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Properties

Label 45738.2
Level 45738
Weight 2
Dimension 14014420
Nonzero newspaces 128
Sturm bound 225815040

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Defining parameters

Level: \( N \) = \( 45738 = 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(225815040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(45738))\).

Total New Old
Modular forms 56568960 14014420 42554540
Cusp forms 56338561 14014420 42324141
Eisenstein series 230399 0 230399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(45738))\)

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
45738.2.a \(\chi_{45738}(1, \cdot)\) 45738.2.a.a 1 1
45738.2.a.b 1
45738.2.a.c 1
45738.2.a.d 1
45738.2.a.e 1
45738.2.a.f 1
45738.2.a.g 1
45738.2.a.h 1
45738.2.a.i 1
45738.2.a.j 1
45738.2.a.k 1
45738.2.a.l 1
45738.2.a.m 1
45738.2.a.n 1
45738.2.a.o 1
45738.2.a.p 1
45738.2.a.q 1
45738.2.a.r 1
45738.2.a.s 1
45738.2.a.t 1
45738.2.a.u 1
45738.2.a.v 1
45738.2.a.w 1
45738.2.a.x 1
45738.2.a.y 1
45738.2.a.z 1
45738.2.a.ba 1
45738.2.a.bb 1
45738.2.a.bc 1
45738.2.a.bd 1
45738.2.a.be 1
45738.2.a.bf 1
45738.2.a.bg 1
45738.2.a.bh 1
45738.2.a.bi 1
45738.2.a.bj 1
45738.2.a.bk 1
45738.2.a.bl 1
45738.2.a.bm 1
45738.2.a.bn 1
45738.2.a.bo 1
45738.2.a.bp 1
45738.2.a.bq 1
45738.2.a.br 1
45738.2.a.bs 1
45738.2.a.bt 1
45738.2.a.bu 1
45738.2.a.bv 1
45738.2.a.bw 1
45738.2.a.bx 1
45738.2.a.by 1
45738.2.a.bz 1
45738.2.a.ca 1
45738.2.a.cb 1
45738.2.a.cc 1
45738.2.a.cd 1
45738.2.a.ce 1
45738.2.a.cf 1
45738.2.a.cg 1
45738.2.a.ch 1
45738.2.a.ci 1
45738.2.a.cj 1
45738.2.a.ck 1
45738.2.a.cl 1
45738.2.a.cm 1
45738.2.a.cn 1
45738.2.a.co 1
45738.2.a.cp 1
45738.2.a.cq 1
45738.2.a.cr 1
45738.2.a.cs 1
45738.2.a.ct 1
45738.2.a.cu 1
45738.2.a.cv 1
45738.2.a.cw 1
45738.2.a.cx 1
45738.2.a.cy 1
45738.2.a.cz 1
45738.2.a.da 1
45738.2.a.db 1
45738.2.a.dc 1
45738.2.a.dd 1
45738.2.a.de 1
45738.2.a.df 1
45738.2.a.dg 1
45738.2.a.dh 1
45738.2.a.di 1
45738.2.a.dj 1
45738.2.a.dk 1
45738.2.a.dl 1
45738.2.a.dm 1
45738.2.a.dn 1
45738.2.a.do 1
45738.2.a.dp 1
45738.2.a.dq 1
45738.2.a.dr 1
45738.2.a.ds 2
45738.2.a.dt 2
45738.2.a.du 2
45738.2.a.dv 2
45738.2.a.dw 2
45738.2.a.dx 2
45738.2.a.dy 2
45738.2.a.dz 2
45738.2.a.ea 2
45738.2.a.eb 2
45738.2.a.ec 2
45738.2.a.ed 2
45738.2.a.ee 2
45738.2.a.ef 2
45738.2.a.eg 2
45738.2.a.eh 2
