# Properties

 Label 3640.2 Level 3640 Weight 2 Dimension 187672 Nonzero newspaces 150 Sturm bound 1548288 Trace bound 41

## Defining parameters

 Level: $$N$$ = $$3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$150$$ Sturm bound: $$1548288$$ Trace bound: $$41$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3640))$$.

Total New Old
Modular forms 393984 190312 203672
Cusp forms 380161 187672 192489
Eisenstein series 13823 2640 11183

## Trace form

 $$187672 q - 88 q^{2} - 88 q^{3} - 88 q^{4} - 4 q^{5} - 248 q^{6} - 112 q^{7} - 208 q^{8} - 220 q^{9} + O(q^{10})$$ $$187672 q - 88 q^{2} - 88 q^{3} - 88 q^{4} - 4 q^{5} - 248 q^{6} - 112 q^{7} - 208 q^{8} - 220 q^{9} - 124 q^{10} - 288 q^{11} - 40 q^{12} - 16 q^{13} - 200 q^{14} - 296 q^{15} - 184 q^{16} - 204 q^{17} + 96 q^{18} - 72 q^{19} - 8 q^{20} - 32 q^{21} - 8 q^{22} - 48 q^{23} + 168 q^{24} - 232 q^{25} - 176 q^{26} - 160 q^{27} + 80 q^{28} - 84 q^{29} - 12 q^{30} - 192 q^{31} - 48 q^{32} - 248 q^{33} - 72 q^{34} - 140 q^{35} - 472 q^{36} - 12 q^{37} - 96 q^{38} - 8 q^{39} - 272 q^{40} - 564 q^{41} - 144 q^{42} + 80 q^{43} + 8 q^{44} + 74 q^{45} + 16 q^{46} + 240 q^{47} + 40 q^{48} - 116 q^{49} - 32 q^{50} + 320 q^{51} + 280 q^{52} + 192 q^{53} + 168 q^{54} + 256 q^{55} - 144 q^{56} - 80 q^{57} + 368 q^{58} + 392 q^{59} + 160 q^{60} + 236 q^{61} + 176 q^{62} + 272 q^{63} + 56 q^{64} - 206 q^{65} - 344 q^{66} + 64 q^{67} + 8 q^{68} + 128 q^{69} - 36 q^{70} - 624 q^{71} - 48 q^{72} - 112 q^{73} + 184 q^{74} - 208 q^{75} + 72 q^{76} + 88 q^{77} - 176 q^{78} - 320 q^{79} + 24 q^{80} - 372 q^{81} + 72 q^{82} - 312 q^{83} + 104 q^{84} + 26 q^{85} + 56 q^{86} + 48 q^{87} - 24 q^{88} - 64 q^{89} - 280 q^{90} - 220 q^{91} - 472 q^{92} + 168 q^{93} - 184 q^{94} + 24 q^{95} - 792 q^{96} + 136 q^{97} - 136 q^{98} + 272 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3640))$$

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
3640.2.a $$\chi_{3640}(1, \cdot)$$ 3640.2.a.a 1 1
3640.2.a.b 1
3640.2.a.c 1
3640.2.a.d 1
3640.2.a.e 1
3640.2.a.f 1
3640.2.a.g 1
3640.2.a.h 1
3640.2.a.i 1
3640.2.a.j 1
3640.2.a.k 2
3640.2.a.l 2
3640.2.a.m 2
3640.2.a.n 2
3640.2.a.o 3
3640.2.a.p 3
3640.2.a.q 3
3640.2.a.r 4
3640.2.a.s 4
3640.2.a.t 4
3640.2.a.u 4
3640.2.a.v 4
3640.2.a.w 4
3640.2.a.x 4
3640.2.a.y 5
3640.2.a.z 5
3640.2.a.ba 7
3640.2.b $$\chi_{3640}(3249, \cdot)$$ n/a 128 1
3640.2.d $$\chi_{3640}(1091, \cdot)$$ n/a 448 1
3640.2.g $$\chi_{3640}(1821, \cdot)$$ n/a 288 1
3640.2.i $$\chi_{3640}(1119, \cdot)$$ None 0 1
