# Properties

 Label 9360.2 Level 9360 Weight 2 Dimension 934064 Nonzero newspaces 260 Sturm bound 9289728

## Defining parameters

 Level: $$N$$ = $$9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$260$$ Sturm bound: $$9289728$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9360))$$.

Total New Old
Modular forms 2343936 939412 1404524
Cusp forms 2300929 934064 1366865
Eisenstein series 43007 5348 37659

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9360))$$

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
9360.2.a $$\chi_{9360}(1, \cdot)$$ 9360.2.a.a 1 1
9360.2.a.b 1
9360.2.a.c 1
9360.2.a.d 1
9360.2.a.e 1
9360.2.a.f 1
9360.2.a.g 1
9360.2.a.h 1
9360.2.a.i 1
9360.2.a.j 1
9360.2.a.k 1
9360.2.a.l 1
9360.2.a.m 1
9360.2.a.n 1
9360.2.a.o 1
9360.2.a.p 1
9360.2.a.q 1
9360.2.a.r 1
9360.2.a.s 1
9360.2.a.t 1
9360.2.a.u 1
9360.2.a.v 1
9360.2.a.w 1
9360.2.a.x 1
9360.2.a.y 1
9360.2.a.z 1
9360.2.a.ba 1
9360.2.a.bb 1
9360.2.a.bc 1
9360.2.a.bd 1
9360.2.a.be 1
9360.2.a.bf 1
9360.2.a.bg 1
9360.2.a.bh 1
9360.2.a.bi 1
9360.2.a.bj 1
9360.2.a.bk 1
9360.2.a.bl 1
9360.2.a.bm 1
9360.2.a.bn 1
9360.2.a.bo 1
9360.2.a.bp 1
9360.2.a.bq 1
9360.2.a.br 1
9360.2.a.bs 1
9360.2.a.bt 1
9360.2.a.bu 1
9360.2.a.bv 1
9360.2.a.bw 1
9360.2.a.bx 1
9360.2.a.by 1
9360.2.a.bz 1
9360.2.a.ca 1
9360.2.a.cb 1
9360.2.a.cc 2
9360.2.a.cd 2
9360.2.a.ce 2
9360.2.a.cf 2
9360.2.a.cg 2
9360.2.a.ch 2
9360.2.a.ci 2
9360.2.a.cj 2
9360.2.a.ck 2
9360.2.a.cl 2
9360.2.a.cm 2
9360.2.a.cn 2
9360.2.a.co 2
9360.2.a.cp 2
9360.2.a.cq 2
9360.2.a.cr 2
9360.2.a.cs 2
9360.2.a.ct 2
9360.2.a.cu 2
9360.2.a.cv 2
9360.2.a.cw 2
9360.2.a.cx 3
9360.2.a.cy 3
9360.2.a.cz 3
9360.2.a.da 3
9360.2.a.db 3
9360.2.a.dc 3
9360.2.a.dd 3
9360.2.a.de 3
9360.2.b $$\chi_{9360}(2809, \cdot)$$ None 0 1
9360.2.e $$\chi_{9360}(8711, \cdot)$$ None 0 1
9360.2.g $$\chi_{9360}(7201, \cdot)$$ n/a 140 1
9360.2.h $$\chi_{9360}(9359, \cdot)$$ n/a 168 1
9360.2.k $$\chi_{9360}(4031, \cdot)$$ 9360.2.k.a 16 1
9360.2.k.b 16
9360.2.k.c 32
9360.2.k.d 32
9360.2.l $$\chi_{9360}(7489, \cdot)$$ n/a 180 1
9360.2.n $$\chi_{9360}(4679, \cdot)$$ None 0 1
9360.2.q $$\chi_{9360}(2521, \cdot)$$ None 0 1
9360.2.r $$\chi_{9360}(5329, \cdot)$$ n/a 208 1
9360.2.u $$\chi_{9360}(1871, \cdot)$$ n/a 112 1
9360.2.w $$\chi_{9360}(4681, \cdot)$$ None 0 1
9360.2.x $$\chi_{9360}(6839, \cdot)$$ None 0 1
9360.2.ba $$\chi_{9360}(6551, \cdot)$$ None 0 1
9360.2.bb $$\chi_{9360}(649, \cdot)$$ None 0 1
9360.2.bd $$\chi_{9360}(2159, \cdot)$$ n/a 144 1
9360.2.bg $$\chi_{9360}(2161, \cdot)$$ n/a 280 2