45738.2.a.ei 2
45738.2.a.ej 2
45738.2.a.ek 2
45738.2.a.el 2
45738.2.a.em 2
45738.2.a.en 2
45738.2.a.eo 2
45738.2.a.ep 2
45738.2.a.eq 2
45738.2.a.er 2
45738.2.a.es 2
45738.2.a.et 2
45738.2.a.eu 2
45738.2.a.ev 2
45738.2.a.ew 2
45738.2.a.ex 2
45738.2.a.ey 2
45738.2.a.ez 2
45738.2.a.fa 2
45738.2.a.fb 2
45738.2.a.fc 2
45738.2.a.fd 2
45738.2.a.fe 2
45738.2.a.ff 2
45738.2.a.fg 2
45738.2.a.fh 2
45738.2.a.fi 2
45738.2.a.fj 2
45738.2.a.fk 2
45738.2.a.fl 2
45738.2.a.fm 2
45738.2.a.fn 2
45738.2.a.fo 2
45738.2.a.fp 2
45738.2.a.fq 3
45738.2.a.fr 3
45738.2.a.fs 3
45738.2.a.ft 3
45738.2.a.fu 3
45738.2.a.fv 3
45738.2.a.fw 3
45738.2.a.fx 3
45738.2.a.fy 3
45738.2.a.fz 3
45738.2.a.ga 3
45738.2.a.gb 3
45738.2.a.gc 3
45738.2.a.gd 3
45738.2.a.ge 3
45738.2.a.gf 3
45738.2.a.gg 3
45738.2.a.gh 3
45738.2.a.gi 3
45738.2.a.gj 3
45738.2.a.gk 3
45738.2.a.gl 3
45738.2.a.gm 3
45738.2.a.gn 3
45738.2.a.go 4
45738.2.a.gp 4
45738.2.a.gq 4
45738.2.a.gr 4
45738.2.a.gs 4
45738.2.a.gt 4
45738.2.a.gu 4
45738.2.a.gv 4
45738.2.a.gw 5
45738.2.a.gx 5
45738.2.a.gy 5
45738.2.a.gz 5
45738.2.a.ha 5
45738.2.a.hb 5
45738.2.a.hc 5
45738.2.a.hd 5
45738.2.a.he 5
45738.2.a.hf 5
45738.2.a.hg 5
45738.2.a.hh 5
45738.2.a.hi 6
45738.2.a.hj 6
45738.2.a.hk 6
45738.2.a.hl 6
45738.2.a.hm 6
45738.2.a.hn 6
45738.2.a.ho 6
45738.2.a.hp 6
45738.2.a.hq 8
45738.2.a.hr 8
45738.2.a.hs 8
45738.2.a.ht 8
45738.2.a.hu 8
45738.2.a.hv 8
45738.2.a.hw 8
45738.2.a.hx 8
45738.2.a.hy 10
45738.2.a.hz 10
45738.2.a.ia 10
45738.2.a.ib 10
45738.2.a.ic 10
45738.2.a.id 10
45738.2.a.ie 10
45738.2.a.if 10
45738.2.a.ig 10
45738.2.a.ih 10
45738.2.a.ii 10
45738.2.a.ij 10
45738.2.a.ik 10
45738.2.a.il 10
45738.2.a.im 10
45738.2.a.in 10
45738.2.a.io 12
45738.2.a.ip 12
45738.2.a.iq 12
45738.2.a.ir 12
45738.2.a.is 12
45738.2.a.it 12
45738.2.a.iu 12
45738.2.a.iv 12
45738.2.a.iw 12
45738.2.a.ix 12
45738.2.a.iy 12
45738.2.a.iz 12
45738.2.a.ja 12
45738.2.a.jb 12
45738.2.a.jc 12
45738.2.a.jd 12
45738.2.a.je 12
45738.2.a.jf 12
45738.2.a.jg 12
45738.2.a.jh 12
45738.2.c \(\chi_{45738}(19601, \cdot)\) n/a 864 1
45738.2.e \(\chi_{45738}(32185, \cdot)\) n/a 1152 1
45738.2.g \(\chi_{45738}(39689, \cdot)\) n/a 1164 1
45738.2.i \(\chi_{45738}(17425, \cdot)\) n/a 1744 2
45738.2.j \(\chi_{45738}(15247, \cdot)\) n/a 1308 2
45738.2.k \(\chi_{45738}(6535, \cdot)\) n/a 2324 2
45738.2.l \(\chi_{45738}(2179, \cdot)\) n/a 1744 2
