↑

Properties

Label 45486.2
Level 45486
Weight 2
Dimension 14119580
Nonzero newspaces 184
Sturm bound 224570880

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 45486 = 2 \cdot 3^{2} \cdot 7 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 184 \)
Sturm bound: \(224570880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(45486))\).

Total New Old
Modular forms 56239488 14119580 42119908
Cusp forms 56045953 14119580 41926373
Eisenstein series 193535 0 193535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(45486))\)

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
45486.2.a \(\chi_{45486}(1, \cdot)\) 45486.2.a.a 1 1
45486.2.a.b 1
45486.2.a.c 1
45486.2.a.d 1
45486.2.a.e 1
45486.2.a.f 1
45486.2.a.g 1
45486.2.a.h 1
45486.2.a.i 1
45486.2.a.j 1
45486.2.a.k 1
45486.2.a.l 1
45486.2.a.m 1
45486.2.a.n 1
45486.2.a.o 1
45486.2.a.p 1
45486.2.a.q 1
45486.2.a.r 1
45486.2.a.s 1
45486.2.a.t 1
45486.2.a.u 1
45486.2.a.v 1
45486.2.a.w 1
45486.2.a.x 1
45486.2.a.y 1
45486.2.a.z 1
45486.2.a.ba 1
45486.2.a.bb 1
45486.2.a.bc 1
45486.2.a.bd 1
45486.2.a.be 1
45486.2.a.bf 1
45486.2.a.bg 1
45486.2.a.bh 1
45486.2.a.bi 1
45486.2.a.bj 1
45486.2.a.bk 1
45486.2.a.bl 1
45486.2.a.bm 1
45486.2.a.bn 1
45486.2.a.bo 1
45486.2.a.bp 2
45486.2.a.bq 2
45486.2.a.br 2
45486.2.a.bs 2
45486.2.a.bt 2
45486.2.a.bu 2
45486.2.a.bv 2
45486.2.a.bw 2
45486.2.a.bx 2
45486.2.a.by 2
45486.2.a.bz 2
45486.2.a.ca 2
45486.2.a.cb 2
45486.2.a.cc 2
45486.2.a.cd 2
45486.2.a.ce 2
45486.2.a.cf 2
45486.2.a.cg 2
45486.2.a.ch 2
45486.2.a.ci 2
45486.2.a.cj 2
45486.2.a.ck 2
45486.2.a.cl 2
45486.2.a.cm 2
45486.2.a.cn 2
45486.2.a.co 2
45486.2.a.cp 2
45486.2.a.cq 2
45486.2.a.cr 2
45486.2.a.cs 2
45486.2.a.ct 2
45486.2.a.cu 2
45486.2.a.cv 2
45486.2.a.cw 2
45486.2.a.cx 2
45486.2.a.cy 2
45486.2.a.cz 2
45486.2.a.da 2
45486.2.a.db 2
45486.2.a.dc 2
45486.2.a.dd 2
45486.2.a.de 2
45486.2.a.df 2
45486.2.a.dg 2
45486.2.a.dh 2
45486.2.a.di 2
45486.2.a.dj 2
45486.2.a.dk 2
45486.2.a.dl 2
45486.2.a.dm 2
45486.2.a.dn 2
45486.2.a.do 3
45486.2.a.dp 3
45486.2.a.dq 3
45486.2.a.dr 3
45486.2.a.ds 3
45486.2.a.dt 3
45486.2.a.du 3
45486.2.a.dv 3
45486.2.a.dw 3
45486.2.a.dx 3
45486.2.a.dy 3
45486.2.a.dz 3
45486.2.a.ea 3
45486.2.a.eb 3
45486.2.a.ec 3
45486.2.a.ed 3
45486.2.a.ee 3
45486.2.a.ef 4
45486.2.a.eg 4
45486.2.a.eh 4
45486.2.a.ei 4
45486.2.a.ej 4
45486.2.a.ek 4
45486.2.a.el 4
45486.2.a.em 4
45486.2.a.en 4
45486.2.a.eo 4
45486.2.a.ep 4
45486.2.a.eq 4
45486.2.a.er 5
45486.2.a.es 5
45486.2.a.et 5
45486.2.a.eu 5
45486.2.a.ev 6
45486.2.a.ew 6
45486.2.a.ex 6
45486.2.a.ey 6
45486.2.a.ez 6
45486.2.a.fa 6
45486.2.a.fb 6
45486.2.a.fc 6
45486.2.a.fd 6
45486.2.a.fe 6
45486.2.a.ff 6
45486.2.a.fg 6
45486.2.a.fh 6
45486.2.a.fi 6
45486.2.a.fj 6
45486.2.a.fk 6
45486.2.a.fl 6
45486.2.a.fm 6