9360.2.bh $$\chi_{9360}(3121, \cdot)$$ n/a 576 2
9360.2.bi $$\chi_{9360}(5281, \cdot)$$ n/a 672 2
9360.2.bj $$\chi_{9360}(2401, \cdot)$$ n/a 672 2
9360.2.bl $$\chi_{9360}(1763, \cdot)$$ n/a 1344 2
9360.2.bn $$\chi_{9360}(6157, \cdot)$$ n/a 1672 2
9360.2.bp $$\chi_{9360}(4211, \cdot)$$ n/a 896 2
9360.2.bq $$\chi_{9360}(2989, \cdot)$$ n/a 1672 2
9360.2.bs $$\chi_{9360}(577, \cdot)$$ n/a 416 2
9360.2.bt $$\chi_{9360}(5543, \cdot)$$ None 0 2
9360.2.by $$\chi_{9360}(73, \cdot)$$ None 0 2
9360.2.bz $$\chi_{9360}(863, \cdot)$$ n/a 336 2
9360.2.cb $$\chi_{9360}(2341, \cdot)$$ n/a 960 2
9360.2.cc $$\chi_{9360}(4499, \cdot)$$ n/a 1152 2
9360.2.ce $$\chi_{9360}(1477, \cdot)$$ n/a 1672 2
9360.2.cg $$\chi_{9360}(6443, \cdot)$$ n/a 1344 2
9360.2.ci $$\chi_{9360}(5491, \cdot)$$ n/a 1120 2
9360.2.cl $$\chi_{9360}(5309, \cdot)$$ n/a 1344 2
9360.2.cn $$\chi_{9360}(233, \cdot)$$ None 0 2
9360.2.co $$\chi_{9360}(1457, \cdot)$$ n/a 288 2
9360.2.cr $$\chi_{9360}(703, \cdot)$$ n/a 360 2
9360.2.cs $$\chi_{9360}(3223, \cdot)$$ None 0 2
9360.2.cv $$\chi_{9360}(3619, \cdot)$$ n/a 1672 2
9360.2.cw $$\chi_{9360}(1061, \cdot)$$ n/a 896 2
9360.2.cz $$\chi_{9360}(6209, \cdot)$$ n/a 336 2
9360.2.da $$\chi_{9360}(1529, \cdot)$$ None 0 2
9360.2.dc $$\chi_{9360}(6391, \cdot)$$ None 0 2
9360.2.df $$\chi_{9360}(1711, \cdot)$$ n/a 280 2
9360.2.dg $$\chi_{9360}(2107, \cdot)$$ n/a 1440 2
9360.2.dh $$\chi_{9360}(6317, \cdot)$$ n/a 1344 2
9360.2.dk $$\chi_{9360}(1637, \cdot)$$ n/a 1344 2
9360.2.dl $$\chi_{9360}(6787, \cdot)$$ n/a 1440 2
9360.2.dq $$\chi_{9360}(4627, \cdot)$$ n/a 1672 2
9360.2.dr $$\chi_{9360}(3797, \cdot)$$ n/a 1152 2
9360.2.du $$\chi_{9360}(53, \cdot)$$ n/a 1152 2
9360.2.dv $$\chi_{9360}(883, \cdot)$$ n/a 1672 2
9360.2.dx $$\chi_{9360}(4519, \cdot)$$ None 0 2
9360.2.dy $$\chi_{9360}(1279, \cdot)$$ n/a 420 2
9360.2.ea $$\chi_{9360}(161, \cdot)$$ n/a 224 2
9360.2.ed $$\chi_{9360}(3401, \cdot)$$ None 0 2
9360.2.ef $$\chi_{9360}(629, \cdot)$$ n/a 1344 2
9360.2.eg $$\chi_{9360}(811, \cdot)$$ n/a 1120 2
9360.2.ei $$\chi_{9360}(2287, \cdot)$$ n/a 420 2
9360.2.el $$\chi_{9360}(5383, \cdot)$$ None 0 2
9360.2.em $$\chi_{9360}(2393, \cdot)$$ None 0 2
9360.2.ep $$\chi_{9360}(4913, \cdot)$$ n/a 336 2
9360.2.eq $$\chi_{9360}(2501, \cdot)$$ n/a 896 2
9360.2.et $$\chi_{9360}(2179, \cdot)$$ n/a 1672 2
9360.2.eu $$\chi_{9360}(5507, \cdot)$$ n/a 1344 2
9360.2.ew $$\chi_{9360}(2413, \cdot)$$ n/a 1672 2
9360.2.ey $$\chi_{9360}(1691, \cdot)$$ n/a 768 2
9360.2.fb $$\chi_{9360}(469, \cdot)$$ n/a 1440 2
