Properties

 Label 6240.2 Level 6240 Weight 2 Dimension 393096 Nonzero newspaces 144 Sturm bound 4128768

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Defining parameters

 Level: $$N$$ = $$6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$144$$ Sturm bound: $$4128768$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6240))$$.

Total New Old
Modular forms 1044480 395736 648744
Cusp forms 1019905 393096 626809
Eisenstein series 24575 2640 21935

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6240))$$

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
6240.2.a $$\chi_{6240}(1, \cdot)$$ 6240.2.a.a 1 1
6240.2.a.b 1
6240.2.a.c 1
6240.2.a.d 1
6240.2.a.e 1
6240.2.a.f 1
6240.2.a.g 1
6240.2.a.h 1
6240.2.a.i 1
6240.2.a.j 1
6240.2.a.k 1
6240.2.a.l 1
6240.2.a.m 1
6240.2.a.n 1
6240.2.a.o 1
6240.2.a.p 1
6240.2.a.q 1
6240.2.a.r 1
6240.2.a.s 1
6240.2.a.t 1
6240.2.a.u 1
6240.2.a.v 1
6240.2.a.w 1
6240.2.a.x 1
6240.2.a.y 1
6240.2.a.z 1
6240.2.a.ba 1
6240.2.a.bb 1
6240.2.a.bc 1
6240.2.a.bd 1
6240.2.a.be 1
6240.2.a.bf 1
6240.2.a.bg 2
6240.2.a.bh 2
6240.2.a.bi 2
6240.2.a.bj 2
6240.2.a.bk 2
6240.2.a.bl 2
6240.2.a.bm 2
6240.2.a.bn 2
6240.2.a.bo 2
6240.2.a.bp 2
6240.2.a.bq 2
6240.2.a.br 2
6240.2.a.bs 2
6240.2.a.bt 2
6240.2.a.bu 2
6240.2.a.bv 2
6240.2.a.bw 3
6240.2.a.bx 3
6240.2.a.by 3
6240.2.a.bz 3
6240.2.a.ca 3
6240.2.a.cb 3
6240.2.a.cc 3
6240.2.a.cd 3
6240.2.a.ce 4
6240.2.a.cf 4
6240.2.b $$\chi_{6240}(4369, \cdot)$$ n/a 144 1
6240.2.e $$\chi_{6240}(911, \cdot)$$ n/a 192 1
6240.2.g $$\chi_{6240}(961, \cdot)$$ n/a 112 1
6240.2.h $$\chi_{6240}(6239, \cdot)$$ n/a 336 1
6240.2.k $$\chi_{6240}(4031, \cdot)$$ n/a 192 1
6240.2.l $$\chi_{6240}(1249, \cdot)$$ n/a 144 1
6240.2.n $$\chi_{6240}(3119, \cdot)$$ n/a 328 1
6240.2.q $$\chi_{6240}(4081, \cdot)$$ n/a 112 1
6240.2.r $$\chi_{6240}(2209, \cdot)$$ n/a 168 1
6240.2.u $$\chi_{6240}(4991, \cdot)$$ n/a 224 1
6240.2.w $$\chi_{6240}(3121, \cdot)$$ 6240.2.w.a 2 1
6240.2.w.b 2
6240.2.w.c 4
6240.2.w.d 4
6240.2.w.e 16
6240.2.w.f 20
6240.2.w.g 22
6240.2.w.h 26
6240.2.x $$\chi_{6240}(2159, \cdot)$$ n/a 288 1
6240.2.ba $$\chi_{6240}(1871, \cdot)$$ n/a 224 1
6240.2.bb $$\chi_{6240}(5329, \cdot)$$ n/a 168 1
6240.2.bd $$\chi_{6240}(5279, \cdot)$$ n/a 288 1
6240.2.bg $$\chi_{6240}(2401, \cdot)$$ n/a 224 2
6240.2.bi $$\chi_{6240}(983, \cdot)$$ None 0 2
6240.2.bk $$\chi_{6240}(3817, \cdot)$$ None 0 2
6240.2.bm $$\chi_{6240}(311, \cdot)$$ None 0 2
