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Properties

Label 21168.2
Level 21168
Weight 2
Dimension 5193144
Nonzero newspaces 128
Sturm bound 48771072

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Defining parameters

Level: \( N \) = \( 21168 = 2^{4} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(48771072\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(21168))\).

Total New Old
Modular forms 12243168 5207112 7036056
Cusp forms 12142369 5193144 6949225
Eisenstein series 100799 13968 86831

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(21168))\)

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
21168.2.a \(\chi_{21168}(1, \cdot)\) 21168.2.a.a 1 1
21168.2.a.b 1
21168.2.a.c 1
21168.2.a.d 1
21168.2.a.e 1
21168.2.a.f 1
21168.2.a.g 1
21168.2.a.h 1
21168.2.a.i 1
21168.2.a.j 1
21168.2.a.k 1
21168.2.a.l 1
21168.2.a.m 1
21168.2.a.n 1
21168.2.a.o 1
21168.2.a.p 1
21168.2.a.q 1
21168.2.a.r 1
21168.2.a.s 1
21168.2.a.t 1
21168.2.a.u 1
21168.2.a.v 1
21168.2.a.w 1
21168.2.a.x 1
21168.2.a.y 1
21168.2.a.z 1
21168.2.a.ba 1
21168.2.a.bb 1
21168.2.a.bc 1
21168.2.a.bd 1
21168.2.a.be 1
21168.2.a.bf 1
21168.2.a.bg 1
21168.2.a.bh 1
21168.2.a.bi 1
21168.2.a.bj 1
21168.2.a.bk 1
21168.2.a.bl 1
21168.2.a.bm 1
21168.2.a.bn 1
21168.2.a.bo 1
21168.2.a.bp 1
21168.2.a.bq 1
21168.2.a.br 1
21168.2.a.bs 1
21168.2.a.bt 1
21168.2.a.bu 1
21168.2.a.bv 1
21168.2.a.bw 1
21168.2.a.bx 1
21168.2.a.by 1
21168.2.a.bz 1
21168.2.a.ca 1
21168.2.a.cb 1
21168.2.a.cc 1
21168.2.a.cd 1
21168.2.a.ce 1
21168.2.a.cf 1
21168.2.a.cg 1
21168.2.a.ch 1
21168.2.a.ci 1
21168.2.a.cj 1
21168.2.a.ck 1
21168.2.a.cl 1
21168.2.a.cm 1
21168.2.a.cn 1
21168.2.a.co 1
21168.2.a.cp 1
21168.2.a.cq 1
21168.2.a.cr 1
21168.2.a.cs 1
21168.2.a.ct 1
21168.2.a.cu 1
21168.2.a.cv 1
21168.2.a.cw 1
21168.2.a.cx 1
21168.2.a.cy 1
21168.2.a.cz 1
21168.2.a.da 1
21168.2.a.db 1
21168.2.a.dc 1
21168.2.a.dd 1
21168.2.a.de 1
21168.2.a.df 1
21168.2.a.dg 1
21168.2.a.dh 1
21168.2.a.di 1
21168.2.a.dj 1
21168.2.a.dk 1
21168.2.a.dl 1
21168.2.a.dm 1
21168.2.a.dn 1
21168.2.a.do 1
21168.2.a.dp 1
21168.2.a.dq 1
21168.2.a.dr 1
21168.2.a.ds 1
21168.2.a.dt 1
21168.2.a.du 1
21168.2.a.dv 1
21168.2.a.dw 1
21168.2.a.dx 1
21168.2.a.dy 2
21168.2.a.dz 2
21168.2.a.ea 2
21168.2.a.eb 2
21168.2.a.ec 2
21168.2.a.ed 2
21168.2.a.ee 2
21168.2.a.ef 2
21168.2.a.eg 2
21168.2.a.eh 2
21168.2.a.ei 2
21168.2.a.ej 2
21168.2.a.ek 2
21168.2.a.el 2
21168.2.a.em 2
21168.2.a.en 2
21168.2.a.eo 2
21168.2.a.ep 2
21168.2.a.eq 2
21168.2.a.er 2
21168.2.a.es 2
21168.2.a.et 2
21168.2.a.eu 2
21168.2.a.ev 2
21168.2.a.ew 2
21168.2.a.ex 2
21168.2.a.ey 2
21168.2.a.ez 2