3640.2.j $$\chi_{3640}(2211, \cdot)$$ n/a 384 1
3640.2.l $$\chi_{3640}(729, \cdot)$$ n/a 108 1
3640.2.o $$\chi_{3640}(3639, \cdot)$$ None 0 1
3640.2.q $$\chi_{3640}(701, \cdot)$$ n/a 336 1
3640.2.r $$\chi_{3640}(2549, \cdot)$$ n/a 432 1
3640.2.t $$\chi_{3640}(391, \cdot)$$ None 0 1
3640.2.w $$\chi_{3640}(2521, \cdot)$$ 3640.2.w.a 2 1
3640.2.w.b 2
3640.2.w.c 2
3640.2.w.d 2
3640.2.w.e 2
3640.2.w.f 2
3640.2.w.g 2
3640.2.w.h 2
3640.2.w.i 4
3640.2.w.j 4
3640.2.w.k 4
3640.2.w.l 6
3640.2.w.m 6
3640.2.w.n 8
3640.2.w.o 12
3640.2.w.p 24
3640.2.y $$\chi_{3640}(1819, \cdot)$$ n/a 664 1
3640.2.z $$\chi_{3640}(2911, \cdot)$$ None 0 1
3640.2.bb $$\chi_{3640}(1429, \cdot)$$ n/a 504 1
3640.2.be $$\chi_{3640}(2939, \cdot)$$ n/a 576 1
3640.2.bg $$\chi_{3640}(841, \cdot)$$ n/a 168 2
3640.2.bh $$\chi_{3640}(2081, \cdot)$$ n/a 192 2
3640.2.bi $$\chi_{3640}(3201, \cdot)$$ n/a 224 2
3640.2.bj $$\chi_{3640}(81, \cdot)$$ n/a 224 2
3640.2.bm $$\chi_{3640}(629, \cdot)$$ n/a 1328 2
3640.2.bn $$\chi_{3640}(1191, \cdot)$$ None 0 2
3640.2.bo $$\chi_{3640}(99, \cdot)$$ n/a 1008 2
3640.2.bp $$\chi_{3640}(1721, \cdot)$$ n/a 224 2
3640.2.bt $$\chi_{3640}(1273, \cdot)$$ n/a 336 2
3640.2.bu $$\chi_{3640}(573, \cdot)$$ n/a 1152 2
3640.2.bx $$\chi_{3640}(183, \cdot)$$ None 0 2
3640.2.by $$\chi_{3640}(883, \cdot)$$ n/a 1008 2
3640.2.ca $$\chi_{3640}(447, \cdot)$$ None 0 2
3640.2.cd $$\chi_{3640}(1513, \cdot)$$ n/a 252 2
3640.2.ce $$\chi_{3640}(57, \cdot)$$ n/a 252 2
3640.2.ch $$\chi_{3640}(1903, \cdot)$$ None 0 2
3640.2.cj $$\chi_{3640}(3333, \cdot)$$ n/a 1008 2
3640.2.ck $$\chi_{3640}(1763, \cdot)$$ n/a 1328 2
3640.2.cn $$\chi_{3640}(83, \cdot)$$ n/a 1328 2
3640.2.co $$\chi_{3640}(1373, \cdot)$$ n/a 1008 2
3640.2.cq $$\chi_{3640}(1247, \cdot)$$ None 0 2
3640.2.ct $$\chi_{3640}(547, \cdot)$$ n/a 864 2
3640.2.cu $$\chi_{3640}(937, \cdot)$$ n/a 288 2
3640.2.cx $$\chi_{3640}(1637, \cdot)$$ n/a 1328 2
3640.2.da $$\chi_{3640}(1331, \cdot)$$ n/a 672 2
3640.2.db $$\chi_{3640}(489, \cdot)$$ n/a 336 2
3640.2.dc $$\chi_{3640}(1581, \cdot)$$ n/a 896 2
3640.2.dd $$\chi_{3640}(239, \cdot)$$ None 0 2
3640.2.dg $$\chi_{3640}(1101, \cdot)$$ n/a 896 2
3640.2.di $$\chi_{3640}(3279, \cdot)$$ None 0 2
3640.2.dl $$\chi_{3640}(849, \cdot)$$ n/a 336 2
3640.2.dn $$\chi_{3640}(1011, \cdot)$$ n/a 896 2
3640.2.do $$\chi_{3640}(719, \cdot)$$ None 0 2
3640.2.dq $$\chi_{3640}(1941, \cdot)$$ n/a 896 2
3640.2.dt $$\chi_{3640}(731, \cdot)$$ n/a 896 2
3640.2.dv $$\chi_{3640}(9, \cdot)$$ n/a 336 2