6240.2.bn $$\chi_{6240}(649, \cdot)$$ None 0 2
6240.2.bp $$\chi_{6240}(577, \cdot)$$ n/a 336 2
6240.2.bq $$\chi_{6240}(47, \cdot)$$ n/a 656 2
6240.2.bv $$\chi_{6240}(3697, \cdot)$$ n/a 336 2
6240.2.bw $$\chi_{6240}(863, \cdot)$$ n/a 672 2
6240.2.by $$\chi_{6240}(1561, \cdot)$$ None 0 2
6240.2.bz $$\chi_{6240}(599, \cdot)$$ None 0 2
6240.2.cb $$\chi_{6240}(697, \cdot)$$ None 0 2
6240.2.cd $$\chi_{6240}(4103, \cdot)$$ None 0 2
6240.2.cf $$\chi_{6240}(1591, \cdot)$$ None 0 2
6240.2.ci $$\chi_{6240}(1529, \cdot)$$ None 0 2
6240.2.ck $$\chi_{6240}(2417, \cdot)$$ n/a 656 2
6240.2.cl $$\chi_{6240}(833, \cdot)$$ n/a 576 2
6240.2.co $$\chi_{6240}(703, \cdot)$$ n/a 288 2
6240.2.cp $$\chi_{6240}(2287, \cdot)$$ n/a 336 2
6240.2.cs $$\chi_{6240}(2839, \cdot)$$ None 0 2
6240.2.ct $$\chi_{6240}(281, \cdot)$$ None 0 2
6240.2.cw $$\chi_{6240}(1409, \cdot)$$ n/a 672 2
6240.2.cx $$\chi_{6240}(3089, \cdot)$$ n/a 656 2
6240.2.cz $$\chi_{6240}(1711, \cdot)$$ n/a 224 2
6240.2.dc $$\chi_{6240}(31, \cdot)$$ n/a 224 2
6240.2.dd $$\chi_{6240}(2263, \cdot)$$ None 0 2
6240.2.de $$\chi_{6240}(3353, \cdot)$$ None 0 2
6240.2.dh $$\chi_{6240}(233, \cdot)$$ None 0 2
6240.2.di $$\chi_{6240}(5383, \cdot)$$ None 0 2
6240.2.dn $$\chi_{6240}(103, \cdot)$$ None 0 2
6240.2.do $$\chi_{6240}(5513, \cdot)$$ None 0 2
6240.2.dr $$\chi_{6240}(2393, \cdot)$$ None 0 2
6240.2.ds $$\chi_{6240}(3223, \cdot)$$ None 0 2
6240.2.du $$\chi_{6240}(2959, \cdot)$$ n/a 336 2
6240.2.dv $$\chi_{6240}(1279, \cdot)$$ n/a 336 2
6240.2.dx $$\chi_{6240}(161, \cdot)$$ n/a 448 2
6240.2.ea $$\chi_{6240}(1841, \cdot)$$ n/a 448 2
6240.2.ec $$\chi_{6240}(2969, \cdot)$$ None 0 2
6240.2.ed $$\chi_{6240}(151, \cdot)$$ None 0 2
6240.2.ef $$\chi_{6240}(1663, \cdot)$$ n/a 336 2
6240.2.ei $$\chi_{6240}(1327, \cdot)$$ n/a 288 2
6240.2.ej $$\chi_{6240}(1457, \cdot)$$ n/a 576 2
6240.2.em $$\chi_{6240}(1793, \cdot)$$ n/a 672 2
6240.2.en $$\chi_{6240}(1721, \cdot)$$ None 0 2
6240.2.eq $$\chi_{6240}(1399, \cdot)$$ None 0 2
6240.2.er $$\chi_{6240}(4727, \cdot)$$ None 0 2
6240.2.et $$\chi_{6240}(73, \cdot)$$ None 0 2
6240.2.ev $$\chi_{6240}(2471, \cdot)$$ None 0 2
6240.2.ey $$\chi_{6240}(2809, \cdot)$$ None 0 2
6240.2.fb $$\chi_{6240}(1487, \cdot)$$ n/a 656 2
6240.2.fc $$\chi_{6240}(3073, \cdot)$$ n/a 336 2
6240.2.fd $$\chi_{6240}(4607, \cdot)$$ n/a 672 2
6240.2.fe $$\chi_{6240}(2257, \cdot)$$ n/a 336 2
6240.2.fh $$\chi_{6240}(2521, \cdot)$$ None 0 2
