Properties

Label 3276.2
Level 3276
Weight 2
Dimension 125962
Nonzero newspaces 168
Sturm bound 1161216
Trace bound 40

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Defining parameters

Level: \( N \) = \( 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 168 \)
Sturm bound: \(1161216\)
Trace bound: \(40\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3276))\).

Total New Old
Modular forms 296064 127938 168126
Cusp forms 284545 125962 158583
Eisenstein series 11519 1976 9543

Trace form

\( 125962 q - 66 q^{2} - 74 q^{4} - 138 q^{5} - 84 q^{6} + 4 q^{7} - 150 q^{8} - 192 q^{9} + O(q^{10}) \) \( 125962 q - 66 q^{2} - 74 q^{4} - 138 q^{5} - 84 q^{6} + 4 q^{7} - 150 q^{8} - 192 q^{9} - 196 q^{10} - 6 q^{11} - 48 q^{12} - 130 q^{13} - 162 q^{14} + 12 q^{15} - 50 q^{16} - 120 q^{17} - 66 q^{19} - 12 q^{20} - 234 q^{21} - 168 q^{22} - 78 q^{23} - 60 q^{24} - 270 q^{25} - 90 q^{26} - 36 q^{27} - 222 q^{28} - 450 q^{29} - 84 q^{30} - 118 q^{31} - 126 q^{32} - 108 q^{33} - 16 q^{34} - 204 q^{36} - 384 q^{37} + 72 q^{38} - 66 q^{39} + 140 q^{40} - 30 q^{41} + 32 q^{43} + 228 q^{44} - 108 q^{45} + 216 q^{46} + 30 q^{47} + 132 q^{48} - 156 q^{49} + 342 q^{50} + 96 q^{51} + 178 q^{52} - 162 q^{53} + 120 q^{54} + 96 q^{55} + 162 q^{56} - 264 q^{57} + 176 q^{58} + 102 q^{59} + 84 q^{60} - 224 q^{61} + 96 q^{62} + 210 q^{63} - 146 q^{64} + 168 q^{65} - 60 q^{66} + 58 q^{67} + 228 q^{68} + 36 q^{69} - 48 q^{70} + 360 q^{71} + 24 q^{72} - 58 q^{73} + 12 q^{74} + 384 q^{75} + 180 q^{77} + 132 q^{78} + 78 q^{79} + 216 q^{80} + 264 q^{81} - 16 q^{82} + 420 q^{83} - 84 q^{84} + 106 q^{85} + 192 q^{86} + 192 q^{87} + 24 q^{88} + 402 q^{89} + 36 q^{90} - 48 q^{91} - 132 q^{92} + 240 q^{93} - 48 q^{94} + 42 q^{95} - 120 q^{96} + 28 q^{97} - 258 q^{98} + 132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3276))\)

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
3276.2.a \(\chi_{3276}(1, \cdot)\) 3276.2.a.a 1 1
3276.2.a.b 1
3276.2.a.c 1
3276.2.a.d 1
3276.2.a.e 1
3276.2.a.f 1
3276.2.a.g 1
3276.2.a.h 1
3276.2.a.i 1
3276.2.a.j 1
3276.2.a.k 1
3276.2.a.l 2
3276.2.a.m 2
3276.2.a.n 2
3276.2.a.o 2
3276.2.a.p 2
3276.2.a.q 2
3276.2.a.r 3
3276.2.a.s 4
3276.2.c \(\chi_{3276}(2575, \cdot)\) n/a 240 1
3276.2.e \(\chi_{3276}(2521, \cdot)\) 3276.2.e.a 2 1
3276.2.e.b 2
3276.2.e.c 2
3276.2.e.d 2
3276.2.e.e 4
3276.2.e.f 8
3276.2.e.g 16
3276.2.f \(\chi_{3276}(3095, \cdot)\) n/a 144 1
