1
5040.2.a.e 1
5040.2.a.f 1
5040.2.a.g 1
5040.2.a.h 1
5040.2.a.i 1
5040.2.a.j 1
5040.2.a.k 1
5040.2.a.l 1
5040.2.a.m 1
5040.2.a.n 1
5040.2.a.o 1
5040.2.a.p 1
5040.2.a.q 1
5040.2.a.r 1
5040.2.a.s 1
5040.2.a.t 1
5040.2.a.u 1
5040.2.a.v 1
5040.2.a.w 1
5040.2.a.x 1
5040.2.a.y 1
5040.2.a.z 1
5040.2.a.ba 1
5040.2.a.bb 1
5040.2.a.bc 1
5040.2.a.bd 1
5040.2.a.be 1
5040.2.a.bf 1
5040.2.a.bg 1
5040.2.a.bh 1
5040.2.a.bi 1
5040.2.a.bj 1
5040.2.a.bk 1
5040.2.a.bl 1
5040.2.a.bm 1
5040.2.a.bn 1
5040.2.a.bo 1
5040.2.a.bp 1
5040.2.a.bq 2
5040.2.a.br 2
5040.2.a.bs 2
5040.2.a.bt 2
5040.2.a.bu 2
5040.2.a.bv 2
5040.2.a.bw 2
5040.2.a.bx 2
5040.2.a.by 2
5040.2.d \(\chi_{5040}(4591, \cdot)\) 5040.2.d.a 4 1
5040.2.d.b 4
5040.2.d.c 8
5040.2.d.d 8
5040.2.d.e 8
5040.2.d.f 12
5040.2.d.g 12
5040.2.d.h 24
5040.2.e \(\chi_{5040}(71, \cdot)\) None 0 1
5040.2.f \(\chi_{5040}(881, \cdot)\) 5040.2.f.a 4 1
5040.2.f.b 4
5040.2.f.c 4
5040.2.f.d 4
5040.2.f.e 8
5040.2.f.f 8
5040.2.f.g 8
5040.2.f.h 8
5040.2.f.i 8
5040.2.f.j 8
5040.2.g \(\chi_{5040}(2521, \cdot)\) None 0 1
5040.2.j \(\chi_{5040}(3529, \cdot)\) None 0 1
5040.2.k \(\chi_{5040}(1889, \cdot)\) 5040.2.k.a 4 1
5040.2.k.b 4
5040.2.k.c 4
5040.2.k.d 4
5040.2.k.e 8
5040.2.k.f 8
5040.2.k.g 16
5040.2.k.h 24
5040.2.k.i 24
5040.2.p \(\chi_{5040}(1079, \cdot)\) None 0 1
5040.2.q \(\chi_{5040}(559, \cdot)\) n/a 120 1
5040.2.t \(\chi_{5040}(1009, \cdot)\) 5040.2.t.a 2 1
5040.2.t.b 2
5040.2.t.c 2
5040.2.t.d 2
5040.2.t.e 2
5040.2.t.f 2
5040.2.t.g 2
5040.2.t.h 2
5040.2.t.i 2
5040.2.t.j 2
5040.2.t.k 2
5040.2.t.l 2
5040.2.t.m 2
5040.2.t.n 2
5040.2.t.o 2
5040.2.t.p 2
5040.2.t.q 2
5040.2.t.r 2
5040.2.t.s 2
5040.2.t.t 4
5040.2.t.u 4
5040.2.t.v 6
5040.2.t.w 6
5040.2.t.x 6
5040.2.t.y 6
5040.2.t.z 6
5040.2.t.ba 6
5040.2.t.bb 8
5040.2.u \(\chi_{5040}(4409, \cdot)\) None 0 1
5040.2.v \(\chi_{5040}(3599, \cdot)\) 5040.2.v.a 12 1
5040.2.v.b 12
5040.2.v.c 24
5040.2.v.d 24
5040.2.w \(\chi_{5040}(3079, \cdot)\) None 0 1
5040.2.z \(\chi_{5040}(2071, \cdot)\) None 0 1
5040.2.ba \(\chi_{5040}(2591, \cdot)\) 5040.2.ba.a 8 1
5040.2.ba.b 8
5040.2.ba.c 16
5040.2.ba.d 16
5040.2.bf \(\chi_{5040}(3401, \cdot)\) None 0 1
5040.2.bg \(\chi_{5040}(2641, \cdot)\) n/a 384 2
5040.2.bh \(\chi_{5040}(1681, \cdot)\) n/a 288 2