45738.2.m \(\chi_{45738}(12853, \cdot)\) n/a 3456 4
45738.2.n \(\chi_{45738}(10405, \cdot)\) n/a 1728 2
45738.2.p \(\chi_{45738}(37025, \cdot)\) n/a 1728 2
45738.2.r \(\chi_{45738}(7019, \cdot)\) n/a 2324 2
45738.2.w \(\chi_{45738}(17909, \cdot)\) n/a 1744 2
45738.2.y \(\chi_{45738}(9197, \cdot)\) n/a 1744 2
45738.2.ba \(\chi_{45738}(6533, \cdot)\) n/a 2304 2
45738.2.bd \(\chi_{45738}(30007, \cdot)\) n/a 1728 2
45738.2.bf \(\chi_{45738}(1693, \cdot)\) n/a 1728 2
45738.2.bh \(\chi_{45738}(10889, \cdot)\) n/a 1728 2
45738.2.bj \(\chi_{45738}(4355, \cdot)\) n/a 1296 2
45738.2.bk \(\chi_{45738}(25651, \cdot)\) n/a 2304 2
45738.2.bn \(\chi_{45738}(2663, \cdot)\) n/a 1744 2
45738.2.bp \(\chi_{45738}(5083, \cdot)\) n/a 11772 6
45738.2.bq \(\chi_{45738}(1453, \cdot)\) n/a 15696 6
45738.2.br \(\chi_{45738}(11617, \cdot)\) n/a 15696 6
45738.2.bt \(\chi_{45738}(6803, \cdot)\) n/a 4608 4
45738.2.bv \(\chi_{45738}(10639, \cdot)\) n/a 4608 4
45738.2.bx \(\chi_{45738}(6749, \cdot)\) n/a 3456 4
45738.2.bz \(\chi_{45738}(4159, \cdot)\) n/a 10560 10
45738.2.ca \(\chi_{45738}(4141, \cdot)\) n/a 6912 8
45738.2.cb \(\chi_{45738}(487, \cdot)\) n/a 9216 8
45738.2.cc \(\chi_{45738}(2017, \cdot)\) n/a 5184 8
45738.2.cd \(\chi_{45738}(4195, \cdot)\) n/a 6912 8
45738.2.ci \(\chi_{45738}(6775, \cdot)\) n/a 15552 6
45738.2.cj \(\chi_{45738}(4597, \cdot)\) n/a 15552 6
45738.2.ck \(\chi_{45738}(4115, \cdot)\) n/a 15696 6
45738.2.cl \(\chi_{45738}(9437, \cdot)\) n/a 11664 6
45738.2.cm \(\chi_{45738}(1937, \cdot)\) n/a 15696 6
45738.2.cn \(\chi_{45738}(725, \cdot)\) n/a 15552 6
45738.2.cw \(\chi_{45738}(5807, \cdot)\) n/a 15552 6
45738.2.cx \(\chi_{45738}(12101, \cdot)\) n/a 15696 6
45738.2.cy \(\chi_{45738}(241, \cdot)\) n/a 15552 6
45738.2.da \(\chi_{45738}(2267, \cdot)\) n/a 14080 10
45738.2.dc \(\chi_{45738}(3079, \cdot)\) n/a 14080 10
45738.2.de \(\chi_{45738}(2969, \cdot)\) n/a 10560 10
45738.2.dh \(\chi_{45738}(4625, \cdot)\) n/a 6912 8
45738.2.dk \(\chi_{45738}(4105, \cdot)\) n/a 9216 8
45738.2.dl \(\chi_{45738}(2339, \cdot)\) n/a 5184 8
45738.2.dn \(\chi_{45738}(233, \cdot)\) n/a 6912 8
45738.2.dp \(\chi_{45738}(4087, \cdot)\) n/a 6912 8
45738.2.dr \(\chi_{45738}(1207, \cdot)\) n/a 6912 8
45738.2.du \(\chi_{45738}(4589, \cdot)\) n/a 9216 8
45738.2.dw \(\chi_{45738}(251, \cdot)\) n/a 6912 8