45486.2.a.fn 8
45486.2.a.fo 8
45486.2.a.fp 8
45486.2.a.fq 8
45486.2.a.fr 8
45486.2.a.fs 8
45486.2.a.ft 8
45486.2.a.fu 8
45486.2.a.fv 8
45486.2.a.fw 8
45486.2.a.fx 8
45486.2.a.fy 8
45486.2.a.fz 9
45486.2.a.ga 9
45486.2.a.gb 9
45486.2.a.gc 9
45486.2.a.gd 9
45486.2.a.ge 9
45486.2.a.gf 9
45486.2.a.gg 9
45486.2.a.gh 9
45486.2.a.gi 9
45486.2.a.gj 10
45486.2.a.gk 10
45486.2.a.gl 10
45486.2.a.gm 10
45486.2.a.gn 12
45486.2.a.go 12
45486.2.a.gp 12
45486.2.a.gq 12
45486.2.a.gr 12
45486.2.a.gs 12
45486.2.a.gt 15
45486.2.a.gu 15
45486.2.a.gv 15
45486.2.a.gw 15
45486.2.a.gx 15
45486.2.a.gy 15
45486.2.a.gz 15
45486.2.a.ha 15
45486.2.a.hb 16
45486.2.a.hc 16
45486.2.a.hd 16
45486.2.a.he 16
45486.2.b \(\chi_{45486}(6497, \cdot)\) n/a 680 1
45486.2.e \(\chi_{45486}(20215, \cdot)\) n/a 1136 1
45486.2.f \(\chi_{45486}(18773, \cdot)\) n/a 912 1
45486.2.i \(\chi_{45486}(2167, \cdot)\) n/a 5456 2
45486.2.j \(\chi_{45486}(17035, \cdot)\) n/a 5440 2
45486.2.k \(\chi_{45486}(15163, \cdot)\) n/a 4092 2
45486.2.l \(\chi_{45486}(12205, \cdot)\) n/a 2264 2
45486.2.m \(\chi_{45486}(25993, \cdot)\) n/a 2272 2
45486.2.n \(\chi_{45486}(40363, \cdot)\) n/a 4080 2
45486.2.o \(\chi_{45486}(14869, \cdot)\) n/a 1700 2
45486.2.p \(\chi_{45486}(10537, \cdot)\) n/a 5440 2
45486.2.q \(\chi_{45486}(20869, \cdot)\) n/a 5440 2
45486.2.r \(\chi_{45486}(1873, \cdot)\) n/a 2264 2
45486.2.s \(\chi_{45486}(10039, \cdot)\) n/a 4080 2
45486.2.t \(\chi_{45486}(25699, \cdot)\) n/a 5440 2
45486.2.u \(\chi_{45486}(17329, \cdot)\) n/a 5456 2
45486.2.w \(\chi_{45486}(8663, \cdot)\) n/a 5440 2
45486.2.y \(\chi_{45486}(20509, \cdot)\) n/a 5440 2
45486.2.z \(\chi_{45486}(14509, \cdot)\) n/a 2264 2
45486.2.bc \(\chi_{45486}(9679, \cdot)\) n/a 5440 2
45486.2.bd \(\chi_{45486}(32783, \cdot)\) n/a 5440 2
45486.2.bg \(\chi_{45486}(7289, \cdot)\) n/a 1808 2
45486.2.bh \(\chi_{45486}(21953, \cdot)\) n/a 4080 2
45486.2.bj \(\chi_{45486}(9385, \cdot)\) n/a 5440 2
45486.2.bl \(\chi_{45486}(2819, \cdot)\) n/a 5440 2
45486.2.bo \(\chi_{45486}(33641, \cdot)\) n/a 1824 2
45486.2.bp \(\chi_{45486}(26645, \cdot)\) n/a 5440 2
45486.2.bx \(\chi_{45486}(3317, \cdot)\) n/a 5440 2
45486.2.by \(\chi_{45486}(31769, \cdot)\) n/a 1816 2
45486.2.cd \(\chi_{45486}(31475, \cdot)\) n/a 5440 2
45486.2.ce \(\chi_{45486}(7943, \cdot)\) n/a 5456 2
45486.2.cf \(\chi_{45486}(7649, \cdot)\) n/a 1808 2
45486.2.cg \(\chi_{45486}(3611, \cdot)\) n/a 5456 2
45486.2.cm \(\chi_{45486}(37613, \cdot)\) n/a 5440 2
45486.2.cp \(\chi_{45486}(2459, \cdot)\) n/a 5440 2
45486.2.cq \(\chi_{45486}(26783, \cdot)\) n/a 1360 2
45486.2.cu \(\chi_{45486}(5053, \cdot)\) n/a 5440 2
45486.2.cv \(\chi_{45486}(8011, \cdot)\) n/a 2264 2
45486.2.cw \(\chi_{45486}(2887, \cdot)\) n/a 5440 2
45486.2.cx \(\chi_{45486}(33505, \cdot)\) n/a 5440 2
