# Properties

 Label 4680.2 Level 4680 Weight 2 Dimension 232996 Nonzero newspaces 150 Sturm bound 2322432

## Defining parameters

 Level: $$N$$ = $$4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$150$$ Sturm bound: $$2322432$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4680))$$.

Total New Old
Modular forms 589824 235372 354452
Cusp forms 571393 232996 338397
Eisenstein series 18431 2376 16055

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4680))$$

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
4680.2.a $$\chi_{4680}(1, \cdot)$$ 4680.2.a.a 1 1
4680.2.a.b 1
4680.2.a.c 1
4680.2.a.d 1
4680.2.a.e 1
4680.2.a.f 1
4680.2.a.g 1
4680.2.a.h 1
4680.2.a.i 1
4680.2.a.j 1
4680.2.a.k 1
4680.2.a.l 1
4680.2.a.m 1
4680.2.a.n 1
4680.2.a.o 1
4680.2.a.p 1
4680.2.a.q 1
4680.2.a.r 1
4680.2.a.s 1
4680.2.a.t 1
4680.2.a.u 1
4680.2.a.v 1
4680.2.a.w 2
4680.2.a.x 2
4680.2.a.y 2
4680.2.a.z 2
4680.2.a.ba 2
4680.2.a.bb 2
4680.2.a.bc 2
4680.2.a.bd 2
4680.2.a.be 2
4680.2.a.bf 2
4680.2.a.bg 3
4680.2.a.bh 3
4680.2.a.bi 3
4680.2.a.bj 3
4680.2.a.bk 3
4680.2.a.bl 3
4680.2.b $$\chi_{4680}(469, \cdot)$$ n/a 360 1
4680.2.e $$\chi_{4680}(1691, \cdot)$$ n/a 192 1
4680.2.g $$\chi_{4680}(2521, \cdot)$$ 4680.2.g.a 2 1
4680.2.g.b 2
4680.2.g.c 2
4680.2.g.d 2
4680.2.g.e 2
4680.2.g.f 4
4680.2.g.g 4
4680.2.g.h 4
4680.2.g.i 6
4680.2.g.j 6
4680.2.g.k 8
4680.2.g.l 12
4680.2.g.m 16
4680.2.h $$\chi_{4680}(4679, \cdot)$$ None 0 1
4680.2.k $$\chi_{4680}(4031, \cdot)$$ None 0 1
4680.2.l $$\chi_{4680}(2809, \cdot)$$ 4680.2.l.a 2 1
4680.2.l.b 2
4680.2.l.c 2
4680.2.l.d 6
4680.2.l.e 6
4680.2.l.f 8
4680.2.l.g 8
4680.2.l.h 10
4680.2.l.i 10
4680.2.l.j 18
4680.2.l.k 18
4680.2.n $$\chi_{4680}(2339, \cdot)$$ n/a 336 1
4680.2.q $$\chi_{4680}(181, \cdot)$$ n/a 280 1
4680.2.r $$\chi_{4680}(649, \cdot)$$ n/a 104 1
4680.2.u $$\chi_{4680}(1871, \cdot)$$ None 0 1
4680.2.w $$\chi_{4680}(2341, \cdot)$$ n/a 240 1
4680.2.x $$\chi_{4680}(4499, \cdot)$$ n/a 288 1
4680.2.ba $$\chi_{4680}(4211, \cdot)$$ n/a 224 1
4680.2.bb $$\chi_{4680}(2989, \cdot)$$ n/a 416 1
4680.2.bd $$\chi_{4680}(2159, \cdot)$$ None 0 1
4680.2.bg $$\chi_{4680}(2161, \cdot)$$ n/a 140 2
4680.2.bh $$\chi_{4680}(1561, \cdot)$$ n/a 288 2
4680.2.bi $$\chi_{4680}(601, \cdot)$$ n/a 336 2
4680.2.bj $$\chi_{4680}(2401, \cdot)$$ n/a 336 2
