# Properties

 Label 9555.2 Level 9555 Weight 2 Dimension 2054244 Nonzero newspaces 200 Sturm bound 12644352

## Defining parameters

 Level: $$N$$ = $$9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$200$$ Sturm bound: $$12644352$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9555))$$.

Total New Old
Modular forms 3184128 2067044 1117084
Cusp forms 3138049 2054244 1083805
Eisenstein series 46079 12800 33279

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9555))$$

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
9555.2.a $$\chi_{9555}(1, \cdot)$$ 9555.2.a.a 1 1
9555.2.a.b 1
9555.2.a.c 1
9555.2.a.d 1
9555.2.a.e 1
9555.2.a.f 1
9555.2.a.g 1
9555.2.a.h 1
9555.2.a.i 1
9555.2.a.j 1
9555.2.a.k 1
9555.2.a.l 1
9555.2.a.m 1
9555.2.a.n 1
9555.2.a.o 1
9555.2.a.p 1
9555.2.a.q 1
9555.2.a.r 1
9555.2.a.s 1
9555.2.a.t 1
9555.2.a.u 1
9555.2.a.v 1
9555.2.a.w 2
9555.2.a.x 2
9555.2.a.y 2
9555.2.a.z 2
9555.2.a.ba 2
9555.2.a.bb 2
9555.2.a.bc 2
9555.2.a.bd 2
9555.2.a.be 2
9555.2.a.bf 2
9555.2.a.bg 2
9555.2.a.bh 2
9555.2.a.bi 2
9555.2.a.bj 2
9555.2.a.bk 3
9555.2.a.bl 3
9555.2.a.bm 3
9555.2.a.bn 3
9555.2.a.bo 3
9555.2.a.bp 3
9555.2.a.bq 3
9555.2.a.br 4
9555.2.a.bs 4
9555.2.a.bt 4
9555.2.a.bu 5
9555.2.a.bv 5
9555.2.a.bw 5
9555.2.a.bx 5
9555.2.a.by 5
9555.2.a.bz 5
9555.2.a.ca 5
9555.2.a.cb 5
9555.2.a.cc 5
9555.2.a.cd 6
9555.2.a.ce 6
9555.2.a.cf 7
9555.2.a.cg 7
9555.2.a.ch 7
9555.2.a.ci 7
9555.2.a.cj 7
9555.2.a.ck 7
9555.2.a.cl 8
9555.2.a.cm 8
9555.2.a.cn 8
9555.2.a.co 8
9555.2.a.cp 9
9555.2.a.cq 9
9555.2.a.cr 10
9555.2.a.cs 10
9555.2.a.ct 10
9555.2.a.cu 10
9555.2.a.cv 14
9555.2.a.cw 14
9555.2.a.cx 14
9555.2.a.cy 14
9555.2.d $$\chi_{9555}(6761, \cdot)$$ n/a 640 1
9555.2.e $$\chi_{9555}(6616, \cdot)$$ n/a 384 1
9555.2.f $$\chi_{9555}(5734, \cdot)$$ n/a 492 1
9555.2.g $$\chi_{9555}(9554, \cdot)$$ n/a 1104 1
9555.2.j $$\chi_{9555}(2794, \cdot)$$ n/a 576 1
9555.2.k $$\chi_{9555}(2939, \cdot)$$ n/a 960 1
9555.2.p $$\chi_{9555}(3821, \cdot)$$ n/a 744 1
9555.2.q $$\chi_{9555}(2206, \cdot)$$ n/a 764 2
9555.2.r $$\chi_{9555}(3901, \cdot)$$ n/a 640 2
9555.2.s $$\chi_{9555}(6106, \cdot)$$ n/a 748 2
9555.2.t $$\chi_{9555}(6841, \cdot)$$ n/a 748 2
9555.2.v $$\chi_{9555}(148, \cdot)$$ n/a 1148 2
9555.2.w $$\chi_{9555}(1763, \cdot)$$ n/a 2208 2
9555.2.y $$\chi_{9555}(1273, \cdot)$$ n/a 1120 2
9555.2.z $$\chi_{9555}(638, \cdot)$$ n/a 1968 2
9555.2.bc $$\chi_{9555}(3284, \cdot)$$ n/a 2256 2
9555.2.bd $$\chi_{9555}(2449, \cdot)$$ n/a 1120 2
9555.2.bi $$\chi_{9555}(1126, \cdot)$$ n/a 752 2
9555.2.bj $$\chi_{9555}(2696, \cdot)$$ n/a 1528 2
9555.2.bm $$\chi_{9555}(2302, \cdot)$$ n/a 960 2
9555.2.bn $$\chi_{9555}(5342, \cdot)$$ n/a 2256 2
9555.2.bo $$\chi_{9555}(4558, \cdot)$$ n/a 1148 2
9555.2.br $$\chi_{9555}(6908, \cdot)$$ n/a 2208 2