3276.2.h \(\chi_{3276}(1637, \cdot)\) 3276.2.h.a 8 1
3276.2.h.b 16
3276.2.h.c 16
3276.2.j \(\chi_{3276}(2339, \cdot)\) n/a 168 1
3276.2.l \(\chi_{3276}(2393, \cdot)\) 3276.2.l.a 8 1
3276.2.l.b 24
3276.2.o \(\chi_{3276}(1819, \cdot)\) n/a 276 1
3276.2.q \(\chi_{3276}(625, \cdot)\) n/a 192 2
3276.2.r \(\chi_{3276}(1873, \cdot)\) 3276.2.r.a 2 2
3276.2.r.b 2
3276.2.r.c 2
3276.2.r.d 2
3276.2.r.e 4
3276.2.r.f 4
3276.2.r.g 6
3276.2.r.h 6
3276.2.r.i 6
3276.2.r.j 8
3276.2.r.k 10
3276.2.r.l 12
3276.2.r.m 16
3276.2.s \(\chi_{3276}(1849, \cdot)\) n/a 168 2
3276.2.t \(\chi_{3276}(373, \cdot)\) n/a 224 2
3276.2.u \(\chi_{3276}(289, \cdot)\) 3276.2.u.a 2 2
3276.2.u.b 2
3276.2.u.c 2
3276.2.u.d 2
3276.2.u.e 2
3276.2.u.f 2
3276.2.u.g 2
3276.2.u.h 4
3276.2.u.i 4
3276.2.u.j 12
3276.2.u.k 18
3276.2.u.l 18
3276.2.u.m 24
3276.2.v \(\chi_{3276}(1093, \cdot)\) n/a 144 2
3276.2.w \(\chi_{3276}(841, \cdot)\) n/a 168 2
3276.2.x \(\chi_{3276}(2557, \cdot)\) 3276.2.x.a 2 2
3276.2.x.b 2
3276.2.x.c 2
3276.2.x.d 2
3276.2.x.e 2
3276.2.x.f 2
3276.2.x.g 2
3276.2.x.h 4
3276.2.x.i 4
3276.2.x.j 12
3276.2.x.k 18
3276.2.x.l 18
3276.2.x.m 24
3276.2.y \(\chi_{3276}(529, \cdot)\) n/a 224 2
3276.2.z \(\chi_{3276}(757, \cdot)\) 3276.2.z.a 2 2
3276.2.z.b 2
3276.2.z.c 2
3276.2.z.d 4
3276.2.z.e 4
3276.2.z.f 6
3276.2.z.g 8
3276.2.z.h 8
3276.2.z.i 8
3276.2.z.j 12
3276.2.z.k 12
3276.2.ba \(\chi_{3276}(445, \cdot)\) n/a 224 2
3276.2.bb \(\chi_{3276}(2473, \cdot)\) n/a 224 2
3276.2.bc \(\chi_{3276}(1717, \cdot)\) n/a 192 2
3276.2.bd \(\chi_{3276}(1763, \cdot)\) n/a 448 2
3276.2.bg \(\chi_{3276}(2647, \cdot)\) n/a 420 2
3276.2.bi \(\chi_{3276}(1945, \cdot)\) 3276.2.bi.a 4 2
3276.2.bi.b 4
3276.2.bi.c 16
3276.2.bi.d 20
3276.2.bi.e 20
3276.2.bi.f 32
3276.2.bj \(\chi_{3276}(2465, \cdot)\) 3276.2.bj.a 28 2
3276.2.bj.b 28
3276.2.bl \(\chi_{3276}(961, \cdot)\) n/a 224 2
3276.2.bn \(\chi_{3276}(1795, \cdot)\) n/a 1152 2
3276.2.bp \(\chi_{3276}(347, \cdot)\) n/a 1328 2
3276.2.bs \(\chi_{3276}(881, \cdot)\) 3276.2.bs.a 72 2
3276.2.bu \(\chi_{3276}(173, \cdot)\) n/a 224 2
3276.2.bw \(\chi_{3276}(191, \cdot)\) n/a 1328 2
3276.2.by \(\chi_{3276}(575, \cdot)\) n/a 336 2
3276.2.bz \(\chi_{3276}(2201, \cdot)\) n/a 224 2
3276.2.cc \(\chi_{3276}(1543, \cdot)\) n/a 1328 2
3276.2.cd \(\chi_{3276}(1213, \cdot)\) n/a 224 2
3276.2.cf \(\chi_{3276}(1765, \cdot)\) 3276.2.cf.a 12 2
3276.2.cf.b 12
3276.2.cf.c 16
3276.2.cf.d 32
3276.2.ch \(\chi_{3276}(55, \cdot)\) n/a 552 2