4680.2.bk $$\chi_{4680}(73, \cdot)$$ n/a 210 2
4680.2.bl $$\chi_{4680}(827, \cdot)$$ n/a 672 2
4680.2.bq $$\chi_{4680}(2413, \cdot)$$ n/a 832 2
4680.2.br $$\chi_{4680}(863, \cdot)$$ None 0 2
4680.2.bt $$\chi_{4680}(1637, \cdot)$$ n/a 672 2
4680.2.bu $$\chi_{4680}(1457, \cdot)$$ n/a 144 2
4680.2.bx $$\chi_{4680}(703, \cdot)$$ None 0 2
4680.2.by $$\chi_{4680}(883, \cdot)$$ n/a 832 2
4680.2.cb $$\chi_{4680}(1529, \cdot)$$ n/a 168 2
4680.2.cc $$\chi_{4680}(629, \cdot)$$ n/a 672 2
4680.2.ce $$\chi_{4680}(811, \cdot)$$ n/a 560 2
4680.2.ch $$\chi_{4680}(1711, \cdot)$$ None 0 2
4680.2.cj $$\chi_{4680}(2179, \cdot)$$ n/a 832 2
4680.2.ck $$\chi_{4680}(1279, \cdot)$$ None 0 2
4680.2.cm $$\chi_{4680}(161, \cdot)$$ n/a 112 2
4680.2.cp $$\chi_{4680}(1061, \cdot)$$ n/a 448 2
4680.2.cq $$\chi_{4680}(2287, \cdot)$$ None 0 2
4680.2.ct $$\chi_{4680}(2107, \cdot)$$ n/a 720 2
4680.2.cu $$\chi_{4680}(53, \cdot)$$ n/a 576 2
4680.2.cx $$\chi_{4680}(233, \cdot)$$ n/a 168 2
4680.2.da $$\chi_{4680}(1763, \cdot)$$ n/a 672 2
4680.2.db $$\chi_{4680}(1513, \cdot)$$ n/a 210 2
4680.2.dc $$\chi_{4680}(4103, \cdot)$$ None 0 2
4680.2.dd $$\chi_{4680}(1477, \cdot)$$ n/a 832 2
4680.2.dh $$\chi_{4680}(4021, \cdot)$$ n/a 1344 2
4680.2.di $$\chi_{4680}(3299, \cdot)$$ n/a 2000 2
4680.2.dk $$\chi_{4680}(529, \cdot)$$ n/a 504 2
4680.2.dn $$\chi_{4680}(191, \cdot)$$ None 0 2
4680.2.do $$\chi_{4680}(959, \cdot)$$ None 0 2
4680.2.dr $$\chi_{4680}(1681, \cdot)$$ n/a 336 2
4680.2.dt $$\chi_{4680}(2291, \cdot)$$ n/a 1344 2
4680.2.du $$\chi_{4680}(2869, \cdot)$$ n/a 2000 2
4680.2.dx $$\chi_{4680}(2219, \cdot)$$ n/a 2000 2
4680.2.dy $$\chi_{4680}(2941, \cdot)$$ n/a 1344 2
4680.2.ea $$\chi_{4680}(1031, \cdot)$$ None 0 2
4680.2.ed $$\chi_{4680}(1609, \cdot)$$ n/a 504 2
4680.2.ee $$\chi_{4680}(1091, \cdot)$$ n/a 1344 2
4680.2.eh $$\chi_{4680}(1429, \cdot)$$ n/a 2000 2
4680.2.ek $$\chi_{4680}(1439, \cdot)$$ None 0 2
4680.2.em $$\chi_{4680}(829, \cdot)$$ n/a 832 2
4680.2.en $$\chi_{4680}(251, \cdot)$$ n/a 448 2
4680.2.eq $$\chi_{4680}(599, \cdot)$$ None 0 2
4680.2.et $$\chi_{4680}(2209, \cdot)$$ n/a 504 2
4680.2.eu $$\chi_{4680}(311, \cdot)$$ None 0 2
4680.2.ex $$\chi_{4680}(1979, \cdot)$$ n/a 672 2
4680.2.ey $$\chi_{4680}(1621, \cdot)$$ n/a 560 2
4680.2.fa $$\chi_{4680}(2591, \cdot)$$ None 0 2