9360.2.fe $$\chi_{9360}(4103, \cdot)$$ None 0 2
9360.2.ff $$\chi_{9360}(6193, \cdot)$$ n/a 416 2
9360.2.fg $$\chi_{9360}(4607, \cdot)$$ n/a 336 2
9360.2.fh $$\chi_{9360}(1513, \cdot)$$ None 0 2
9360.2.fk $$\chi_{9360}(181, \cdot)$$ n/a 1120 2
9360.2.fn $$\chi_{9360}(2339, \cdot)$$ n/a 1344 2
9360.2.fp $$\chi_{9360}(7093, \cdot)$$ n/a 1672 2
9360.2.fr $$\chi_{9360}(827, \cdot)$$ n/a 1344 2
9360.2.ft $$\chi_{9360}(6361, \cdot)$$ None 0 2
9360.2.fu $$\chi_{9360}(2279, \cdot)$$ None 0 2
9360.2.fw $$\chi_{9360}(529, \cdot)$$ n/a 1000 2
9360.2.fz $$\chi_{9360}(191, \cdot)$$ n/a 672 2
9360.2.ga $$\chi_{9360}(959, \cdot)$$ n/a 1008 2
9360.2.gd $$\chi_{9360}(1681, \cdot)$$ n/a 672 2
9360.2.gf $$\chi_{9360}(4631, \cdot)$$ None 0 2
9360.2.gg $$\chi_{9360}(1849, \cdot)$$ None 0 2
9360.2.gj $$\chi_{9360}(5879, \cdot)$$ None 0 2
9360.2.gk $$\chi_{9360}(601, \cdot)$$ None 0 2
9360.2.gm $$\chi_{9360}(5711, \cdot)$$ n/a 672 2
9360.2.gp $$\chi_{9360}(2929, \cdot)$$ n/a 1000 2
9360.2.gq $$\chi_{9360}(311, \cdot)$$ None 0 2
9360.2.gt $$\chi_{9360}(3769, \cdot)$$ None 0 2
9360.2.gw $$\chi_{9360}(1439, \cdot)$$ n/a 336 2
9360.2.gy $$\chi_{9360}(1369, \cdot)$$ None 0 2
9360.2.gz $$\chi_{9360}(4391, \cdot)$$ None 0 2
9360.2.hc $$\chi_{9360}(5279, \cdot)$$ n/a 864 2
9360.2.hf $$\chi_{9360}(2209, \cdot)$$ n/a 1000 2
9360.2.hg $$\chi_{9360}(4991, \cdot)$$ n/a 672 2
9360.2.hj $$\chi_{9360}(6119, \cdot)$$ None 0 2
9360.2.hk $$\chi_{9360}(3961, \cdot)$$ None 0 2
9360.2.hm $$\chi_{9360}(2591, \cdot)$$ n/a 224 2
9360.2.hp $$\chi_{9360}(3169, \cdot)$$ n/a 416 2
9360.2.hq $$\chi_{9360}(1561, \cdot)$$ None 0 2
9360.2.ht $$\chi_{9360}(599, \cdot)$$ None 0 2
9360.2.hw $$\chi_{9360}(1199, \cdot)$$ n/a 1008 2
9360.2.hy $$\chi_{9360}(1609, \cdot)$$ None 0 2
9360.2.hz $$\chi_{9360}(1031, \cdot)$$ None 0 2
9360.2.ic $$\chi_{9360}(3839, \cdot)$$ n/a 1008 2
9360.2.id $$\chi_{9360}(4801, \cdot)$$ n/a 672 2
9360.2.if $$\chi_{9360}(1751, \cdot)$$ None 0 2
9360.2.ii $$\chi_{9360}(8089, \cdot)$$ None 0 2
9360.2.ij $$\chi_{9360}(911, \cdot)$$ n/a 576 2
9360.2.im $$\chi_{9360}(1249, \cdot)$$ n/a 864 2
9360.2.in $$\chi_{9360}(361, \cdot)$$ None 0 2
9360.2.iq $$\chi_{9360}(2519, \cdot)$$ None 0 2
9360.2.is $$\chi_{9360}(289, \cdot)$$ n/a 416 2
9360.2.it $$\chi_{9360}(3311, \cdot)$$ n/a 224 2
9360.2.iw $$\chi_{9360}(1559, \cdot)$$ None 0 2
9360.2.ix $$\chi_{9360}(5641, \cdot)$$ None 0 2
9360.2.ja $$\chi_{9360}(5929, \cdot)$$ None 0 2
9360.2.jb $$\chi_{9360}(2471, \cdot)$$ None 0 2
9360.2.je $$\chi_{9360}(719, \cdot)$$ n/a 336 2
9360.2.jf $$\chi_{9360}(5041, \cdot)$$ n/a 280 2