9555.2.bs $$\chi_{9555}(3019, \cdot)$$ n/a 1120 2
9555.2.bt $$\chi_{9555}(1109, \cdot)$$ n/a 2208 2
9555.2.by $$\chi_{9555}(2726, \cdot)$$ n/a 1492 2
9555.2.bz $$\chi_{9555}(1096, \cdot)$$ n/a 748 2
9555.2.cc $$\chi_{9555}(1244, \cdot)$$ n/a 2208 2
9555.2.cd $$\chi_{9555}(4489, \cdot)$$ n/a 1120 2
9555.2.ce $$\chi_{9555}(881, \cdot)$$ n/a 1496 2
9555.2.cf $$\chi_{9555}(7136, \cdot)$$ n/a 1496 2
9555.2.co $$\chi_{9555}(6254, \cdot)$$ n/a 1920 2
9555.2.cp $$\chi_{9555}(6694, \cdot)$$ n/a 1120 2
9555.2.cq $$\chi_{9555}(5144, \cdot)$$ n/a 2208 2
9555.2.cr $$\chi_{9555}(589, \cdot)$$ n/a 1152 2
9555.2.cs $$\chi_{9555}(4196, \cdot)$$ n/a 1492 2
9555.2.cv $$\chi_{9555}(361, \cdot)$$ n/a 748 2
9555.2.cw $$\chi_{9555}(3461, \cdot)$$ n/a 1492 2
9555.2.dd $$\chi_{9555}(3314, \cdot)$$ n/a 2208 2
9555.2.de $$\chi_{9555}(79, \cdot)$$ n/a 960 2
9555.2.df $$\chi_{9555}(6614, \cdot)$$ n/a 2208 2
9555.2.dg $$\chi_{9555}(7939, \cdot)$$ n/a 1144 2
9555.2.dh $$\chi_{9555}(3676, \cdot)$$ n/a 764 2
9555.2.di $$\chi_{9555}(146, \cdot)$$ n/a 1496 2
9555.2.dj $$\chi_{9555}(961, \cdot)$$ n/a 744 2
9555.2.dk $$\chi_{9555}(521, \cdot)$$ n/a 1280 2
9555.2.dr $$\chi_{9555}(374, \cdot)$$ n/a 2208 2
9555.2.ds $$\chi_{9555}(2284, \cdot)$$ n/a 1120 2
9555.2.dv $$\chi_{9555}(4931, \cdot)$$ n/a 1492 2
9555.2.dw $$\chi_{9555}(3754, \cdot)$$ n/a 1120 2
9555.2.dx $$\chi_{9555}(1979, \cdot)$$ n/a 2208 2
9555.2.ea $$\chi_{9555}(1366, \cdot)$$ n/a 2688 6
9555.2.ec $$\chi_{9555}(227, \cdot)$$ n/a 4416 4
9555.2.ed $$\chi_{9555}(1402, \cdot)$$ n/a 2240 4
9555.2.eg $$\chi_{9555}(1243, \cdot)$$ n/a 2240 4
9555.2.ei $$\chi_{9555}(4037, \cdot)$$ n/a 4416 4
9555.2.ek $$\chi_{9555}(2498, \cdot)$$ n/a 4416 4
9555.2.el $$\chi_{9555}(3088, \cdot)$$ n/a 2296 4
9555.2.en $$\chi_{9555}(67, \cdot)$$ n/a 2240 4
9555.2.ep $$\chi_{9555}(668, \cdot)$$ n/a 4416 4
9555.2.er $$\chi_{9555}(1733, \cdot)$$ n/a 4416 4
9555.2.es $$\chi_{9555}(178, \cdot)$$ n/a 2240 4
9555.2.ex $$\chi_{9555}(2039, \cdot)$$ n/a 4416 4
9555.2.ey $$\chi_{9555}(3694, \cdot)$$ n/a 2240 4
9555.2.ez $$\chi_{9555}(1501, \cdot)$$ n/a 1496 4
9555.2.fa $$\chi_{9555}(851, \cdot)$$ n/a 2984 4
9555.2.ff $$\chi_{9555}(5567, \cdot)$$ n/a 4416 4
9555.2.fg $$\chi_{9555}(472, \cdot)$$ n/a 2240 4
9555.2.fh $$\chi_{9555}(263, \cdot)$$ n/a 4416 4
9555.2.fi $$\chi_{9555}(1648, \cdot)$$ n/a 2240 4
9555.2.fl $$\chi_{9555}(313, \cdot)$$ n/a 1920 4
9555.2.fm $$\chi_{9555}(2402, \cdot)$$ n/a 4512 4
9555.2.fn $$\chi_{9555}(4507, \cdot)$$ n/a 2240 4
9555.2.fo $$\chi_{9555}(1598, \cdot)$$ n/a 4416 4
9555.2.fv $$\chi_{9555}(4526, \cdot)$$ n/a 2984 4
9555.2.fw $$\chi_{9555}(1961, \cdot)$$ n/a 3064 4
9555.2.fx $$\chi_{9555}(3841, \cdot)$$ n/a 1496 4
9555.2.fy $$\chi_{9555}(1861, \cdot)$$ n/a 1488 4
9555.2.gd $$\chi_{9555}(1451, \cdot)$$ n/a 2992 4