21168.2.a.fa 2
21168.2.a.fb 2
21168.2.a.fc 2
21168.2.a.fd 2
21168.2.a.fe 2
21168.2.a.ff 2
21168.2.a.fg 2
21168.2.a.fh 2
21168.2.a.fi 2
21168.2.a.fj 3
21168.2.a.fk 3
21168.2.a.fl 3
21168.2.a.fm 3
21168.2.a.fn 3
21168.2.a.fo 3
21168.2.a.fp 3
21168.2.a.fq 3
21168.2.a.fr 3
21168.2.a.fs 3
21168.2.a.ft 3
21168.2.a.fu 3
21168.2.a.fv 3
21168.2.a.fw 3
21168.2.a.fx 3
21168.2.a.fy 3
21168.2.a.fz 4
21168.2.a.ga 4
21168.2.a.gb 4
21168.2.a.gc 4
21168.2.a.gd 4
21168.2.a.ge 4
21168.2.a.gf 4
21168.2.a.gg 4
21168.2.a.gh 4
21168.2.a.gi 4
21168.2.a.gj 4
21168.2.a.gk 4
21168.2.a.gl 4
21168.2.a.gm 4
21168.2.a.gn 4
21168.2.a.go 4
21168.2.a.gp 4
21168.2.a.gq 4
21168.2.a.gr 4
21168.2.a.gs 4
21168.2.a.gt 6
21168.2.a.gu 6
21168.2.a.gv 6
21168.2.a.gw 6
21168.2.b \(\chi_{21168}(1567, \cdot)\) n/a 320 1
21168.2.h \(\chi_{21168}(11663, \cdot)\) n/a 328 1
21168.2.k \(\chi_{21168}(7937, \cdot)\) n/a 320 1
21168.2.q \(\chi_{21168}(17425, \cdot)\) n/a 472 2
21168.2.r \(\chi_{21168}(7057, \cdot)\) n/a 482 2
21168.2.s \(\chi_{21168}(3889, \cdot)\) n/a 640 2
21168.2.t \(\chi_{21168}(3313, \cdot)\) n/a 472 2
21168.2.v \(\chi_{21168}(6371, \cdot)\) n/a 2624 2
21168.2.x \(\chi_{21168}(6859, \cdot)\) n/a 2560 2
21168.2.z \(\chi_{21168}(5293, \cdot)\) n/a 2624 2
21168.2.bb \(\chi_{21168}(2645, \cdot)\) n/a 2560 2
21168.2.bf \(\chi_{21168}(4735, \cdot)\) n/a 480 2
21168.2.bh \(\chi_{21168}(7919, \cdot)\) n/a 480 2
21168.2.bt \(\chi_{21168}(4049, \cdot)\) n/a 640 2
21168.2.ca \(\chi_{21168}(11105, \cdot)\) n/a 472 2
21168.2.cc \(\chi_{21168}(881, \cdot)\) n/a 472 2
21168.2.ch \(\chi_{21168}(4607, \cdot)\) n/a 492 2
21168.2.cj \(\chi_{21168}(1439, \cdot)\) n/a 480 2
21168.2.cq \(\chi_{21168}(863, \cdot)\) n/a 640 2
21168.2.cs \(\chi_{21168}(12367, \cdot)\) n/a 640 2
21168.2.cx \(\chi_{21168}(8623, \cdot)\) n/a 480 2
21168.2.cz \(\chi_{21168}(11791, \cdot)\) n/a 480 2
21168.2.df \(\chi_{21168}(4625, \cdot)\) n/a 472 2
21168.2.dk \(\chi_{21168}(3025, \cdot)\) n/a 2688 6
21168.2.dl \(\chi_{21168}(2353, \cdot)\) n/a 4398 6
21168.2.dm \(\chi_{21168}(961, \cdot)\) n/a 4296 6
21168.2.dn \(\chi_{21168}(1537, \cdot)\) n/a 4296 6
21168.2.do \(\chi_{21168}(3331, \cdot)\) n/a 3808 4
21168.2.dq \(\chi_{21168}(2843, \cdot)\) n/a 3896 4
21168.2.ds \(\chi_{21168}(5653, \cdot)\) n/a 3808 4
21168.2.dv \(\chi_{21168}(5813, \cdot)\) n/a 3808 4
21168.2.dw \(\chi_{21168}(2861, \cdot)\) n/a 5120 4
21168.2.dy \(\chi_{21168}(5077, \cdot)\) n/a 5120 4
21168.2.eb \(\chi_{21168}(1549, \cdot)\) n/a 3808 4
21168.2.ec \(\chi_{21168}(2285, \cdot)\) n/a 3808 4
21168.2.ee \(\chi_{21168}(2627, \cdot)\) n/a 3808 4