9360.2.jh $$\chi_{9360}(1511, \cdot)$$ None 0 2
9360.2.jk $$\chi_{9360}(2089, \cdot)$$ None 0 2
9360.2.jl $$\chi_{9360}(961, \cdot)$$ n/a 672 2
9360.2.jo $$\chi_{9360}(3119, \cdot)$$ n/a 1008 2
9360.2.jp $$\chi_{9360}(121, \cdot)$$ None 0 2
9360.2.js $$\chi_{9360}(8519, \cdot)$$ None 0 2
9360.2.ju $$\chi_{9360}(3409, \cdot)$$ n/a 1000 2
9360.2.jv $$\chi_{9360}(3071, \cdot)$$ n/a 672 2
9360.2.jy $$\chi_{9360}(7439, \cdot)$$ n/a 1008 2
9360.2.ka $$\chi_{9360}(4489, \cdot)$$ None 0 2
9360.2.kd $$\chi_{9360}(4151, \cdot)$$ None 0 2
9360.2.ke $$\chi_{9360}(2759, \cdot)$$ None 0 2
9360.2.kh $$\chi_{9360}(3721, \cdot)$$ None 0 2
9360.2.kj $$\chi_{9360}(2831, \cdot)$$ n/a 672 2
9360.2.kk $$\chi_{9360}(49, \cdot)$$ n/a 1000 2
9360.2.km $$\chi_{9360}(227, \cdot)$$ n/a 8032 4
9360.2.ko $$\chi_{9360}(2173, \cdot)$$ n/a 8032 4
9360.2.kq $$\chi_{9360}(61, \cdot)$$ n/a 5376 4
9360.2.kt $$\chi_{9360}(419, \cdot)$$ n/a 8032 4
9360.2.ku $$\chi_{9360}(3503, \cdot)$$ n/a 2016 4
9360.2.kv $$\chi_{9360}(3577, \cdot)$$ None 0 4
9360.2.la $$\chi_{9360}(167, \cdot)$$ None 0 4
9360.2.lb $$\chi_{9360}(97, \cdot)$$ n/a 2000 4
9360.2.lc $$\chi_{9360}(491, \cdot)$$ n/a 5376 4
9360.2.lf $$\chi_{9360}(2149, \cdot)$$ n/a 8032 4
9360.2.lh $$\chi_{9360}(1597, \cdot)$$ n/a 8032 4
9360.2.lj $$\chi_{9360}(2243, \cdot)$$ n/a 8032 4
9360.2.ll $$\chi_{9360}(2893, \cdot)$$ n/a 8032 4
9360.2.ln $$\chi_{9360}(947, \cdot)$$ n/a 8032 4
9360.2.lo $$\chi_{9360}(853, \cdot)$$ n/a 8032 4
9360.2.lq $$\chi_{9360}(4427, \cdot)$$ n/a 2688 4
9360.2.ls $$\chi_{9360}(1333, \cdot)$$ n/a 3344 4
9360.2.lu $$\chi_{9360}(83, \cdot)$$ n/a 8032 4
9360.2.lw $$\chi_{9360}(2029, \cdot)$$ n/a 6912 4
9360.2.lz $$\chi_{9360}(131, \cdot)$$ n/a 4608 4
9360.2.mb $$\chi_{9360}(1499, \cdot)$$ n/a 8032 4
9360.2.md $$\chi_{9360}(179, \cdot)$$ n/a 2688 4
9360.2.me $$\chi_{9360}(901, \cdot)$$ n/a 2240 4
9360.2.mg $$\chi_{9360}(1141, \cdot)$$ n/a 5376 4
9360.2.mi $$\chi_{9360}(817, \cdot)$$ n/a 2000 4
9360.2.mj $$\chi_{9360}(1463, \cdot)$$ None 0 4
9360.2.mm $$\chi_{9360}(697, \cdot)$$ None 0 4
9360.2.mn $$\chi_{9360}(1487, \cdot)$$ n/a 2016 4
9360.2.mq $$\chi_{9360}(1007, \cdot)$$ n/a 672 4
9360.2.mr $$\chi_{9360}(2377, \cdot)$$ None 0 4
9360.2.mw $$\chi_{9360}(1367, \cdot)$$ None 0 4
9360.2.mx $$\chi_{9360}(2593, \cdot)$$ n/a 832 4
9360.2.na $$\chi_{9360}(2257, \cdot)$$ n/a 2000 4
9360.2.nb $$\chi_{9360}(983, \cdot)$$ None 0 4
9360.2.ne $$\chi_{9360}(4153, \cdot)$$ None 0 4
9360.2.nf $$\chi_{9360}(2927, \cdot)$$ n/a 2016 4