3640.2.dw $$\chi_{3640}(2389, \cdot)$$ n/a 1328 2
3640.2.dy $$\chi_{3640}(3111, \cdot)$$ None 0 2
3640.2.ec $$\chi_{3640}(339, \cdot)$$ n/a 1152 2
3640.2.ed $$\chi_{3640}(139, \cdot)$$ n/a 1328 2
3640.2.ei $$\chi_{3640}(389, \cdot)$$ n/a 1328 2
3640.2.ej $$\chi_{3640}(309, \cdot)$$ n/a 1008 2
3640.2.em $$\chi_{3640}(1791, \cdot)$$ None 0 2
3640.2.en $$\chi_{3640}(311, \cdot)$$ None 0 2
3640.2.eq $$\chi_{3640}(1179, \cdot)$$ n/a 1328 2
3640.2.er $$\chi_{3640}(2271, \cdot)$$ None 0 2
3640.2.et $$\chi_{3640}(2109, \cdot)$$ n/a 1328 2
3640.2.ev $$\chi_{3640}(2859, \cdot)$$ n/a 1328 2
3640.2.ew $$\chi_{3640}(699, \cdot)$$ n/a 1328 2
3640.2.ez $$\chi_{3640}(1401, \cdot)$$ n/a 168 2
3640.2.fa $$\chi_{3640}(961, \cdot)$$ n/a 224 2
3640.2.ff $$\chi_{3640}(1231, \cdot)$$ None 0 2
3640.2.fg $$\chi_{3640}(1431, \cdot)$$ None 0 2
3640.2.fj $$\chi_{3640}(989, \cdot)$$ n/a 1152 2
3640.2.fk $$\chi_{3640}(29, \cdot)$$ n/a 1008 2
3640.2.fm $$\chi_{3640}(2019, \cdot)$$ n/a 1328 2
3640.2.fo $$\chi_{3640}(641, \cdot)$$ n/a 224 2
3640.2.fp $$\chi_{3640}(289, \cdot)$$ n/a 336 2
3640.2.fr $$\chi_{3640}(451, \cdot)$$ n/a 896 2
3640.2.ft $$\chi_{3640}(2781, \cdot)$$ n/a 896 2
3640.2.fu $$\chi_{3640}(3221, \cdot)$$ n/a 672 2
3640.2.fx $$\chi_{3640}(2519, \cdot)$$ None 0 2
3640.2.fy $$\chi_{3640}(1039, \cdot)$$ None 0 2
3640.2.gd $$\chi_{3640}(1569, \cdot)$$ n/a 248 2
3640.2.ge $$\chi_{3640}(2809, \cdot)$$ n/a 288 2
3640.2.gh $$\chi_{3640}(131, \cdot)$$ n/a 768 2
3640.2.gi $$\chi_{3640}(3051, \cdot)$$ n/a 896 2
3640.2.gk $$\chi_{3640}(1661, \cdot)$$ n/a 896 2
3640.2.gm $$\chi_{3640}(199, \cdot)$$ None 0 2
3640.2.gn $$\chi_{3640}(1291, \cdot)$$ n/a 896 2
3640.2.gp $$\chi_{3640}(569, \cdot)$$ n/a 336 2
3640.2.gr $$\chi_{3640}(1959, \cdot)$$ None 0 2
3640.2.gs $$\chi_{3640}(2159, \cdot)$$ None 0 2
3640.2.gv $$\chi_{3640}(261, \cdot)$$ n/a 768 2
3640.2.gw $$\chi_{3640}(2661, \cdot)$$ n/a 672 2
3640.2.hb $$\chi_{3640}(2131, \cdot)$$ n/a 896 2
3640.2.hc $$\chi_{3640}(251, \cdot)$$ n/a 896 2
3640.2.hf $$\chi_{3640}(2129, \cdot)$$ n/a 256 2
3640.2.hg $$\chi_{3640}(1689, \cdot)$$ n/a 336 2
3640.2.hi $$\chi_{3640}(159, \cdot)$$ None 0 2
3640.2.hk $$\chi_{3640}(1381, \cdot)$$ n/a 896 2
3640.2.hl $$\chi_{3640}(121, \cdot)$$ n/a 224 2
3640.2.hn $$\chi_{3640}(1739, \cdot)$$ n/a 1328 2
3640.2.hq $$\chi_{3640}(1829, \cdot)$$ n/a 1328 2
3640.2.hs $$\chi_{3640}(2551, \cdot)$$ None 0 2
3640.2.ht $$\chi_{3640}(1459, \cdot)$$ n/a 1328 2
3640.2.hx $$\chi_{3640}(2831, \cdot)$$ None 0 2