45486.2.dc \(\chi_{45486}(33211, \cdot)\) n/a 2264 2
45486.2.dd \(\chi_{45486}(10177, \cdot)\) n/a 5440 2
45486.2.de \(\chi_{45486}(6791, \cdot)\) n/a 4080 2
45486.2.df \(\chi_{45486}(32489, \cdot)\) n/a 1808 2
45486.2.dk \(\chi_{45486}(13787, \cdot)\) n/a 1808 2
45486.2.dl \(\chi_{45486}(21659, \cdot)\) n/a 4080 2
45486.2.dm \(\chi_{45486}(8957, \cdot)\) n/a 5440 2
45486.2.dn \(\chi_{45486}(2165, \cdot)\) n/a 5440 2
45486.2.dr \(\chi_{45486}(38335, \cdot)\) n/a 5440 2
45486.2.ds \(\chi_{45486}(5347, \cdot)\) n/a 2272 2
45486.2.dv \(\chi_{45486}(3181, \cdot)\) n/a 5440 2
45486.2.dx \(\chi_{45486}(1445, \cdot)\) n/a 5456 2
45486.2.eb \(\chi_{45486}(22811, \cdot)\) n/a 5440 2
45486.2.ee \(\chi_{45486}(13649, \cdot)\) n/a 5440 2
45486.2.ef \(\chi_{45486}(1151, \cdot)\) n/a 1808 2
45486.2.ei \(\chi_{45486}(5875, \cdot)\) n/a 16320 6
45486.2.ej \(\chi_{45486}(5443, \cdot)\) n/a 16320 6
45486.2.ek \(\chi_{45486}(3277, \cdot)\) n/a 5100 6
45486.2.el \(\chi_{45486}(11425, \cdot)\) n/a 12240 6
45486.2.em \(\chi_{45486}(3133, \cdot)\) n/a 6804 6
45486.2.en \(\chi_{45486}(11797, \cdot)\) n/a 16320 6
45486.2.eo \(\chi_{45486}(415, \cdot)\) n/a 6804 6
45486.2.ep \(\chi_{45486}(6199, \cdot)\) n/a 16320 6
45486.2.eq \(\chi_{45486}(967, \cdot)\) n/a 12240 6
45486.2.er \(\chi_{45486}(1751, \cdot)\) n/a 12240 6
45486.2.es \(\chi_{45486}(4577, \cdot)\) n/a 16320 6
45486.2.ex \(\chi_{45486}(8909, \cdot)\) n/a 5448 6
45486.2.ey \(\chi_{45486}(11219, \cdot)\) n/a 16320 6
45486.2.ez \(\chi_{45486}(3917, \cdot)\) n/a 16320 6
45486.2.fa \(\chi_{45486}(12401, \cdot)\) n/a 5448 6
45486.2.fh \(\chi_{45486}(1777, \cdot)\) n/a 16320 6
45486.2.fi \(\chi_{45486}(307, \cdot)\) n/a 6792 6
45486.2.fj \(\chi_{45486}(1921, \cdot)\) n/a 16320 6
45486.2.fk \(\chi_{45486}(4639, \cdot)\) n/a 16320 6
45486.2.ft \(\chi_{45486}(5353, \cdot)\) n/a 16320 6
45486.2.fu \(\chi_{45486}(13123, \cdot)\) n/a 6804 6
45486.2.fv \(\chi_{45486}(2411, \cdot)\) n/a 5448 6
45486.2.fw \(\chi_{45486}(4721, \cdot)\) n/a 16320 6
45486.2.fx \(\chi_{45486}(1199, \cdot)\) n/a 16320 6
45486.2.fy \(\chi_{45486}(5903, \cdot)\) n/a 5448 6
45486.2.gh \(\chi_{45486}(11453, \cdot)\) n/a 12240 6
45486.2.gi \(\chi_{45486}(2465, \cdot)\) n/a 4080 6
45486.2.gj \(\chi_{45486}(11975, \cdot)\) n/a 16320 6
45486.2.gk \(\chi_{45486}(4205, \cdot)\) n/a 16320 6
45486.2.gl \(\chi_{45486}(13619, \cdot)\) n/a 16320 6
45486.2.gm \(\chi_{45486}(4631, \cdot)\) n/a 16320 6
45486.2.gn \(\chi_{45486}(22049, \cdot)\) n/a 5424 6
45486.2.go \(\chi_{45486}(7643, \cdot)\) n/a 16320 6
45486.2.gv \(\chi_{45486}(14341, \cdot)\) n/a 16320 6
45486.2.gw \(\chi_{45486}(6625, \cdot)\) n/a 6804 6
45486.2.hb \(\chi_{45486}(1021, \cdot)\) n/a 16320 6
45486.2.hc \(\chi_{45486}(2395, \cdot)\) n/a 17100 18