9360.2.nh $$\chi_{9360}(1069, \cdot)$$ n/a 8032 4
9360.2.nj $$\chi_{9360}(2629, \cdot)$$ n/a 3344 4
9360.2.nk $$\chi_{9360}(971, \cdot)$$ n/a 1792 4
9360.2.nm $$\chi_{9360}(731, \cdot)$$ n/a 5376 4
9360.2.no $$\chi_{9360}(779, \cdot)$$ n/a 8032 4
9360.2.nr $$\chi_{9360}(1741, \cdot)$$ n/a 5376 4
9360.2.nt $$\chi_{9360}(1643, \cdot)$$ n/a 8032 4
9360.2.nv $$\chi_{9360}(973, \cdot)$$ n/a 3344 4
9360.2.nx $$\chi_{9360}(4067, \cdot)$$ n/a 2688 4
9360.2.nz $$\chi_{9360}(5533, \cdot)$$ n/a 8032 4
9360.2.oa $$\chi_{9360}(1523, \cdot)$$ n/a 8032 4
9360.2.oc $$\chi_{9360}(877, \cdot)$$ n/a 8032 4
9360.2.of $$\chi_{9360}(5501, \cdot)$$ n/a 5376 4
9360.2.og $$\chi_{9360}(6259, \cdot)$$ n/a 8032 4
9360.2.oi $$\chi_{9360}(367, \cdot)$$ n/a 2016 4
9360.2.ol $$\chi_{9360}(823, \cdot)$$ None 0 4
9360.2.om $$\chi_{9360}(4073, \cdot)$$ None 0 4
9360.2.op $$\chi_{9360}(113, \cdot)$$ n/a 2000 4
9360.2.oq $$\chi_{9360}(3629, \cdot)$$ n/a 8032 4
9360.2.ot $$\chi_{9360}(691, \cdot)$$ n/a 5376 4
9360.2.ou $$\chi_{9360}(749, \cdot)$$ n/a 8032 4
9360.2.ox $$\chi_{9360}(931, \cdot)$$ n/a 5376 4
9360.2.oz $$\chi_{9360}(379, \cdot)$$ n/a 3344 4
9360.2.pb $$\chi_{9360}(6619, \cdot)$$ n/a 8032 4
9360.2.pc $$\chi_{9360}(5141, \cdot)$$ n/a 5376 4
9360.2.pe $$\chi_{9360}(3941, \cdot)$$ n/a 1792 4
9360.2.pg $$\chi_{9360}(2263, \cdot)$$ None 0 4
9360.2.pj $$\chi_{9360}(1663, \cdot)$$ n/a 2016 4
9360.2.pk $$\chi_{9360}(17, \cdot)$$ n/a 672 4
9360.2.pn $$\chi_{9360}(257, \cdot)$$ n/a 2000 4
9360.2.po $$\chi_{9360}(2057, \cdot)$$ None 0 4
9360.2.pr $$\chi_{9360}(1673, \cdot)$$ None 0 4
9360.2.ps $$\chi_{9360}(1927, \cdot)$$ None 0 4
9360.2.pv $$\chi_{9360}(2167, \cdot)$$ None 0 4
9360.2.pw $$\chi_{9360}(2383, \cdot)$$ n/a 2016 4
9360.2.pz $$\chi_{9360}(127, \cdot)$$ n/a 840 4
9360.2.qa $$\chi_{9360}(1793, \cdot)$$ n/a 2000 4
9360.2.qd $$\chi_{9360}(3017, \cdot)$$ None 0 4
9360.2.qe $$\chi_{9360}(331, \cdot)$$ n/a 5376 4
9360.2.qg $$\chi_{9360}(2251, \cdot)$$ n/a 2240 4
9360.2.qj $$\chi_{9360}(2069, \cdot)$$ n/a 2688 4
9360.2.ql $$\chi_{9360}(3269, \cdot)$$ n/a 8032 4
9360.2.qn $$\chi_{9360}(2621, \cdot)$$ n/a 5376 4
9360.2.qo $$\chi_{9360}(2059, \cdot)$$ n/a 8032 4
9360.2.qr $$\chi_{9360}(31, \cdot)$$ n/a 1344 4
9360.2.qs $$\chi_{9360}(151, \cdot)$$ None 0 4
9360.2.qu $$\chi_{9360}(4649, \cdot)$$ None 0 4
9360.2.qx $$\chi_{9360}(1409, \cdot)$$ n/a 2000 4
9360.2.qy $$\chi_{9360}(799, \cdot)$$ n/a 2016 4
9360.2.rb $$\chi_{9360}(1879, \cdot)$$ None 0 4
9360.2.rc $$\chi_{9360}(3521, \cdot)$$ n/a 1344 4