3640.2.hz $$\chi_{3640}(2669, \cdot)$$ n/a 1328 2
3640.2.ic $$\chi_{3640}(201, \cdot)$$ n/a 448 4
3640.2.id $$\chi_{3640}(739, \cdot)$$ n/a 2656 4
3640.2.ie $$\chi_{3640}(431, \cdot)$$ None 0 4
3640.2.if $$\chi_{3640}(1389, \cdot)$$ n/a 2656 4
3640.2.ik $$\chi_{3640}(89, \cdot)$$ n/a 672 4
3640.2.il $$\chi_{3640}(851, \cdot)$$ n/a 1792 4
3640.2.iq $$\chi_{3640}(941, \cdot)$$ n/a 1792 4
3640.2.ir $$\chi_{3640}(799, \cdot)$$ None 0 4
3640.2.is $$\chi_{3640}(461, \cdot)$$ n/a 1792 4
3640.2.it $$\chi_{3640}(359, \cdot)$$ None 0 4
3640.2.iu $$\chi_{3640}(291, \cdot)$$ n/a 1792 4
3640.2.iv $$\chi_{3640}(769, \cdot)$$ n/a 672 4
3640.2.iw $$\chi_{3640}(1051, \cdot)$$ n/a 1344 4
3640.2.ix $$\chi_{3640}(369, \cdot)$$ n/a 672 4
3640.2.jc $$\chi_{3640}(319, \cdot)$$ None 0 4
3640.2.jd $$\chi_{3640}(1181, \cdot)$$ n/a 1792 4
3640.2.jh $$\chi_{3640}(1277, \cdot)$$ n/a 2656 4
3640.2.ji $$\chi_{3640}(537, \cdot)$$ n/a 672 4
3640.2.jl $$\chi_{3640}(667, \cdot)$$ n/a 2656 4
3640.2.jm $$\chi_{3640}(263, \cdot)$$ None 0 4
3640.2.jp $$\chi_{3640}(747, \cdot)$$ n/a 2656 4
3640.2.jq $$\chi_{3640}(557, \cdot)$$ n/a 2656 4
3640.2.jt $$\chi_{3640}(877, \cdot)$$ n/a 2656 4
3640.2.ju $$\chi_{3640}(1307, \cdot)$$ n/a 2656 4
3640.2.jw $$\chi_{3640}(513, \cdot)$$ n/a 672 4
3640.2.jz $$\chi_{3640}(943, \cdot)$$ None 0 4
3640.2.ka $$\chi_{3640}(383, \cdot)$$ None 0 4
3640.2.kd $$\chi_{3640}(193, \cdot)$$ n/a 672 4
3640.2.ke $$\chi_{3640}(627, \cdot)$$ n/a 2656 4
3640.2.kh $$\chi_{3640}(303, \cdot)$$ None 0 4
3640.2.ki $$\chi_{3640}(173, \cdot)$$ n/a 2656 4
3640.2.kl $$\chi_{3640}(913, \cdot)$$ n/a 672 4
3640.2.km $$\chi_{3640}(313, \cdot)$$ n/a 576 4
3640.2.ko $$\chi_{3640}(1837, \cdot)$$ n/a 2656 4
3640.2.kq $$\chi_{3640}(517, \cdot)$$ n/a 2656 4
3640.2.kt $$\chi_{3640}(1777, \cdot)$$ n/a 672 4
3640.2.kv $$\chi_{3640}(633, \cdot)$$ n/a 672 4
3640.2.kx $$\chi_{3640}(493, \cdot)$$ n/a 2656 4
3640.2.ky $$\chi_{3640}(207, \cdot)$$ None 0 4
3640.2.la $$\chi_{3640}(1387, \cdot)$$ n/a 2016 4
3640.2.lc $$\chi_{3640}(107, \cdot)$$ n/a 2656 4
3640.2.lf $$\chi_{3640}(23, \cdot)$$ None 0 4
3640.2.lh $$\chi_{3640}(127, \cdot)$$ None 0 4
3640.2.lj $$\chi_{3640}(443, \cdot)$$ n/a 2304 4
3640.2.lk $$\chi_{3640}(47, \cdot)$$ None 0 4
3640.2.ln $$\chi_{3640}(1633, \cdot)$$ n/a 672 4
3640.2.lo $$\chi_{3640}(177, \cdot)$$ n/a 672 4
3640.2.lr $$\chi_{3640}(983, \cdot)$$ None 0 4
3640.2.ls $$\chi_{3640}(787, \cdot)$$ n/a 2656 4
3640.2.lu $$\chi_{3640}(197, \cdot)$$ n/a 2016 4
3640.2.lx $$\chi_{3640}(643, \cdot)$$ n/a 2656 4