3276.2.cj \(\chi_{3276}(1699, \cdot)\) n/a 1328 2
3276.2.cm \(\chi_{3276}(205, \cdot)\) n/a 224 2
3276.2.co \(\chi_{3276}(1949, \cdot)\) n/a 224 2
3276.2.cq \(\chi_{3276}(443, \cdot)\) n/a 1152 2
3276.2.cs \(\chi_{3276}(23, \cdot)\) n/a 1328 2
3276.2.cu \(\chi_{3276}(1277, \cdot)\) 3276.2.cu.a 76 2
3276.2.cv \(\chi_{3276}(965, \cdot)\) n/a 224 2
3276.2.cx \(\chi_{3276}(1499, \cdot)\) n/a 1008 2
3276.2.da \(\chi_{3276}(179, \cdot)\) n/a 448 2
3276.2.dc \(\chi_{3276}(1361, \cdot)\) n/a 224 2
3276.2.dd \(\chi_{3276}(727, \cdot)\) n/a 1328 2
3276.2.df \(\chi_{3276}(199, \cdot)\) n/a 552 2
3276.2.dm \(\chi_{3276}(355, \cdot)\) n/a 1328 2
3276.2.dn \(\chi_{3276}(979, \cdot)\) n/a 1328 2
3276.2.dq \(\chi_{3276}(103, \cdot)\) n/a 1328 2
3276.2.ds \(\chi_{3276}(2287, \cdot)\) n/a 552 2
3276.2.dw \(\chi_{3276}(1115, \cdot)\) n/a 448 2
3276.2.dy \(\chi_{3276}(155, \cdot)\) n/a 1008 2
3276.2.dz \(\chi_{3276}(1517, \cdot)\) n/a 224 2
3276.2.ec \(\chi_{3276}(2057, \cdot)\) n/a 224 2
3276.2.ed \(\chi_{3276}(521, \cdot)\) 3276.2.ed.a 64 2
3276.2.ef \(\chi_{3276}(1613, \cdot)\) n/a 192 2
3276.2.eh \(\chi_{3276}(935, \cdot)\) n/a 448 2
3276.2.ej \(\chi_{3276}(779, \cdot)\) n/a 1328 2
3276.2.em \(\chi_{3276}(407, \cdot)\) n/a 1008 2
3276.2.en \(\chi_{3276}(1031, \cdot)\) n/a 1328 2
3276.2.eq \(\chi_{3276}(209, \cdot)\) n/a 192 2
3276.2.es \(\chi_{3276}(269, \cdot)\) 3276.2.es.a 76 2
3276.2.et \(\chi_{3276}(2383, \cdot)\) n/a 1328 2
3276.2.ex \(\chi_{3276}(2467, \cdot)\) n/a 552 2
3276.2.fa \(\chi_{3276}(3163, \cdot)\) n/a 1328 2
3276.2.fc \(\chi_{3276}(1615, \cdot)\) n/a 1328 2
3276.2.fe \(\chi_{3276}(361, \cdot)\) 3276.2.fe.a 2 2
3276.2.fe.b 2
3276.2.fe.c 2
3276.2.fe.d 2
3276.2.fe.e 2
3276.2.fe.f 4
3276.2.fe.g 14
3276.2.fe.h 16
3276.2.fe.i 18
3276.2.fe.j 32
3276.2.fh \(\chi_{3276}(589, \cdot)\) n/a 168 2
3276.2.fj \(\chi_{3276}(139, \cdot)\) n/a 1328 2
3276.2.fk \(\chi_{3276}(1459, \cdot)\) n/a 552 2
3276.2.fm \(\chi_{3276}(277, \cdot)\) n/a 224 2
3276.2.fp \(\chi_{3276}(911, \cdot)\) n/a 864 2
3276.2.fr \(\chi_{3276}(107, \cdot)\) n/a 448 2
3276.2.ft \(\chi_{3276}(2981, \cdot)\) n/a 224 2
3276.2.fu \(\chi_{3276}(2105, \cdot)\) 3276.2.fu.a 72 2
3276.2.fw \(\chi_{3276}(857, \cdot)\) n/a 224 2
3276.2.fy \(\chi_{3276}(101, \cdot)\) n/a 224 2
3276.2.ga \(\chi_{3276}(263, \cdot)\) n/a 1328 2
3276.2.gc \(\chi_{3276}(1691, \cdot)\) n/a 384 2
3276.2.ge \(\chi_{3276}(1535, \cdot)\) n/a 1152 2