6240.2.fk $$\chi_{6240}(1559, \cdot)$$ None 0 2
6240.2.fm $$\chi_{6240}(3193, \cdot)$$ None 0 2
6240.2.fo $$\chi_{6240}(1607, \cdot)$$ None 0 2
6240.2.fr $$\chi_{6240}(1439, \cdot)$$ n/a 672 2
6240.2.ft $$\chi_{6240}(49, \cdot)$$ n/a 336 2
6240.2.fu $$\chi_{6240}(2831, \cdot)$$ n/a 448 2
6240.2.fx $$\chi_{6240}(1199, \cdot)$$ n/a 656 2
6240.2.fy $$\chi_{6240}(2161, \cdot)$$ n/a 224 2
6240.2.ga $$\chi_{6240}(2591, \cdot)$$ n/a 448 2
6240.2.gd $$\chi_{6240}(3169, \cdot)$$ n/a 336 2
6240.2.ge $$\chi_{6240}(1681, \cdot)$$ n/a 224 2
6240.2.gh $$\chi_{6240}(719, \cdot)$$ n/a 656 2
6240.2.gj $$\chi_{6240}(289, \cdot)$$ n/a 336 2
6240.2.gk $$\chi_{6240}(191, \cdot)$$ n/a 448 2
6240.2.gn $$\chi_{6240}(959, \cdot)$$ n/a 672 2
6240.2.go $$\chi_{6240}(1921, \cdot)$$ n/a 224 2
6240.2.gq $$\chi_{6240}(3311, \cdot)$$ n/a 448 2
6240.2.gt $$\chi_{6240}(529, \cdot)$$ n/a 336 2
6240.2.gu $$\chi_{6240}(2059, \cdot)$$ n/a 2688 4
6240.2.gw $$\chi_{6240}(2501, \cdot)$$ n/a 3584 4
6240.2.gy $$\chi_{6240}(77, \cdot)$$ n/a 5344 4
6240.2.gz $$\chi_{6240}(547, \cdot)$$ n/a 2304 4
6240.2.he $$\chi_{6240}(677, \cdot)$$ n/a 4608 4
6240.2.hf $$\chi_{6240}(883, \cdot)$$ n/a 2688 4
6240.2.hh $$\chi_{6240}(2189, \cdot)$$ n/a 5344 4
6240.2.hj $$\chi_{6240}(2371, \cdot)$$ n/a 1792 4
6240.2.hk $$\chi_{6240}(181, \cdot)$$ n/a 1792 4
6240.2.hm $$\chi_{6240}(1379, \cdot)$$ n/a 4608 4
6240.2.hp $$\chi_{6240}(781, \cdot)$$ n/a 1536 4
6240.2.hr $$\chi_{6240}(779, \cdot)$$ n/a 5344 4
6240.2.ht $$\chi_{6240}(2293, \cdot)$$ n/a 2688 4
6240.2.hu $$\chi_{6240}(203, \cdot)$$ n/a 5344 4
6240.2.hx $$\chi_{6240}(1643, \cdot)$$ n/a 5344 4
6240.2.hy $$\chi_{6240}(853, \cdot)$$ n/a 2688 4
6240.2.ia $$\chi_{6240}(83, \cdot)$$ n/a 5344 4
6240.2.id $$\chi_{6240}(2413, \cdot)$$ n/a 2688 4
6240.2.ie $$\chi_{6240}(733, \cdot)$$ n/a 2688 4
6240.2.ih $$\chi_{6240}(1763, \cdot)$$ n/a 5344 4
6240.2.ij $$\chi_{6240}(1429, \cdot)$$ n/a 2688 4
6240.2.il $$\chi_{6240}(131, \cdot)$$ n/a 3072 4
6240.2.im $$\chi_{6240}(469, \cdot)$$ n/a 2304 4
6240.2.io $$\chi_{6240}(1091, \cdot)$$ n/a 3584 4
6240.2.iq $$\chi_{6240}(941, \cdot)$$ n/a 3584 4
6240.2.is $$\chi_{6240}(499, \cdot)$$ n/a 2688 4
6240.2.iw $$\chi_{6240}(1507, \cdot)$$ n/a 2688 4
6240.2.ix $$\chi_{6240}(53, \cdot)$$ n/a 4608 4
6240.2.iy $$\chi_{6240}(2107, \cdot)$$ n/a 2304 4
6240.2.iz $$\chi_{6240}(1637, \cdot)$$ n/a 5344 4
6240.2.jd $$\chi_{6240}(811, \cdot)$$ n/a 1792 4