45738.2.dy \(\chi_{45738}(4679, \cdot)\) n/a 6912 8
45738.2.ed \(\chi_{45738}(269, \cdot)\) n/a 9216 8
45738.2.ef \(\chi_{45738}(1691, \cdot)\) n/a 6912 8
45738.2.eh \(\chi_{45738}(1909, \cdot)\) n/a 6912 8
45738.2.ei \(\chi_{45738}(3763, \cdot)\) n/a 21120 20
45738.2.ej \(\chi_{45738}(2377, \cdot)\) n/a 28160 20
45738.2.ek \(\chi_{45738}(1387, \cdot)\) n/a 15840 20
45738.2.el \(\chi_{45738}(793, \cdot)\) n/a 21120 20
45738.2.em \(\chi_{45738}(2671, \cdot)\) n/a 62208 24
45738.2.en \(\chi_{45738}(1213, \cdot)\) n/a 62208 24
45738.2.eo \(\chi_{45738}(1219, \cdot)\) n/a 46656 24
45738.2.ep \(\chi_{45738}(379, \cdot)\) n/a 42240 40
45738.2.er \(\chi_{45738}(89, \cdot)\) n/a 21120 20
45738.2.eu \(\chi_{45738}(703, \cdot)\) n/a 28160 20
45738.2.ev \(\chi_{45738}(197, \cdot)\) n/a 15840 20
45738.2.ex \(\chi_{45738}(989, \cdot)\) n/a 21120 20
45738.2.ez \(\chi_{45738}(307, \cdot)\) n/a 21120 20
45738.2.fb \(\chi_{45738}(901, \cdot)\) n/a 21120 20
45738.2.fe \(\chi_{45738}(1187, \cdot)\) n/a 28160 20
45738.2.fg \(\chi_{45738}(881, \cdot)\) n/a 21120 20
45738.2.fi \(\chi_{45738}(1277, \cdot)\) n/a 21120 20
45738.2.fn \(\chi_{45738}(2861, \cdot)\) n/a 28160 20
45738.2.fp \(\chi_{45738}(3761, \cdot)\) n/a 21120 20
45738.2.fr \(\chi_{45738}(2089, \cdot)\) n/a 21120 20
45738.2.fs \(\chi_{45738}(481, \cdot)\) n/a 62208 24
45738.2.ft \(\chi_{45738}(2417, \cdot)\) n/a 62208 24
45738.2.fu \(\chi_{45738}(3155, \cdot)\) n/a 62208 24
45738.2.gd \(\chi_{45738}(1697, \cdot)\) n/a 62208 24
45738.2.ge \(\chi_{45738}(3119, \cdot)\) n/a 62208 24
45738.2.gf \(\chi_{45738}(1049, \cdot)\) n/a 62208 24
45738.2.gg \(\chi_{45738}(239, \cdot)\) n/a 46656 24
45738.2.gh \(\chi_{45738}(2581, \cdot)\) n/a 62208 24
45738.2.gi \(\chi_{45738}(475, \cdot)\) n/a 62208 24
45738.2.gn \(\chi_{45738}(529, \cdot)\) n/a 190080 60
45738.2.go \(\chi_{45738}(67, \cdot)\) n/a 190080 60
45738.2.gp \(\chi_{45738}(463, \cdot)\) n/a 142560 60
45738.2.gr \(\chi_{45738}(701, \cdot)\) n/a 42240 40
45738.2.gt \(\chi_{45738}(811, \cdot)\) n/a 56320 40
45738.2.gv \(\chi_{45738}(377, \cdot)\) n/a 56320 40
45738.2.gx \(\chi_{45738}(37, \cdot)\) n/a 84480 80
45738.2.gy \(\chi_{45738}(631, \cdot)\) n/a 63360 80
45738.2.gz \(\chi_{45738}(163, \cdot)\) n/a 112640 80
45738.2.ha \(\chi_{45738}(289, \cdot)\) n/a 84480 80
45738.2.hb \(\chi_{45738}(1363, \cdot)\) n/a 190080 60