45486.2.hf \(\chi_{45486}(2015, \cdot)\) n/a 18144 18
45486.2.hg \(\chi_{45486}(1063, \cdot)\) n/a 22752 18
45486.2.hj \(\chi_{45486}(1709, \cdot)\) n/a 13680 18
45486.2.hk \(\chi_{45486}(457, \cdot)\) n/a 109440 36
45486.2.hl \(\chi_{45486}(1033, \cdot)\) n/a 109440 36
45486.2.hm \(\chi_{45486}(463, \cdot)\) n/a 82080 36
45486.2.hn \(\chi_{45486}(919, \cdot)\) n/a 45648 36
45486.2.ho \(\chi_{45486}(1075, \cdot)\) n/a 109440 36
45486.2.hp \(\chi_{45486}(961, \cdot)\) n/a 109440 36
45486.2.hq \(\chi_{45486}(505, \cdot)\) n/a 34200 36
45486.2.hr \(\chi_{45486}(2059, \cdot)\) n/a 82080 36
45486.2.hs \(\chi_{45486}(1369, \cdot)\) n/a 45648 36
45486.2.ht \(\chi_{45486}(163, \cdot)\) n/a 45648 36
45486.2.hu \(\chi_{45486}(799, \cdot)\) n/a 82080 36
45486.2.hv \(\chi_{45486}(121, \cdot)\) n/a 109440 36
45486.2.hw \(\chi_{45486}(1255, \cdot)\) n/a 109440 36
45486.2.hz \(\chi_{45486}(1223, \cdot)\) n/a 36576 36
45486.2.ia \(\chi_{45486}(1679, \cdot)\) n/a 109440 36
45486.2.id \(\chi_{45486}(1109, \cdot)\) n/a 109440 36
45486.2.ih \(\chi_{45486}(1559, \cdot)\) n/a 109440 36
45486.2.ij \(\chi_{45486}(787, \cdot)\) n/a 109440 36
45486.2.im \(\chi_{45486}(559, \cdot)\) n/a 45504 36
45486.2.in \(\chi_{45486}(31, \cdot)\) n/a 109440 36
45486.2.ir \(\chi_{45486}(2279, \cdot)\) n/a 109440 36
45486.2.is \(\chi_{45486}(905, \cdot)\) n/a 109440 36
45486.2.it \(\chi_{45486}(113, \cdot)\) n/a 82080 36
45486.2.iu \(\chi_{45486}(863, \cdot)\) n/a 36576 36
45486.2.iz \(\chi_{45486}(683, \cdot)\) n/a 36576 36
45486.2.ja \(\chi_{45486}(2003, \cdot)\) n/a 82080 36
45486.2.jb \(\chi_{45486}(601, \cdot)\) n/a 109440 36
45486.2.jc \(\chi_{45486}(1405, \cdot)\) n/a 45648 36
45486.2.jh \(\chi_{45486}(1741, \cdot)\) n/a 109440 36
45486.2.ji \(\chi_{45486}(493, \cdot)\) n/a 109440 36
45486.2.jj \(\chi_{45486}(829, \cdot)\) n/a 45648 36
45486.2.jk \(\chi_{45486}(265, \cdot)\) n/a 109440 36
45486.2.jo \(\chi_{45486}(449, \cdot)\) n/a 27360 36
45486.2.jp \(\chi_{45486}(65, \cdot)\) n/a 109440 36
45486.2.js \(\chi_{45486}(977, \cdot)\) n/a 109440 36
45486.2.jy \(\chi_{45486}(419, \cdot)\) n/a 109440 36
45486.2.jz \(\chi_{45486}(467, \cdot)\) n/a 36576 36
45486.2.ka \(\chi_{45486}(761, \cdot)\) n/a 109440 36
45486.2.kb \(\chi_{45486}(353, \cdot)\) n/a 109440 36
45486.2.kg \(\chi_{45486}(647, \cdot)\) n/a 36576 36
45486.2.kh \(\chi_{45486}(83, \cdot)\) n/a 109440 36
45486.2.kp \(\chi_{45486}(311, \cdot)\) n/a 109440 36
45486.2.kq \(\chi_{45486}(125, \cdot)\) n/a 36288 36
45486.2.kt \(\chi_{45486}(425, \cdot)\) n/a 109440 36
45486.2.kv \(\chi_{45486}(1291, \cdot)\) n/a 109440 36
45486.2.kx \(\chi_{45486}(407, \cdot)\) n/a 82080 36
45486.2.ky \(\chi_{45486}(107, \cdot)\) n/a 36576 36
45486.2.lb \(\chi_{45486}(1019, \cdot)\) n/a 109440 36