4680.2.fd $$\chi_{4680}(1369, \cdot)$$ n/a 208 2
4680.2.fe $$\chi_{4680}(781, \cdot)$$ n/a 1152 2
4680.2.fh $$\chi_{4680}(1379, \cdot)$$ n/a 1728 2
4680.2.fk $$\chi_{4680}(1199, \cdot)$$ None 0 2
4680.2.fm $$\chi_{4680}(589, \cdot)$$ n/a 2000 2
4680.2.fn $$\chi_{4680}(3371, \cdot)$$ n/a 1344 2
4680.2.fq $$\chi_{4680}(3839, \cdot)$$ None 0 2
4680.2.fr $$\chi_{4680}(121, \cdot)$$ n/a 336 2
4680.2.ft $$\chi_{4680}(731, \cdot)$$ n/a 1344 2
4680.2.fw $$\chi_{4680}(1069, \cdot)$$ n/a 2000 2
4680.2.fx $$\chi_{4680}(911, \cdot)$$ None 0 2
4680.2.ga $$\chi_{4680}(1249, \cdot)$$ n/a 432 2
4680.2.gb $$\chi_{4680}(901, \cdot)$$ n/a 560 2
4680.2.ge $$\chi_{4680}(179, \cdot)$$ n/a 672 2
4680.2.gg $$\chi_{4680}(289, \cdot)$$ n/a 212 2
4680.2.gh $$\chi_{4680}(1511, \cdot)$$ None 0 2
4680.2.gk $$\chi_{4680}(779, \cdot)$$ n/a 2000 2
4680.2.gl $$\chi_{4680}(1741, \cdot)$$ n/a 1344 2
4680.2.go $$\chi_{4680}(2029, \cdot)$$ n/a 1728 2
4680.2.gp $$\chi_{4680}(131, \cdot)$$ n/a 1152 2
4680.2.gs $$\chi_{4680}(719, \cdot)$$ None 0 2
4680.2.gt $$\chi_{4680}(361, \cdot)$$ n/a 140 2
4680.2.gv $$\chi_{4680}(971, \cdot)$$ n/a 448 2
4680.2.gy $$\chi_{4680}(2629, \cdot)$$ n/a 832 2
4680.2.gz $$\chi_{4680}(961, \cdot)$$ n/a 336 2
4680.2.hc $$\chi_{4680}(1559, \cdot)$$ None 0 2
4680.2.hd $$\chi_{4680}(1141, \cdot)$$ n/a 1344 2
4680.2.hg $$\chi_{4680}(1499, \cdot)$$ n/a 2000 2
4680.2.hi $$\chi_{4680}(3409, \cdot)$$ n/a 504 2
4680.2.hj $$\chi_{4680}(1751, \cdot)$$ None 0 2
4680.2.hm $$\chi_{4680}(2759, \cdot)$$ None 0 2
4680.2.ho $$\chi_{4680}(2149, \cdot)$$ n/a 2000 2
4680.2.hr $$\chi_{4680}(491, \cdot)$$ n/a 1344 2
4680.2.hs $$\chi_{4680}(419, \cdot)$$ n/a 2000 2
4680.2.hv $$\chi_{4680}(61, \cdot)$$ n/a 1344 2
4680.2.hx $$\chi_{4680}(2831, \cdot)$$ None 0 2
4680.2.hy $$\chi_{4680}(49, \cdot)$$ n/a 504 2
4680.2.ia $$\chi_{4680}(167, \cdot)$$ None 0 4
4680.2.ib $$\chi_{4680}(1237, \cdot)$$ n/a 4000 4
4680.2.ig $$\chi_{4680}(1163, \cdot)$$ n/a 4000 4
4680.2.ih $$\chi_{4680}(97, \cdot)$$ n/a 1008 4
4680.2.ii $$\chi_{4680}(817, \cdot)$$ n/a 1008 4
4680.2.ij $$\chi_{4680}(587, \cdot)$$ n/a 4000 4
4680.2.im $$\chi_{4680}(733, \cdot)$$ n/a 4000 4
4680.2.in $$\chi_{4680}(983, \cdot)$$ None 0 4
4680.2.iq $$\chi_{4680}(1007, \cdot)$$ None 0 4
4680.2.ir $$\chi_{4680}(37, \cdot)$$ n/a 1664 4