45738.2.hc \(\chi_{45738}(353, \cdot)\) n/a 190080 60
45738.2.hd \(\chi_{45738}(263, \cdot)\) n/a 190080 60
45738.2.hm \(\chi_{45738}(65, \cdot)\) n/a 190080 60
45738.2.hn \(\chi_{45738}(551, \cdot)\) n/a 190080 60
45738.2.ho \(\chi_{45738}(659, \cdot)\) n/a 142560 60
45738.2.hp \(\chi_{45738}(419, \cdot)\) n/a 190080 60
45738.2.hq \(\chi_{45738}(439, \cdot)\) n/a 190080 60
45738.2.hr \(\chi_{45738}(769, \cdot)\) n/a 190080 60
45738.2.hw \(\chi_{45738}(19, \cdot)\) n/a 84480 80
45738.2.hy \(\chi_{45738}(359, \cdot)\) n/a 84480 80
45738.2.ia \(\chi_{45738}(647, \cdot)\) n/a 112640 80
45738.2.if \(\chi_{45738}(521, \cdot)\) n/a 84480 80
45738.2.ih \(\chi_{45738}(125, \cdot)\) n/a 84480 80
45738.2.ij \(\chi_{45738}(107, \cdot)\) n/a 112640 80
45738.2.im \(\chi_{45738}(73, \cdot)\) n/a 84480 80
45738.2.io \(\chi_{45738}(937, \cdot)\) n/a 84480 80
45738.2.iq \(\chi_{45738}(305, \cdot)\) n/a 84480 80
45738.2.is \(\chi_{45738}(827, \cdot)\) n/a 63360 80
45738.2.it \(\chi_{45738}(271, \cdot)\) n/a 112640 80
45738.2.iw \(\chi_{45738}(467, \cdot)\) n/a 84480 80
45738.2.iy \(\chi_{45738}(169, \cdot)\) n/a 570240 240
45738.2.iz \(\chi_{45738}(445, \cdot)\) n/a 760320 240
45738.2.ja \(\chi_{45738}(25, \cdot)\) n/a 760320 240
45738.2.jf \(\chi_{45738}(13, \cdot)\) n/a 760320 240
45738.2.jg \(\chi_{45738}(61, \cdot)\) n/a 760320 240
45738.2.jh \(\chi_{45738}(29, \cdot)\) n/a 570240 240
45738.2.ji \(\chi_{45738}(335, \cdot)\) n/a 760320 240
45738.2.jj \(\chi_{45738}(95, \cdot)\) n/a 760320 240
45738.2.jk \(\chi_{45738}(47, \cdot)\) n/a 760320 240
45738.2.jt \(\chi_{45738}(5, \cdot)\) n/a 760320 240
45738.2.ju \(\chi_{45738}(149, \cdot)\) n/a 760320 240
45738.2.jv \(\chi_{45738}(607, \cdot)\) n/a 760320 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(45738))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(45738)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1386))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2079))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2178))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5082))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6534))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7623))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15246))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22869))\)\(^{\oplus 2}\)