9360.2.rf $$\chi_{9360}(1241, \cdot)$$ None 0 4
9360.2.rg $$\chi_{9360}(1601, \cdot)$$ n/a 448 4
9360.2.rj $$\chi_{9360}(761, \cdot)$$ None 0 4
9360.2.rl $$\chi_{9360}(1159, \cdot)$$ None 0 4
9360.2.rm $$\chi_{9360}(2719, \cdot)$$ n/a 840 4
9360.2.rp $$\chi_{9360}(2359, \cdot)$$ None 0 4
9360.2.rq $$\chi_{9360}(319, \cdot)$$ n/a 2016 4
9360.2.rt $$\chi_{9360}(41, \cdot)$$ None 0 4
9360.2.ru $$\chi_{9360}(401, \cdot)$$ n/a 1344 4
9360.2.ry $$\chi_{9360}(523, \cdot)$$ n/a 3344 4
9360.2.rz $$\chi_{9360}(413, \cdot)$$ n/a 2688 4
9360.2.sc $$\chi_{9360}(4157, \cdot)$$ n/a 2688 4
9360.2.sd $$\chi_{9360}(1387, \cdot)$$ n/a 3344 4
9360.2.se $$\chi_{9360}(677, \cdot)$$ n/a 6912 4
9360.2.sf $$\chi_{9360}(1507, \cdot)$$ n/a 8032 4
9360.2.sk $$\chi_{9360}(907, \cdot)$$ n/a 8032 4
9360.2.sl $$\chi_{9360}(1517, \cdot)$$ n/a 8032 4
9360.2.so $$\chi_{9360}(4397, \cdot)$$ n/a 8032 4
9360.2.sp $$\chi_{9360}(3787, \cdot)$$ n/a 8032 4
9360.2.ss $$\chi_{9360}(2837, \cdot)$$ n/a 8032 4
9360.2.st $$\chi_{9360}(2227, \cdot)$$ n/a 8032 4
9360.2.sw $$\chi_{9360}(43, \cdot)$$ n/a 8032 4
9360.2.sx $$\chi_{9360}(653, \cdot)$$ n/a 8032 4
9360.2.sy $$\chi_{9360}(3067, \cdot)$$ n/a 8032 4
9360.2.sz $$\chi_{9360}(2237, \cdot)$$ n/a 6912 4
9360.2.te $$\chi_{9360}(77, \cdot)$$ n/a 8032 4
9360.2.tf $$\chi_{9360}(5227, \cdot)$$ n/a 6912 4
9360.2.tg $$\chi_{9360}(173, \cdot)$$ n/a 8032 4
9360.2.th $$\chi_{9360}(763, \cdot)$$ n/a 8032 4
9360.2.tk $$\chi_{9360}(2707, \cdot)$$ n/a 8032 4
9360.2.tl $$\chi_{9360}(5477, \cdot)$$ n/a 8032 4
9360.2.to $$\chi_{9360}(1147, \cdot)$$ n/a 8032 4
9360.2.tp $$\chi_{9360}(3917, \cdot)$$ n/a 8032 4
9360.2.ts $$\chi_{9360}(797, \cdot)$$ n/a 8032 4
9360.2.tt $$\chi_{9360}(7387, \cdot)$$ n/a 8032 4
9360.2.ty $$\chi_{9360}(547, \cdot)$$ n/a 6912 4
9360.2.tz $$\chi_{9360}(4757, \cdot)$$ n/a 8032 4
9360.2.ua $$\chi_{9360}(667, \cdot)$$ n/a 3344 4
9360.2.ub $$\chi_{9360}(1277, \cdot)$$ n/a 2688 4
9360.2.ue $$\chi_{9360}(3077, \cdot)$$ n/a 2688 4
9360.2.uf $$\chi_{9360}(2467, \cdot)$$ n/a 3344 4
9360.2.ui $$\chi_{9360}(2009, \cdot)$$ None 0 4
9360.2.ul $$\chi_{9360}(929, \cdot)$$ n/a 2000 4
9360.2.um $$\chi_{9360}(1111, \cdot)$$ None 0 4
9360.2.up $$\chi_{9360}(271, \cdot)$$ n/a 560 4
9360.2.uq $$\chi_{9360}(631, \cdot)$$ None 0 4
9360.2.ut $$\chi_{9360}(2191, \cdot)$$ n/a 1344 4
9360.2.uv $$\chi_{9360}(1649, \cdot)$$ n/a 2000 4
9360.2.uw $$\chi_{9360}(89, \cdot)$$ None 0 4
9360.2.uz $$\chi_{9360}(449, \cdot)$$ n/a 672 4
9360.2.va $$\chi_{9360}(1289, \cdot)$$ None 0 4
9360.2.vd $$\chi_{9360}(1471, \cdot)$$ n/a 1344 4
