# Properties

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

## 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 the 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

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