5040.2.bi \(\chi_{5040}(2881, \cdot)\) n/a 160 2
5040.2.bj \(\chi_{5040}(961, \cdot)\) n/a 384 2
5040.2.bm \(\chi_{5040}(937, \cdot)\) None 0 2
5040.2.bn \(\chi_{5040}(1457, \cdot)\) n/a 144 2
5040.2.bo \(\chi_{5040}(127, \cdot)\) n/a 180 2
5040.2.bp \(\chi_{5040}(503, \cdot)\) None 0 2
5040.2.bs \(\chi_{5040}(883, \cdot)\) n/a 720 2
5040.2.bv \(\chi_{5040}(4213, \cdot)\) n/a 952 2
5040.2.bx \(\chi_{5040}(197, \cdot)\) n/a 576 2
5040.2.by \(\chi_{5040}(4283, \cdot)\) n/a 768 2
5040.2.ca \(\chi_{5040}(629, \cdot)\) n/a 768 2
5040.2.cd \(\chi_{5040}(1331, \cdot)\) n/a 384 2
5040.2.ce \(\chi_{5040}(2269, \cdot)\) n/a 720 2
5040.2.ch \(\chi_{5040}(811, \cdot)\) n/a 640 2
5040.2.cj \(\chi_{5040}(1261, \cdot)\) n/a 480 2
5040.2.ck \(\chi_{5040}(1819, \cdot)\) n/a 952 2
5040.2.cn \(\chi_{5040}(2141, \cdot)\) n/a 512 2
5040.2.co \(\chi_{5040}(2339, \cdot)\) n/a 576 2
5040.2.cr \(\chi_{5040}(1693, \cdot)\) n/a 952 2
5040.2.cs \(\chi_{5040}(3403, \cdot)\) n/a 720 2
5040.2.cu \(\chi_{5040}(1763, \cdot)\) n/a 768 2
5040.2.cx \(\chi_{5040}(2213, \cdot)\) n/a 576 2
5040.2.da \(\chi_{5040}(2647, \cdot)\) None 0 2
5040.2.db \(\chi_{5040}(1007, \cdot)\) n/a 192 2
5040.2.dc \(\chi_{5040}(433, \cdot)\) n/a 236 2
5040.2.dd \(\chi_{5040}(953, \cdot)\) None 0 2
5040.2.dg \(\chi_{5040}(599, \cdot)\) None 0 2
5040.2.dh \(\chi_{5040}(1039, \cdot)\) n/a 576 2
5040.2.dm \(\chi_{5040}(4489, \cdot)\) None 0 2
5040.2.dn \(\chi_{5040}(689, \cdot)\) n/a 568 2
5040.2.dq \(\chi_{5040}(4721, \cdot)\) n/a 384 2
5040.2.dr \(\chi_{5040}(3481, \cdot)\) None 0 2
5040.2.ds \(\chi_{5040}(31, \cdot)\) n/a 384 2
5040.2.dt \(\chi_{5040}(2711, \cdot)\) None 0 2
5040.2.dy \(\chi_{5040}(199, \cdot)\) None 0 2
5040.2.dz \(\chi_{5040}(1439, \cdot)\) n/a 192 2
5040.2.ea \(\chi_{5040}(89, \cdot)\) None 0 2
5040.2.eb \(\chi_{5040}(289, \cdot)\) n/a 236 2
5040.2.ee \(\chi_{5040}(911, \cdot)\) n/a 288 2
5040.2.ef \(\chi_{5040}(391, \cdot)\) None 0 2
5040.2.ei \(\chi_{5040}(761, \cdot)\) None 0 2
5040.2.en \(\chi_{5040}(3551, \cdot)\) n/a 384 2
5040.2.eo \(\chi_{5040}(871, \cdot)\) None 0 2
5040.2.er \(\chi_{5040}(41, \cdot)\) None 0 2
5040.2.eu \(\chi_{5040}(1049, \cdot)\) None 0 2
5040.2.ev \(\chi_{5040}(2689, \cdot)\) n/a 432 2
5040.2.ey \(\chi_{5040}(1879, \cdot)\) None 0 2