6240.2.jf $$\chi_{6240}(629, \cdot)$$ n/a 5344 4
6240.2.jg $$\chi_{6240}(167, \cdot)$$ None 0 4
6240.2.ji $$\chi_{6240}(457, \cdot)$$ None 0 4
6240.2.jl $$\chi_{6240}(2279, \cdot)$$ None 0 4
6240.2.jm $$\chi_{6240}(121, \cdot)$$ None 0 4
6240.2.jq $$\chi_{6240}(4127, \cdot)$$ n/a 1344 4
6240.2.jr $$\chi_{6240}(817, \cdot)$$ n/a 672 4
6240.2.js $$\chi_{6240}(1007, \cdot)$$ n/a 1312 4
6240.2.jt $$\chi_{6240}(2593, \cdot)$$ n/a 672 4
6240.2.jx $$\chi_{6240}(1849, \cdot)$$ None 0 4
6240.2.jy $$\chi_{6240}(1511, \cdot)$$ None 0 4
6240.2.kb $$\chi_{6240}(553, \cdot)$$ None 0 4
6240.2.kd $$\chi_{6240}(743, \cdot)$$ None 0 4
6240.2.ke $$\chi_{6240}(1159, \cdot)$$ None 0 4
6240.2.kh $$\chi_{6240}(1241, \cdot)$$ None 0 4
6240.2.ki $$\chi_{6240}(257, \cdot)$$ n/a 1344 4
6240.2.kl $$\chi_{6240}(113, \cdot)$$ n/a 1312 4
6240.2.km $$\chi_{6240}(367, \cdot)$$ n/a 672 4
6240.2.kp $$\chi_{6240}(127, \cdot)$$ n/a 672 4
6240.2.kr $$\chi_{6240}(631, \cdot)$$ None 0 4
6240.2.ks $$\chi_{6240}(2489, \cdot)$$ None 0 4
6240.2.kv $$\chi_{6240}(401, \cdot)$$ n/a 896 4
6240.2.kw $$\chi_{6240}(1601, \cdot)$$ n/a 896 4
6240.2.ky $$\chi_{6240}(319, \cdot)$$ n/a 672 4
6240.2.lb $$\chi_{6240}(1519, \cdot)$$ n/a 672 4
6240.2.le $$\chi_{6240}(1543, \cdot)$$ None 0 4
6240.2.lf $$\chi_{6240}(1193, \cdot)$$ None 0 4
6240.2.li $$\chi_{6240}(953, \cdot)$$ None 0 4
6240.2.lj $$\chi_{6240}(1303, \cdot)$$ None 0 4
6240.2.lk $$\chi_{6240}(823, \cdot)$$ None 0 4
6240.2.ll $$\chi_{6240}(1433, \cdot)$$ None 0 4
6240.2.lo $$\chi_{6240}(1673, \cdot)$$ None 0 4
6240.2.lp $$\chi_{6240}(1063, \cdot)$$ None 0 4
6240.2.lt $$\chi_{6240}(1471, \cdot)$$ n/a 448 4
6240.2.lu $$\chi_{6240}(271, \cdot)$$ n/a 448 4
6240.2.lw $$\chi_{6240}(1649, \cdot)$$ n/a 1312 4
6240.2.lz $$\chi_{6240}(449, \cdot)$$ n/a 1344 4
6240.2.mb $$\chi_{6240}(41, \cdot)$$ None 0 4
6240.2.mc $$\chi_{6240}(2359, \cdot)$$ None 0 4
6240.2.mf $$\chi_{6240}(2383, \cdot)$$ n/a 672 4
6240.2.mg $$\chi_{6240}(607, \cdot)$$ n/a 672 4
6240.2.mj $$\chi_{6240}(737, \cdot)$$ n/a 1344 4
6240.2.mk $$\chi_{6240}(17, \cdot)$$ n/a 1312 4
6240.2.mm $$\chi_{6240}(89, \cdot)$$ None 0 4
6240.2.mp $$\chi_{6240}(1111, \cdot)$$ None 0 4
6240.2.mr $$\chi_{6240}(1367, \cdot)$$ None 0 4
6240.2.mt $$\chi_{6240}(1033, \cdot)$$ None 0 4
6240.2.mu $$\chi_{6240}(2759, \cdot)$$ None 0 4
6240.2.mx $$\chi_{6240}(601, \cdot)$$ None 0 4
6240.2.my $$\chi_{6240}(3217, \cdot)$$ n/a 672 4
