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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 available 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

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