21168.2.eg \(\chi_{21168}(2971, \cdot)\) n/a 5120 4
21168.2.ej \(\chi_{21168}(3547, \cdot)\) n/a 3808 4
21168.2.el \(\chi_{21168}(6731, \cdot)\) n/a 3808 4
21168.2.em \(\chi_{21168}(6155, \cdot)\) n/a 5120 4
21168.2.eo \(\chi_{21168}(19, \cdot)\) n/a 3808 4
21168.2.eq \(\chi_{21168}(6173, \cdot)\) n/a 3808 4
21168.2.es \(\chi_{21168}(1765, \cdot)\) n/a 3896 4
21168.2.ez \(\chi_{21168}(1889, \cdot)\) n/a 2688 6
21168.2.fc \(\chi_{21168}(2591, \cdot)\) n/a 2688 6
21168.2.fi \(\chi_{21168}(4591, \cdot)\) n/a 2688 6
21168.2.fk \(\chi_{21168}(3791, \cdot)\) n/a 4320 6
21168.2.fn \(\chi_{21168}(607, \cdot)\) n/a 4320 6
21168.2.fz \(\chi_{21168}(3233, \cdot)\) n/a 4296 6
21168.2.ge \(\chi_{21168}(1697, \cdot)\) n/a 4296 6
21168.2.gi \(\chi_{21168}(3919, \cdot)\) n/a 4320 6
21168.2.gl \(\chi_{21168}(31, \cdot)\) n/a 4320 6
21168.2.gp \(\chi_{21168}(2255, \cdot)\) n/a 4428 6
21168.2.gu \(\chi_{21168}(3215, \cdot)\) n/a 4320 6
21168.2.gw \(\chi_{21168}(2273, \cdot)\) n/a 4296 6
21168.2.hc \(\chi_{21168}(289, \cdot)\) n/a 4008 12
21168.2.hd \(\chi_{21168}(865, \cdot)\) n/a 5376 12
21168.2.he \(\chi_{21168}(1009, \cdot)\) n/a 4008 12
21168.2.hf \(\chi_{21168}(2305, \cdot)\) n/a 4008 12
21168.2.hg \(\chi_{21168}(1133, \cdot)\) n/a 21504 12
21168.2.hi \(\chi_{21168}(757, \cdot)\) n/a 21504 12
21168.2.hk \(\chi_{21168}(811, \cdot)\) n/a 21504 12
21168.2.hm \(\chi_{21168}(323, \cdot)\) n/a 21504 12
21168.2.ho \(\chi_{21168}(619, \cdot)\) n/a 34464 12
21168.2.hr \(\chi_{21168}(275, \cdot)\) n/a 34464 12
21168.2.hs \(\chi_{21168}(949, \cdot)\) n/a 34464 12
21168.2.hu \(\chi_{21168}(589, \cdot)\) n/a 35304 12
21168.2.hx \(\chi_{21168}(293, \cdot)\) n/a 34464 12
21168.2.hz \(\chi_{21168}(1685, \cdot)\) n/a 34464 12
21168.2.ib \(\chi_{21168}(979, \cdot)\) n/a 34464 12
21168.2.id \(\chi_{21168}(1195, \cdot)\) n/a 34464 12
21168.2.ie \(\chi_{21168}(851, \cdot)\) n/a 34464 12
21168.2.ig \(\chi_{21168}(491, \cdot)\) n/a 35304 12
21168.2.ij \(\chi_{21168}(373, \cdot)\) n/a 34464 12
21168.2.ik \(\chi_{21168}(509, \cdot)\) n/a 34464 12
21168.2.iq \(\chi_{21168}(17, \cdot)\) n/a 4008 12
21168.2.iw \(\chi_{21168}(1279, \cdot)\) n/a 4032 12
21168.2.iy \(\chi_{21168}(559, \cdot)\) n/a 4032 12
21168.2.jd \(\chi_{21168}(271, \cdot)\) n/a 5376 12
21168.2.jf \(\chi_{21168}(431, \cdot)\) n/a 5376 12
21168.2.jm \(\chi_{21168}(2879, \cdot)\) n/a 4032 12
21168.2.jo \(\chi_{21168}(575, \cdot)\) n/a 4032 12
21168.2.jt \(\chi_{21168}(2897, \cdot)\) n/a 4008 12
21168.2.jv \(\chi_{21168}(2033, \cdot)\) n/a 4008 12
21168.2.kc \(\chi_{21168}(593, \cdot)\) n/a 5376 12
21168.2.ko \(\chi_{21168}(1871, \cdot)\) n/a 4032 12