5040.2.ez \(\chi_{5040}(4559, \cdot)\) n/a 576 2
5040.2.fa \(\chi_{5040}(1769, \cdot)\) None 0 2
5040.2.fb \(\chi_{5040}(529, \cdot)\) n/a 568 2
5040.2.fe \(\chi_{5040}(1399, \cdot)\) None 0 2
5040.2.ff \(\chi_{5040}(239, \cdot)\) n/a 432 2
5040.2.fi \(\chi_{5040}(521, \cdot)\) None 0 2
5040.2.fn \(\chi_{5040}(431, \cdot)\) n/a 128 2
5040.2.fo \(\chi_{5040}(2791, \cdot)\) None 0 2
5040.2.fr \(\chi_{5040}(361, \cdot)\) None 0 2
5040.2.fs \(\chi_{5040}(1601, \cdot)\) n/a 128 2
5040.2.ft \(\chi_{5040}(2951, \cdot)\) None 0 2
5040.2.fu \(\chi_{5040}(271, \cdot)\) n/a 160 2
5040.2.fx \(\chi_{5040}(209, \cdot)\) n/a 568 2
5040.2.fy \(\chi_{5040}(169, \cdot)\) None 0 2
5040.2.gb \(\chi_{5040}(4399, \cdot)\) n/a 576 2
5040.2.gc \(\chi_{5040}(2039, \cdot)\) None 0 2
5040.2.gh \(\chi_{5040}(2369, \cdot)\) n/a 568 2
5040.2.gi \(\chi_{5040}(1129, \cdot)\) None 0 2
5040.2.gl \(\chi_{5040}(2239, \cdot)\) n/a 576 2
5040.2.gm \(\chi_{5040}(2759, \cdot)\) None 0 2
5040.2.gp \(\chi_{5040}(1751, \cdot)\) None 0 2
5040.2.gq \(\chi_{5040}(1231, \cdot)\) n/a 384 2
5040.2.gt \(\chi_{5040}(121, \cdot)\) None 0 2
5040.2.gu \(\chi_{5040}(1361, \cdot)\) n/a 384 2
5040.2.gv \(\chi_{5040}(1031, \cdot)\) None 0 2
5040.2.gw \(\chi_{5040}(3391, \cdot)\) n/a 384 2
5040.2.gz \(\chi_{5040}(841, \cdot)\) None 0 2
5040.2.ha \(\chi_{5040}(2561, \cdot)\) n/a 384 2
5040.2.hd \(\chi_{5040}(1279, \cdot)\) n/a 240 2
5040.2.he \(\chi_{5040}(359, \cdot)\) None 0 2
5040.2.hj \(\chi_{5040}(2609, \cdot)\) n/a 192 2
5040.2.hk \(\chi_{5040}(1369, \cdot)\) None 0 2
5040.2.hl \(\chi_{5040}(2201, \cdot)\) None 0 2
5040.2.hq \(\chi_{5040}(2551, \cdot)\) None 0 2
5040.2.hr \(\chi_{5040}(191, \cdot)\) n/a 384 2
5040.2.hu \(\chi_{5040}(1199, \cdot)\) n/a 576 2
5040.2.hv \(\chi_{5040}(439, \cdot)\) None 0 2
5040.2.hw \(\chi_{5040}(1969, \cdot)\) n/a 568 2
5040.2.hx \(\chi_{5040}(3209, \cdot)\) None 0 2
5040.2.ic \(\chi_{5040}(2327, \cdot)\) None 0 4
5040.2.id \(\chi_{5040}(1087, \cdot)\) n/a 1152 4
5040.2.ie \(\chi_{5040}(977, \cdot)\) n/a 1136 4
5040.2.if \(\chi_{5040}(313, \cdot)\) None 0 4
5040.2.ii \(\chi_{5040}(1343, \cdot)\) n/a 1152 4
5040.2.ij \(\chi_{5040}(967, \cdot)\) None 0 4
5040.2.im \(\chi_{5040}(233, \cdot)\) None 0 4