4680.2.iw $$\chi_{4680}(323, \cdot)$$ n/a 1344 4
4680.2.ix $$\chi_{4680}(2377, \cdot)$$ n/a 420 4
4680.2.ja $$\chi_{4680}(697, \cdot)$$ n/a 1008 4
4680.2.jb $$\chi_{4680}(203, \cdot)$$ n/a 4000 4
4680.2.je $$\chi_{4680}(1813, \cdot)$$ n/a 4000 4
4680.2.jf $$\chi_{4680}(1463, \cdot)$$ None 0 4
4680.2.jg $$\chi_{4680}(367, \cdot)$$ None 0 4
4680.2.jj $$\chi_{4680}(907, \cdot)$$ n/a 4000 4
4680.2.jk $$\chi_{4680}(797, \cdot)$$ n/a 4000 4
4680.2.jn $$\chi_{4680}(113, \cdot)$$ n/a 1008 4
4680.2.jo $$\chi_{4680}(547, \cdot)$$ n/a 3456 4
4680.2.jr $$\chi_{4680}(103, \cdot)$$ None 0 4
4680.2.js $$\chi_{4680}(17, \cdot)$$ n/a 336 4
4680.2.jv $$\chi_{4680}(257, \cdot)$$ n/a 1008 4
4680.2.jw $$\chi_{4680}(653, \cdot)$$ n/a 4000 4
4680.2.jz $$\chi_{4680}(1277, \cdot)$$ n/a 1344 4
4680.2.ka $$\chi_{4680}(523, \cdot)$$ n/a 1664 4
4680.2.kd $$\chi_{4680}(763, \cdot)$$ n/a 4000 4
4680.2.ke $$\chi_{4680}(1447, \cdot)$$ None 0 4
4680.2.kh $$\chi_{4680}(127, \cdot)$$ None 0 4
4680.2.ki $$\chi_{4680}(857, \cdot)$$ n/a 1008 4
4680.2.kl $$\chi_{4680}(677, \cdot)$$ n/a 3456 4
4680.2.kn $$\chi_{4680}(31, \cdot)$$ None 0 4
4680.2.ko $$\chi_{4680}(931, \cdot)$$ n/a 2688 4
4680.2.kq $$\chi_{4680}(749, \cdot)$$ n/a 4000 4
4680.2.kt $$\chi_{4680}(1409, \cdot)$$ n/a 1008 4
4680.2.ku $$\chi_{4680}(799, \cdot)$$ None 0 4
4680.2.kx $$\chi_{4680}(1939, \cdot)$$ n/a 4000 4
4680.2.ky $$\chi_{4680}(761, \cdot)$$ n/a 672 4
4680.2.lb $$\chi_{4680}(3581, \cdot)$$ n/a 896 4
4680.2.lc $$\chi_{4680}(1241, \cdot)$$ n/a 224 4
4680.2.lf $$\chi_{4680}(821, \cdot)$$ n/a 2688 4
4680.2.lh $$\chi_{4680}(1579, \cdot)$$ n/a 4000 4
4680.2.li $$\chi_{4680}(2359, \cdot)$$ None 0 4
4680.2.ll $$\chi_{4680}(19, \cdot)$$ n/a 1664 4
4680.2.lm $$\chi_{4680}(319, \cdot)$$ None 0 4
4680.2.lp $$\chi_{4680}(461, \cdot)$$ n/a 2688 4
4680.2.lq $$\chi_{4680}(41, \cdot)$$ n/a 672 4
4680.2.ls $$\chi_{4680}(509, \cdot)$$ n/a 4000 4
4680.2.lv $$\chi_{4680}(929, \cdot)$$ n/a 1008 4
4680.2.lw $$\chi_{4680}(691, \cdot)$$ n/a 2688 4
4680.2.lz $$\chi_{4680}(271, \cdot)$$ None 0 4
4680.2.ma $$\chi_{4680}(1891, \cdot)$$ n/a 1120 4
4680.2.md $$\chi_{4680}(1111, \cdot)$$ None 0 4
4680.2.mf $$\chi_{4680}(1289, \cdot)$$ n/a 1008 4
4680.2.mg $$\chi_{4680}(1709, \cdot)$$ n/a 1344 4
4680.2.mj $$\chi_{4680}(89, \cdot)$$ n/a 336 4