3640.2.lz $$\chi_{3640}(1397, \cdot)$$ n/a 2656 4
3640.2.ma $$\chi_{3640}(37, \cdot)$$ n/a 2656 4
3640.2.mc $$\chi_{3640}(587, \cdot)$$ n/a 2656 4
3640.2.mf $$\chi_{3640}(253, \cdot)$$ n/a 2016 4
3640.2.mh $$\chi_{3640}(227, \cdot)$$ n/a 2656 4
3640.2.mj $$\chi_{3640}(457, \cdot)$$ n/a 672 4
3640.2.ml $$\chi_{3640}(167, \cdot)$$ None 0 4
3640.2.mm $$\chi_{3640}(617, \cdot)$$ n/a 504 4
3640.2.mo $$\chi_{3640}(1727, \cdot)$$ None 0 4
3640.2.mr $$\chi_{3640}(327, \cdot)$$ None 0 4
3640.2.mt $$\chi_{3640}(1177, \cdot)$$ n/a 504 4
3640.2.mu $$\chi_{3640}(1007, \cdot)$$ None 0 4
3640.2.mw $$\chi_{3640}(137, \cdot)$$ n/a 672 4
3640.2.mz $$\chi_{3640}(317, \cdot)$$ n/a 2656 4
3640.2.na $$\chi_{3640}(1123, \cdot)$$ n/a 2656 4
3640.2.nd $$\chi_{3640}(187, \cdot)$$ n/a 2656 4
3640.2.ne $$\chi_{3640}(1773, \cdot)$$ n/a 2656 4
3640.2.nh $$\chi_{3640}(807, \cdot)$$ None 0 4
3640.2.nj $$\chi_{3640}(387, \cdot)$$ n/a 2656 4
3640.2.nl $$\chi_{3640}(43, \cdot)$$ n/a 2016 4
3640.2.nm $$\chi_{3640}(1023, \cdot)$$ None 0 4
3640.2.no $$\chi_{3640}(1927, \cdot)$$ None 0 4
3640.2.nq $$\chi_{3640}(1507, \cdot)$$ n/a 2656 4
3640.2.nt $$\chi_{3640}(857, \cdot)$$ n/a 672 4
3640.2.nv $$\chi_{3640}(237, \cdot)$$ n/a 2656 4
3640.2.nx $$\chi_{3640}(997, \cdot)$$ n/a 2656 4
3640.2.ny $$\chi_{3640}(17, \cdot)$$ n/a 672 4
3640.2.oa $$\chi_{3640}(153, \cdot)$$ n/a 672 4
3640.2.oc $$\chi_{3640}(157, \cdot)$$ n/a 2304 4
3640.2.og $$\chi_{3640}(1311, \cdot)$$ None 0 4
3640.2.oh $$\chi_{3640}(509, \cdot)$$ n/a 2656 4
3640.2.om $$\chi_{3640}(499, \cdot)$$ n/a 2656 4
3640.2.on $$\chi_{3640}(41, \cdot)$$ n/a 448 4
3640.2.oo $$\chi_{3640}(379, \cdot)$$ n/a 2016 4
3640.2.op $$\chi_{3640}(801, \cdot)$$ n/a 448 4
3640.2.oq $$\chi_{3640}(229, \cdot)$$ n/a 2656 4
3640.2.or $$\chi_{3640}(71, \cdot)$$ None 0 4
3640.2.os $$\chi_{3640}(349, \cdot)$$ n/a 2656 4
3640.2.ot $$\chi_{3640}(151, \cdot)$$ None 0 4
3640.2.oy $$\chi_{3640}(241, \cdot)$$ n/a 448 4
3640.2.oz $$\chi_{3640}(219, \cdot)$$ n/a 2656 4
3640.2.pe $$\chi_{3640}(1159, \cdot)$$ None 0 4
3640.2.pf $$\chi_{3640}(661, \cdot)$$ n/a 1792 4
3640.2.pg $$\chi_{3640}(929, \cdot)$$ n/a 672 4
3640.2.ph $$\chi_{3640}(11, \cdot)$$ n/a 1792 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3640))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3640)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(455))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(910))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1820))$$$$^{\oplus 2}$$