21168.2.kq \(\chi_{21168}(1711, \cdot)\) n/a 4032 12
21168.2.ku \(\chi_{21168}(529, \cdot)\) n/a 36216 36
21168.2.kv \(\chi_{21168}(193, \cdot)\) n/a 36216 36
21168.2.kw \(\chi_{21168}(337, \cdot)\) n/a 36216 36
21168.2.ky \(\chi_{21168}(253, \cdot)\) n/a 32160 24
21168.2.la \(\chi_{21168}(125, \cdot)\) n/a 32160 24
21168.2.lc \(\chi_{21168}(955, \cdot)\) n/a 32160 24
21168.2.ld \(\chi_{21168}(611, \cdot)\) n/a 32160 24
21168.2.lg \(\chi_{21168}(107, \cdot)\) n/a 43008 24
21168.2.li \(\chi_{21168}(1027, \cdot)\) n/a 43008 24
21168.2.lj \(\chi_{21168}(451, \cdot)\) n/a 32160 24
21168.2.lm \(\chi_{21168}(179, \cdot)\) n/a 32160 24
21168.2.lo \(\chi_{21168}(773, \cdot)\) n/a 32160 24
21168.2.lq \(\chi_{21168}(109, \cdot)\) n/a 43008 24
21168.2.lr \(\chi_{21168}(37, \cdot)\) n/a 32160 24
21168.2.lt \(\chi_{21168}(341, \cdot)\) n/a 32160 24
21168.2.lw \(\chi_{21168}(269, \cdot)\) n/a 43008 24
21168.2.ly \(\chi_{21168}(1045, \cdot)\) n/a 32160 24
21168.2.ma \(\chi_{21168}(827, \cdot)\) n/a 32160 24
21168.2.mc \(\chi_{21168}(307, \cdot)\) n/a 32160 24
21168.2.mf \(\chi_{21168}(257, \cdot)\) n/a 36216 36
21168.2.ml \(\chi_{21168}(943, \cdot)\) n/a 36288 36
21168.2.mo \(\chi_{21168}(223, \cdot)\) n/a 36288 36
21168.2.ms \(\chi_{21168}(95, \cdot)\) n/a 36288 36
21168.2.mx \(\chi_{21168}(239, \cdot)\) n/a 36288 36
21168.2.ng \(\chi_{21168}(689, \cdot)\) n/a 36216 36
21168.2.nl \(\chi_{21168}(209, \cdot)\) n/a 36216 36
21168.2.nq \(\chi_{21168}(527, \cdot)\) n/a 36288 36
21168.2.nv \(\chi_{21168}(367, \cdot)\) n/a 36288 36
21168.2.nx \(\chi_{21168}(5, \cdot)\) n/a 290016 72
21168.2.ny \(\chi_{21168}(277, \cdot)\) n/a 290016 72
21168.2.ob \(\chi_{21168}(155, \cdot)\) n/a 290016 72
21168.2.od \(\chi_{21168}(347, \cdot)\) n/a 290016 72
21168.2.oe \(\chi_{21168}(187, \cdot)\) n/a 290016 72
21168.2.og \(\chi_{21168}(139, \cdot)\) n/a 290016 72
21168.2.oi \(\chi_{21168}(173, \cdot)\) n/a 290016 72
21168.2.ok \(\chi_{21168}(461, \cdot)\) n/a 290016 72
21168.2.on \(\chi_{21168}(85, \cdot)\) n/a 290016 72
21168.2.op \(\chi_{21168}(205, \cdot)\) n/a 290016 72
21168.2.oq \(\chi_{21168}(11, \cdot)\) n/a 290016 72
21168.2.ot \(\chi_{21168}(115, \cdot)\) n/a 290016 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(21168))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(21168)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 60}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2646))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5292))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7056))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10584))\)\(^{\oplus 2}\)