9360.2.ve $$\chi_{9360}(1831, \cdot)$$ None 0 4
9360.2.vh $$\chi_{9360}(281, \cdot)$$ None 0 4
9360.2.vi $$\chi_{9360}(1841, \cdot)$$ n/a 1344 4
9360.2.vk $$\chi_{9360}(2959, \cdot)$$ n/a 2016 4
9360.2.vn $$\chi_{9360}(1399, \cdot)$$ None 0 4
9360.2.vp $$\chi_{9360}(2371, \cdot)$$ n/a 5376 4
9360.2.vq $$\chi_{9360}(2189, \cdot)$$ n/a 8032 4
9360.2.vs $$\chi_{9360}(461, \cdot)$$ n/a 5376 4
9360.2.vu $$\chi_{9360}(3581, \cdot)$$ n/a 1792 4
9360.2.vx $$\chi_{9360}(19, \cdot)$$ n/a 3344 4
9360.2.vz $$\chi_{9360}(1939, \cdot)$$ n/a 8032 4
9360.2.wb $$\chi_{9360}(833, \cdot)$$ n/a 1728 4
9360.2.wc $$\chi_{9360}(857, \cdot)$$ None 0 4
9360.2.we $$\chi_{9360}(1447, \cdot)$$ None 0 4
9360.2.wh $$\chi_{9360}(1063, \cdot)$$ None 0 4
9360.2.wi $$\chi_{9360}(2863, \cdot)$$ n/a 840 4
9360.2.wl $$\chi_{9360}(3103, \cdot)$$ n/a 2016 4
9360.2.wm $$\chi_{9360}(2993, \cdot)$$ n/a 2000 4
9360.2.wp $$\chi_{9360}(737, \cdot)$$ n/a 672 4
9360.2.wq $$\chi_{9360}(953, \cdot)$$ None 0 4
9360.2.wt $$\chi_{9360}(1193, \cdot)$$ None 0 4
9360.2.wv $$\chi_{9360}(103, \cdot)$$ None 0 4
9360.2.ww $$\chi_{9360}(1327, \cdot)$$ n/a 1728 4
9360.2.wz $$\chi_{9360}(1709, \cdot)$$ n/a 2688 4
9360.2.xb $$\chi_{9360}(509, \cdot)$$ n/a 8032 4
9360.2.xc $$\chi_{9360}(3811, \cdot)$$ n/a 5376 4
9360.2.xe $$\chi_{9360}(1891, \cdot)$$ n/a 2240 4
9360.2.xg $$\chi_{9360}(499, \cdot)$$ n/a 8032 4
9360.2.xj $$\chi_{9360}(941, \cdot)$$ n/a 5376 4
9360.2.xk $$\chi_{9360}(1579, \cdot)$$ n/a 8032 4
9360.2.xn $$\chi_{9360}(821, \cdot)$$ n/a 5376 4
9360.2.xp $$\chi_{9360}(1433, \cdot)$$ None 0 4
9360.2.xq $$\chi_{9360}(3137, \cdot)$$ n/a 2000 4
9360.2.xt $$\chi_{9360}(3247, \cdot)$$ n/a 2016 4
9360.2.xu $$\chi_{9360}(1303, \cdot)$$ None 0 4
9360.2.xx $$\chi_{9360}(3451, \cdot)$$ n/a 5376 4
9360.2.xy $$\chi_{9360}(149, \cdot)$$ n/a 8032 4
9360.2.ya $$\chi_{9360}(1813, \cdot)$$ n/a 8032 4
9360.2.yc $$\chi_{9360}(587, \cdot)$$ n/a 8032 4
9360.2.yf $$\chi_{9360}(733, \cdot)$$ n/a 8032 4
9360.2.yh $$\chi_{9360}(683, \cdot)$$ n/a 2688 4
9360.2.yj $$\chi_{9360}(37, \cdot)$$ n/a 3344 4
9360.2.yl $$\chi_{9360}(203, \cdot)$$ n/a 8032 4
9360.2.yn $$\chi_{9360}(1429, \cdot)$$ n/a 8032 4
9360.2.yo $$\chi_{9360}(1091, \cdot)$$ n/a 5376 4
9360.2.yq $$\chi_{9360}(1979, \cdot)$$ n/a 2688 4
9360.2.ys $$\chi_{9360}(2219, \cdot)$$ n/a 8032 4
9360.2.yv $$\chi_{9360}(2941, \cdot)$$ n/a 5376 4
9360.2.yx $$\chi_{9360}(1621, \cdot)$$ n/a 2240 4
9360.2.za $$\chi_{9360}(3287, \cdot)$$ None 0 4
9360.2.zb $$\chi_{9360}(3217, \cdot)$$ n/a 2000 4