3276.2.gh \(\chi_{3276}(659, \cdot)\) n/a 1008 2
3276.2.gj \(\chi_{3276}(17, \cdot)\) 3276.2.gj.a 4 2
3276.2.gj.b 4
3276.2.gj.c 68
3276.2.gl \(\chi_{3276}(545, \cdot)\) n/a 224 2
3276.2.gm \(\chi_{3276}(451, \cdot)\) n/a 552 2
3276.2.go \(\chi_{3276}(391, \cdot)\) n/a 1152 2
3276.2.gr \(\chi_{3276}(121, \cdot)\) n/a 224 2
3276.2.gt \(\chi_{3276}(25, \cdot)\) n/a 224 2
3276.2.gv \(\chi_{3276}(1117, \cdot)\) 3276.2.gv.a 2 2
3276.2.gv.b 2
3276.2.gv.c 4
3276.2.gv.d 8
3276.2.gv.e 12
3276.2.gv.f 12
3276.2.gv.g 20
3276.2.gv.h 32
3276.2.gw \(\chi_{3276}(1681, \cdot)\) n/a 168 2
3276.2.gy \(\chi_{3276}(1147, \cdot)\) n/a 1328 2
3276.2.hb \(\chi_{3276}(859, \cdot)\) n/a 1152 2
3276.2.hd \(\chi_{3276}(703, \cdot)\) n/a 480 2
3276.2.hf \(\chi_{3276}(367, \cdot)\) n/a 1328 2
3276.2.hg \(\chi_{3276}(337, \cdot)\) n/a 168 2
3276.2.hi \(\chi_{3276}(1297, \cdot)\) 3276.2.hi.a 2 2
3276.2.hi.b 2
3276.2.hi.c 2
3276.2.hi.d 2
3276.2.hi.e 2
3276.2.hi.f 4
3276.2.hi.g 14
3276.2.hi.h 16
3276.2.hi.i 18
3276.2.hi.j 32
3276.2.hl \(\chi_{3276}(2291, \cdot)\) n/a 1328 2
3276.2.hm \(\chi_{3276}(797, \cdot)\) n/a 224 2
3276.2.hp \(\chi_{3276}(2285, \cdot)\) 3276.2.hp.a 4 2
3276.2.hp.b 4
3276.2.hp.c 68
3276.2.hr \(\chi_{3276}(2375, \cdot)\) n/a 448 2
3276.2.hs \(\chi_{3276}(1667, \cdot)\) n/a 1008 2
3276.2.hv \(\chi_{3276}(257, \cdot)\) n/a 224 2
3276.2.hx \(\chi_{3276}(677, \cdot)\) n/a 192 2
3276.2.hz \(\chi_{3276}(2963, \cdot)\) n/a 1328 2
3276.2.ib \(\chi_{3276}(439, \cdot)\) n/a 1328 2
3276.2.ie \(\chi_{3276}(283, \cdot)\) n/a 1328 2
3276.2.ig \(\chi_{3276}(1063, \cdot)\) n/a 552 2
3276.2.ij \(\chi_{3276}(95, \cdot)\) n/a 1328 2
3276.2.im \(\chi_{3276}(185, \cdot)\) n/a 224 2
3276.2.io \(\chi_{3276}(2141, \cdot)\) 3276.2.io.a 4 2
3276.2.io.b 4
3276.2.io.c 64
3276.2.iq \(\chi_{3276}(1583, \cdot)\) n/a 336 2
3276.2.is \(\chi_{3276}(2363, \cdot)\) n/a 1328 2
3276.2.it \(\chi_{3276}(1433, \cdot)\) n/a 224 2
3276.2.iw \(\chi_{3276}(1039, \cdot)\) n/a 1328 2
3276.2.iz \(\chi_{3276}(1151, \cdot)\) n/a 896 4
3276.2.jb \(\chi_{3276}(319, \cdot)\) n/a 2656 4
3276.2.jc \(\chi_{3276}(463, \cdot)\) n/a 2016 4
3276.2.jd \(\chi_{3276}(1003, \cdot)\) n/a 2656 4
3276.2.jg \(\chi_{3276}(59, \cdot)\) n/a 2656 4
3276.2.jk \(\chi_{3276}(83, \cdot)\) n/a 2656 4
3276.2.jl \(\chi_{3276}(227, \cdot)\) n/a 2656 4
3276.2.jm \(\chi_{3276}(487, \cdot)\) n/a 1104 4
3276.2.jo \(\chi_{3276}(1165, \cdot)\) n/a 448 4
3276.2.jr \(\chi_{3276}(97, \cdot)\) n/a 448 4