5040.2.in \(\chi_{5040}(577, \cdot)\) n/a 472 4
5040.2.iq \(\chi_{5040}(2257, \cdot)\) n/a 1136 4
5040.2.ir \(\chi_{5040}(137, \cdot)\) None 0 4
5040.2.iw \(\chi_{5040}(247, \cdot)\) None 0 4
5040.2.ix \(\chi_{5040}(383, \cdot)\) n/a 1152 4
5040.2.ja \(\chi_{5040}(143, \cdot)\) n/a 384 4
5040.2.jb \(\chi_{5040}(487, \cdot)\) None 0 4
5040.2.je \(\chi_{5040}(617, \cdot)\) None 0 4
5040.2.jf \(\chi_{5040}(97, \cdot)\) n/a 1136 4
5040.2.jg \(\chi_{5040}(467, \cdot)\) n/a 1536 4
5040.2.jj \(\chi_{5040}(2573, \cdot)\) n/a 1536 4
5040.2.jl \(\chi_{5040}(397, \cdot)\) n/a 1904 4
5040.2.jm \(\chi_{5040}(163, \cdot)\) n/a 1904 4
5040.2.jp \(\chi_{5040}(1003, \cdot)\) n/a 4576 4
5040.2.jq \(\chi_{5040}(493, \cdot)\) n/a 4576 4
5040.2.jt \(\chi_{5040}(83, \cdot)\) n/a 4576 4
5040.2.ju \(\chi_{5040}(317, \cdot)\) n/a 4576 4
5040.2.jx \(\chi_{5040}(563, \cdot)\) n/a 4576 4
5040.2.jy \(\chi_{5040}(533, \cdot)\) n/a 3456 4
5040.2.ka \(\chi_{5040}(13, \cdot)\) n/a 4576 4
5040.2.kd \(\chi_{5040}(67, \cdot)\) n/a 4576 4
5040.2.ke \(\chi_{5040}(2173, \cdot)\) n/a 4576 4
5040.2.kh \(\chi_{5040}(43, \cdot)\) n/a 3456 4
5040.2.ki \(\chi_{5040}(3173, \cdot)\) n/a 4576 4
5040.2.kl \(\chi_{5040}(2243, \cdot)\) n/a 4576 4
5040.2.km \(\chi_{5040}(1651, \cdot)\) n/a 3072 4
5040.2.kp \(\chi_{5040}(589, \cdot)\) n/a 3456 4
5040.2.kq \(\chi_{5040}(491, \cdot)\) n/a 2304 4
5040.2.kt \(\chi_{5040}(1469, \cdot)\) n/a 4576 4
5040.2.kv \(\chi_{5040}(1699, \cdot)\) n/a 4576 4
5040.2.kw \(\chi_{5040}(2221, \cdot)\) n/a 3072 4
5040.2.ky \(\chi_{5040}(779, \cdot)\) n/a 4576 4
5040.2.lb \(\chi_{5040}(101, \cdot)\) n/a 3072 4
5040.2.lc \(\chi_{5040}(341, \cdot)\) n/a 1024 4
5040.2.lf \(\chi_{5040}(179, \cdot)\) n/a 1536 4
5040.2.lg \(\chi_{5040}(541, \cdot)\) n/a 1280 4
5040.2.lj \(\chi_{5040}(19, \cdot)\) n/a 1904 4
5040.2.lk \(\chi_{5040}(619, \cdot)\) n/a 4576 4
5040.2.ln \(\chi_{5040}(781, \cdot)\) n/a 3072 4
5040.2.lp \(\chi_{5040}(1859, \cdot)\) n/a 4576 4
5040.2.lq \(\chi_{5040}(941, \cdot)\) n/a 3072 4
5040.2.ls \(\chi_{5040}(851, \cdot)\) n/a 3072 4
5040.2.lv \(\chi_{5040}(1949, \cdot)\) n/a 4576 4
5040.2.lx \(\chi_{5040}(109, \cdot)\) n/a 1904 4
5040.2.ly \(\chi_{5040}(451, \cdot)\) n/a 1280 4
5040.2.mb \(\chi_{5040}(2131, \cdot)\) n/a 3072 4