9360.2.ze $$\chi_{9360}(1657, \cdot)$$ None 0 4
9360.2.zf $$\chi_{9360}(1727, \cdot)$$ n/a 672 4
9360.2.zi $$\chi_{9360}(47, \cdot)$$ n/a 2016 4
9360.2.zj $$\chi_{9360}(2137, \cdot)$$ None 0 4
9360.2.zk $$\chi_{9360}(1607, \cdot)$$ None 0 4
9360.2.zl $$\chi_{9360}(1633, \cdot)$$ n/a 2000 4
9360.2.zo $$\chi_{9360}(2017, \cdot)$$ n/a 832 4
9360.2.zp $$\chi_{9360}(1943, \cdot)$$ None 0 4
9360.2.zs $$\chi_{9360}(383, \cdot)$$ n/a 2016 4
9360.2.zt $$\chi_{9360}(457, \cdot)$$ None 0 4
9360.2.zw $$\chi_{9360}(829, \cdot)$$ n/a 3344 4
9360.2.zy $$\chi_{9360}(589, \cdot)$$ n/a 8032 4
9360.2.bab $$\chi_{9360}(3371, \cdot)$$ n/a 5376 4
9360.2.bad $$\chi_{9360}(251, \cdot)$$ n/a 1792 4
9360.2.baf $$\chi_{9360}(1379, \cdot)$$ n/a 6912 4
9360.2.bag $$\chi_{9360}(781, \cdot)$$ n/a 4608 4
9360.2.bai $$\chi_{9360}(4883, \cdot)$$ n/a 8032 4
9360.2.bak $$\chi_{9360}(397, \cdot)$$ n/a 3344 4
9360.2.bam $$\chi_{9360}(323, \cdot)$$ n/a 2688 4
9360.2.bao $$\chi_{9360}(2293, \cdot)$$ n/a 8032 4
9360.2.bar $$\chi_{9360}(1883, \cdot)$$ n/a 8032 4
9360.2.bat $$\chi_{9360}(1957, \cdot)$$ n/a 8032 4
9360.2.bav $$\chi_{9360}(1307, \cdot)$$ n/a 8032 4
9360.2.bax $$\chi_{9360}(2533, \cdot)$$ n/a 8032 4
9360.2.baz $$\chi_{9360}(4021, \cdot)$$ n/a 5376 4
9360.2.bba $$\chi_{9360}(3299, \cdot)$$ n/a 8032 4
9360.2.bbe $$\chi_{9360}(1033, \cdot)$$ None 0 4
9360.2.bbf $$\chi_{9360}(1103, \cdot)$$ n/a 2016 4
9360.2.bbg $$\chi_{9360}(3937, \cdot)$$ n/a 2000 4
9360.2.bbh $$\chi_{9360}(2567, \cdot)$$ None 0 4
9360.2.bbl $$\chi_{9360}(2291, \cdot)$$ n/a 5376 4
9360.2.bbm $$\chi_{9360}(2869, \cdot)$$ n/a 8032 4
9360.2.bbo $$\chi_{9360}(1237, \cdot)$$ n/a 8032 4
9360.2.bbq $$\chi_{9360}(1163, \cdot)$$ n/a 8032 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9360))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9360)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 60}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 48}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(720))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(936))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1040))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1170))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1560))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1872))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2340))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3120))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4680))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9360))$$$$^{\oplus 1}$$