45486.2.lc \(\chi_{45486}(103, \cdot)\) n/a 109440 36
45486.2.lf \(\chi_{45486}(145, \cdot)\) n/a 45648 36
45486.2.lg \(\chi_{45486}(1357, \cdot)\) n/a 109440 36
45486.2.li \(\chi_{45486}(569, \cdot)\) n/a 109440 36
45486.2.lk \(\chi_{45486}(841, \cdot)\) n/a 246240 108
45486.2.ll \(\chi_{45486}(529, \cdot)\) n/a 328320 108
45486.2.lm \(\chi_{45486}(1297, \cdot)\) n/a 136728 108
45486.2.ln \(\chi_{45486}(823, \cdot)\) n/a 328320 108
45486.2.lo \(\chi_{45486}(289, \cdot)\) n/a 136728 108
45486.2.lp \(\chi_{45486}(43, \cdot)\) n/a 246240 108
45486.2.lq \(\chi_{45486}(253, \cdot)\) n/a 102600 108
45486.2.lr \(\chi_{45486}(25, \cdot)\) n/a 328320 108
45486.2.ls \(\chi_{45486}(709, \cdot)\) n/a 328320 108
45486.2.lt \(\chi_{45486}(895, \cdot)\) n/a 328320 108
45486.2.ly \(\chi_{45486}(649, \cdot)\) n/a 136728 108
45486.2.lz \(\chi_{45486}(355, \cdot)\) n/a 328320 108
45486.2.mg \(\chi_{45486}(461, \cdot)\) n/a 328320 108
45486.2.mh \(\chi_{45486}(251, \cdot)\) n/a 109728 108
45486.2.mi \(\chi_{45486}(317, \cdot)\) n/a 328320 108
45486.2.mj \(\chi_{45486}(401, \cdot)\) n/a 328320 108
45486.2.mk \(\chi_{45486}(47, \cdot)\) n/a 328320 108
45486.2.ml \(\chi_{45486}(5, \cdot)\) n/a 328320 108
45486.2.mm \(\chi_{45486}(71, \cdot)\) n/a 82080 108
45486.2.mn \(\chi_{45486}(155, \cdot)\) n/a 246240 108
45486.2.mw \(\chi_{45486}(485, \cdot)\) n/a 109296 108
45486.2.mx \(\chi_{45486}(599, \cdot)\) n/a 328320 108
45486.2.my \(\chi_{45486}(803, \cdot)\) n/a 328320 108
45486.2.mz \(\chi_{45486}(17, \cdot)\) n/a 109296 108
45486.2.na \(\chi_{45486}(325, \cdot)\) n/a 136728 108
45486.2.nb \(\chi_{45486}(409, \cdot)\) n/a 328320 108
45486.2.nk \(\chi_{45486}(241, \cdot)\) n/a 328320 108
45486.2.nl \(\chi_{45486}(535, \cdot)\) n/a 328320 108
45486.2.nm \(\chi_{45486}(181, \cdot)\) n/a 136944 108
45486.2.nn \(\chi_{45486}(13, \cdot)\) n/a 328320 108
45486.2.nu \(\chi_{45486}(53, \cdot)\) n/a 109296 108
45486.2.nv \(\chi_{45486}(515, \cdot)\) n/a 328320 108
45486.2.nw \(\chi_{45486}(605, \cdot)\) n/a 328320 108
45486.2.nx \(\chi_{45486}(719, \cdot)\) n/a 109296 108
45486.2.oc \(\chi_{45486}(1175, \cdot)\) n/a 328320 108
45486.2.od \(\chi_{45486}(29, \cdot)\) n/a 246240 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(45486))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(45486)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1197))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2394))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2527))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5054))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6498))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7581))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22743))\)\(^{\oplus 2}\)