6240.2.mz $$\chi_{6240}(383, \cdot)$$ n/a 1344 4
6240.2.ne $$\chi_{6240}(97, \cdot)$$ n/a 672 4
6240.2.nf $$\chi_{6240}(527, \cdot)$$ n/a 1312 4
6240.2.ng $$\chi_{6240}(1369, \cdot)$$ None 0 4
6240.2.nj $$\chi_{6240}(1031, \cdot)$$ None 0 4
6240.2.nk $$\chi_{6240}(2377, \cdot)$$ None 0 4
6240.2.nm $$\chi_{6240}(1463, \cdot)$$ None 0 4
6240.2.no $$\chi_{6240}(149, \cdot)$$ n/a 10688 8
6240.2.nq $$\chi_{6240}(331, \cdot)$$ n/a 3584 8
6240.2.ns $$\chi_{6240}(1147, \cdot)$$ n/a 5376 8
6240.2.nt $$\chi_{6240}(173, \cdot)$$ n/a 10688 8
6240.2.ny $$\chi_{6240}(43, \cdot)$$ n/a 5376 8
6240.2.nz $$\chi_{6240}(1277, \cdot)$$ n/a 10688 8
6240.2.ob $$\chi_{6240}(19, \cdot)$$ n/a 5376 8
6240.2.od $$\chi_{6240}(461, \cdot)$$ n/a 7168 8
6240.2.oe $$\chi_{6240}(589, \cdot)$$ n/a 5376 8
6240.2.og $$\chi_{6240}(731, \cdot)$$ n/a 7168 8
6240.2.oj $$\chi_{6240}(1069, \cdot)$$ n/a 5376 8
6240.2.ol $$\chi_{6240}(251, \cdot)$$ n/a 7168 8
6240.2.on $$\chi_{6240}(37, \cdot)$$ n/a 5376 8
6240.2.oo $$\chi_{6240}(323, \cdot)$$ n/a 10688 8
6240.2.or $$\chi_{6240}(1307, \cdot)$$ n/a 10688 8
6240.2.os $$\chi_{6240}(973, \cdot)$$ n/a 5376 8
6240.2.ou $$\chi_{6240}(947, \cdot)$$ n/a 10688 8
6240.2.ox $$\chi_{6240}(877, \cdot)$$ n/a 5376 8
6240.2.oy $$\chi_{6240}(397, \cdot)$$ n/a 5376 8
6240.2.pb $$\chi_{6240}(227, \cdot)$$ n/a 10688 8
6240.2.pd $$\chi_{6240}(901, \cdot)$$ n/a 3584 8
6240.2.pf $$\chi_{6240}(419, \cdot)$$ n/a 10688 8
6240.2.pg $$\chi_{6240}(61, \cdot)$$ n/a 3584 8
6240.2.pi $$\chi_{6240}(179, \cdot)$$ n/a 10688 8
6240.2.pk $$\chi_{6240}(691, \cdot)$$ n/a 3584 8
6240.2.pm $$\chi_{6240}(509, \cdot)$$ n/a 10688 8
6240.2.pq $$\chi_{6240}(653, \cdot)$$ n/a 10688 8
6240.2.pr $$\chi_{6240}(667, \cdot)$$ n/a 5376 8
6240.2.ps $$\chi_{6240}(797, \cdot)$$ n/a 10688 8
6240.2.pt $$\chi_{6240}(523, \cdot)$$ n/a 5376 8
6240.2.px $$\chi_{6240}(821, \cdot)$$ n/a 7168 8
6240.2.pz $$\chi_{6240}(379, \cdot)$$ n/a 5376 8

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6240))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6240)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(480))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1040))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1248))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1560))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2080))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3120))$$$$^{\oplus 2}$$