4680.2.mk $$\chi_{4680}(149, \cdot)$$ n/a 4000 4
4680.2.mn $$\chi_{4680}(1471, \cdot)$$ None 0 4
4680.2.mo $$\chi_{4680}(331, \cdot)$$ n/a 2688 4
4680.2.mr $$\chi_{4680}(941, \cdot)$$ n/a 2688 4
4680.2.ms $$\chi_{4680}(281, \cdot)$$ n/a 672 4
4680.2.mu $$\chi_{4680}(1399, \cdot)$$ None 0 4
4680.2.mx $$\chi_{4680}(499, \cdot)$$ n/a 4000 4
4680.2.mz $$\chi_{4680}(833, \cdot)$$ n/a 864 4
4680.2.na $$\chi_{4680}(77, \cdot)$$ n/a 4000 4
4680.2.nc $$\chi_{4680}(43, \cdot)$$ n/a 4000 4
4680.2.nf $$\chi_{4680}(667, \cdot)$$ n/a 1664 4
4680.2.ng $$\chi_{4680}(1927, \cdot)$$ None 0 4
4680.2.nj $$\chi_{4680}(2167, \cdot)$$ None 0 4
4680.2.nk $$\chi_{4680}(2057, \cdot)$$ n/a 1008 4
4680.2.nn $$\chi_{4680}(737, \cdot)$$ n/a 336 4
4680.2.no $$\chi_{4680}(413, \cdot)$$ n/a 1344 4
4680.2.nr $$\chi_{4680}(173, \cdot)$$ n/a 4000 4
4680.2.nt $$\chi_{4680}(1507, \cdot)$$ n/a 4000 4
4680.2.nu $$\chi_{4680}(1327, \cdot)$$ None 0 4
4680.2.nx $$\chi_{4680}(1517, \cdot)$$ n/a 4000 4
4680.2.ny $$\chi_{4680}(3137, \cdot)$$ n/a 1008 4
4680.2.ob $$\chi_{4680}(823, \cdot)$$ None 0 4
4680.2.oc $$\chi_{4680}(2707, \cdot)$$ n/a 4000 4
4680.2.og $$\chi_{4680}(947, \cdot)$$ n/a 4000 4
4680.2.oh $$\chi_{4680}(457, \cdot)$$ n/a 1008 4
4680.2.ok $$\chi_{4680}(973, \cdot)$$ n/a 1664 4
4680.2.ol $$\chi_{4680}(1727, \cdot)$$ None 0 4
4680.2.oo $$\chi_{4680}(47, \cdot)$$ None 0 4
4680.2.op $$\chi_{4680}(853, \cdot)$$ n/a 4000 4
4680.2.oq $$\chi_{4680}(83, \cdot)$$ n/a 4000 4
4680.2.or $$\chi_{4680}(1633, \cdot)$$ n/a 1008 4
4680.2.ou $$\chi_{4680}(1657, \cdot)$$ n/a 420 4
4680.2.ov $$\chi_{4680}(4067, \cdot)$$ n/a 1344 4
4680.2.oy $$\chi_{4680}(383, \cdot)$$ None 0 4
4680.2.oz $$\chi_{4680}(877, \cdot)$$ n/a 4000 4
4680.2.pe $$\chi_{4680}(1597, \cdot)$$ n/a 4000 4
4680.2.pf $$\chi_{4680}(1103, \cdot)$$ None 0 4
4680.2.pg $$\chi_{4680}(1033, \cdot)$$ n/a 1008 4
4680.2.ph $$\chi_{4680}(227, \cdot)$$ n/a 4000 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4680))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4680)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(936))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1170))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2340))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4680))$$$$^{\oplus 1}$$