3276.2.jt \(\chi_{3276}(1489, \cdot)\) n/a 448 4
3276.2.jw \(\chi_{3276}(977, \cdot)\) n/a 448 4
3276.2.jx \(\chi_{3276}(197, \cdot)\) n/a 112 4
3276.2.jy \(\chi_{3276}(1061, \cdot)\) n/a 144 4
3276.2.jz \(\chi_{3276}(617, \cdot)\) n/a 336 4
3276.2.kc \(\chi_{3276}(557, \cdot)\) n/a 152 4
3276.2.kd \(\chi_{3276}(905, \cdot)\) n/a 448 4
3276.2.kg \(\chi_{3276}(565, \cdot)\) n/a 448 4
3276.2.kh \(\chi_{3276}(1189, \cdot)\) n/a 184 4
3276.2.km \(\chi_{3276}(229, \cdot)\) n/a 448 4
3276.2.kn \(\chi_{3276}(397, \cdot)\) n/a 188 4
3276.2.kq \(\chi_{3276}(73, \cdot)\) n/a 184 4
3276.2.kr \(\chi_{3276}(349, \cdot)\) n/a 448 4
3276.2.kt \(\chi_{3276}(317, \cdot)\) n/a 448 4
3276.2.ku \(\chi_{3276}(149, \cdot)\) n/a 448 4
3276.2.kw \(\chi_{3276}(869, \cdot)\) n/a 336 4
3276.2.kz \(\chi_{3276}(47, \cdot)\) n/a 2656 4
3276.2.la \(\chi_{3276}(383, \cdot)\) n/a 2656 4
3276.2.lc \(\chi_{3276}(167, \cdot)\) n/a 2656 4
3276.2.le \(\chi_{3276}(379, \cdot)\) n/a 840 4
3276.2.lf \(\chi_{3276}(67, \cdot)\) n/a 2656 4
3276.2.lk \(\chi_{3276}(151, \cdot)\) n/a 2656 4
3276.2.ll \(\chi_{3276}(163, \cdot)\) n/a 1104 4
3276.2.lo \(\chi_{3276}(1051, \cdot)\) n/a 2016 4
3276.2.lp \(\chi_{3276}(1243, \cdot)\) n/a 1104 4
3276.2.ls \(\chi_{3276}(1007, \cdot)\) n/a 896 4
3276.2.lt \(\chi_{3276}(1307, \cdot)\) n/a 2656 4
3276.2.lu \(\chi_{3276}(587, \cdot)\) n/a 2656 4
3276.2.lv \(\chi_{3276}(395, \cdot)\) n/a 896 4
3276.2.ly \(\chi_{3276}(215, \cdot)\) n/a 896 4
3276.2.lz \(\chi_{3276}(983, \cdot)\) n/a 2656 4
3276.2.mc \(\chi_{3276}(1087, \cdot)\) n/a 2656 4
3276.2.mf \(\chi_{3276}(799, \cdot)\) n/a 2016 4
3276.2.mh \(\chi_{3276}(1159, \cdot)\) n/a 2656 4
3276.2.mi \(\chi_{3276}(145, \cdot)\) n/a 188 4
3276.2.mk \(\chi_{3276}(821, \cdot)\) n/a 448 4
3276.2.mo \(\chi_{3276}(137, \cdot)\) n/a 448 4
3276.2.mp \(\chi_{3276}(281, \cdot)\) n/a 336 4
3276.2.mr \(\chi_{3276}(409, \cdot)\) n/a 448 4
3276.2.ms \(\chi_{3276}(241, \cdot)\) n/a 448 4
3276.2.mt \(\chi_{3276}(265, \cdot)\) n/a 448 4
3276.2.mx \(\chi_{3276}(305, \cdot)\) n/a 152 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3276))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3276)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(819))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1092))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1638))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3276))\)\(^{\oplus 1}\)