5040.2.mc \(\chi_{5040}(1789, \cdot)\) n/a 4576 4
5040.2.mf \(\chi_{5040}(11, \cdot)\) n/a 3072 4
5040.2.mg \(\chi_{5040}(509, \cdot)\) n/a 4576 4
5040.2.mj \(\chi_{5040}(269, \cdot)\) n/a 1536 4
5040.2.mk \(\chi_{5040}(611, \cdot)\) n/a 1024 4
5040.2.mm \(\chi_{5040}(691, \cdot)\) n/a 3072 4
5040.2.mp \(\chi_{5040}(709, \cdot)\) n/a 4576 4
5040.2.mr \(\chi_{5040}(659, \cdot)\) n/a 3456 4
5040.2.ms \(\chi_{5040}(461, \cdot)\) n/a 3072 4
5040.2.mv \(\chi_{5040}(139, \cdot)\) n/a 4576 4
5040.2.mw \(\chi_{5040}(421, \cdot)\) n/a 2304 4
5040.2.my \(\chi_{5040}(3013, \cdot)\) n/a 4576 4
5040.2.nb \(\chi_{5040}(403, \cdot)\) n/a 4576 4
5040.2.nc \(\chi_{5040}(1373, \cdot)\) n/a 3456 4
5040.2.nf \(\chi_{5040}(3083, \cdot)\) n/a 4576 4
5040.2.ng \(\chi_{5040}(2333, \cdot)\) n/a 4576 4
5040.2.nj \(\chi_{5040}(923, \cdot)\) n/a 4576 4
5040.2.nl \(\chi_{5040}(2563, \cdot)\) n/a 3456 4
5040.2.nm \(\chi_{5040}(157, \cdot)\) n/a 4576 4
5040.2.np \(\chi_{5040}(1843, \cdot)\) n/a 4576 4
5040.2.nq \(\chi_{5040}(853, \cdot)\) n/a 4576 4
5040.2.nt \(\chi_{5040}(227, \cdot)\) n/a 4576 4
5040.2.nu \(\chi_{5040}(653, \cdot)\) n/a 4576 4
5040.2.nx \(\chi_{5040}(53, \cdot)\) n/a 1536 4
5040.2.ny \(\chi_{5040}(2483, \cdot)\) n/a 1536 4
5040.2.oa \(\chi_{5040}(1243, \cdot)\) n/a 1904 4
5040.2.od \(\chi_{5040}(2413, \cdot)\) n/a 1904 4
5040.2.oe \(\chi_{5040}(113, \cdot)\) n/a 864 4
5040.2.of \(\chi_{5040}(1273, \cdot)\) None 0 4
5040.2.oi \(\chi_{5040}(647, \cdot)\) None 0 4
5040.2.oj \(\chi_{5040}(1423, \cdot)\) n/a 480 4
5040.2.om \(\chi_{5040}(1663, \cdot)\) n/a 1152 4
5040.2.on \(\chi_{5040}(887, \cdot)\) None 0 4
5040.2.os \(\chi_{5040}(1753, \cdot)\) None 0 4
5040.2.ot \(\chi_{5040}(2417, \cdot)\) n/a 1136 4
5040.2.ow \(\chi_{5040}(737, \cdot)\) n/a 384 4
5040.2.ox \(\chi_{5040}(73, \cdot)\) None 0 4
5040.2.pa \(\chi_{5040}(167, \cdot)\) None 0 4
5040.2.pb \(\chi_{5040}(463, \cdot)\) n/a 864 4
5040.2.pe \(\chi_{5040}(473, \cdot)\) None 0 4
5040.2.pf \(\chi_{5040}(817, \cdot)\) n/a 1136 4
5040.2.pg \(\chi_{5040}(47, \cdot)\) n/a 1152 4
5040.2.ph \(\chi_{5040}(583, \cdot)\) None 0 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 60}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5040))\)\(^{\oplus 1}\)