Properties

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

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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

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