9555.2.ge $$\chi_{9555}(31, \cdot)$$ n/a 1488 4
9555.2.gf $$\chi_{9555}(619, \cdot)$$ n/a 2240 4
9555.2.gg $$\chi_{9555}(2774, \cdot)$$ n/a 4416 4
9555.2.gl $$\chi_{9555}(1714, \cdot)$$ n/a 2240 4
9555.2.gm $$\chi_{9555}(19, \cdot)$$ n/a 2240 4
9555.2.gn $$\chi_{9555}(344, \cdot)$$ n/a 4512 4
9555.2.go $$\chi_{9555}(704, \cdot)$$ n/a 4416 4
9555.2.gv $$\chi_{9555}(2677, \cdot)$$ n/a 2240 4
9555.2.gw $$\chi_{9555}(932, \cdot)$$ n/a 4512 4
9555.2.gx $$\chi_{9555}(5977, \cdot)$$ n/a 2240 4
9555.2.gy $$\chi_{9555}(2627, \cdot)$$ n/a 3840 4
9555.2.hb $$\chi_{9555}(998, \cdot)$$ n/a 4416 4
9555.2.hc $$\chi_{9555}(607, \cdot)$$ n/a 2240 4
9555.2.hd $$\chi_{9555}(4048, \cdot)$$ n/a 2240 4
9555.2.hf $$\chi_{9555}(293, \cdot)$$ n/a 4416 4
9555.2.hh $$\chi_{9555}(2567, \cdot)$$ n/a 4416 4
9555.2.hk $$\chi_{9555}(1978, \cdot)$$ n/a 2240 4
9555.2.hm $$\chi_{9555}(1177, \cdot)$$ n/a 2296 4
9555.2.ho $$\chi_{9555}(1097, \cdot)$$ n/a 4416 4
9555.2.hp $$\chi_{9555}(362, \cdot)$$ n/a 4416 4
9555.2.hs $$\chi_{9555}(3313, \cdot)$$ n/a 2240 4
9555.2.ht $$\chi_{9555}(1091, \cdot)$$ n/a 6288 6
9555.2.hy $$\chi_{9555}(209, \cdot)$$ n/a 8064 6
9555.2.hz $$\chi_{9555}(64, \cdot)$$ n/a 4704 6
9555.2.ic $$\chi_{9555}(1364, \cdot)$$ n/a 9360 6
9555.2.id $$\chi_{9555}(274, \cdot)$$ n/a 4032 6
9555.2.ie $$\chi_{9555}(1156, \cdot)$$ n/a 3120 6
9555.2.if $$\chi_{9555}(1301, \cdot)$$ n/a 5376 6
9555.2.ii $$\chi_{9555}(16, \cdot)$$ n/a 6264 12
9555.2.ij $$\chi_{9555}(646, \cdot)$$ n/a 6264 12
9555.2.ik $$\chi_{9555}(781, \cdot)$$ n/a 5376 12
9555.2.il $$\chi_{9555}(211, \cdot)$$ n/a 6288 12
9555.2.im $$\chi_{9555}(83, \cdot)$$ n/a 18720 12
9555.2.ip $$\chi_{9555}(463, \cdot)$$ n/a 9408 12
9555.2.is $$\chi_{9555}(428, \cdot)$$ n/a 18720 12
9555.2.it $$\chi_{9555}(118, \cdot)$$ n/a 8064 12
9555.2.iu $$\chi_{9555}(281, \cdot)$$ n/a 12576 12
9555.2.iv $$\chi_{9555}(811, \cdot)$$ n/a 6240 12
9555.2.ja $$\chi_{9555}(34, \cdot)$$ n/a 9408 12
9555.2.jb $$\chi_{9555}(239, \cdot)$$ n/a 18720 12
9555.2.jc $$\chi_{9555}(92, \cdot)$$ n/a 16128 12
9555.2.jd $$\chi_{9555}(727, \cdot)$$ n/a 9408 12
9555.2.jh $$\chi_{9555}(398, \cdot)$$ n/a 18720 12
9555.2.ji $$\chi_{9555}(1282, \cdot)$$ n/a 9408 12
9555.2.jm $$\chi_{9555}(269, \cdot)$$ n/a 18720 12
9555.2.jn $$\chi_{9555}(4, \cdot)$$ n/a 9408 12
9555.2.jo $$\chi_{9555}(836, \cdot)$$ n/a 12552 12
9555.2.jr $$\chi_{9555}(919, \cdot)$$ n/a 9408 12
9555.2.js $$\chi_{9555}(719, \cdot)$$ n/a 18720 12
9555.2.jz $$\chi_{9555}(131, \cdot)$$ n/a 10752 12
9555.2.ka $$\chi_{9555}(571, \cdot)$$ n/a 6288 12
9555.2.kb $$\chi_{9555}(776, \cdot)$$ n/a 12528 12
9555.2.kc $$\chi_{9555}(316, \cdot)$$ n/a 6288 12
9555.2.kd $$\chi_{9555}(484, \cdot)$$ n/a 9408 12
9555.2.ke $$\chi_{9555}(524, \cdot)$$ n/a 18720 12
9555.2.kf $$\chi_{9555}(1054, \cdot)$$ n/a 8064 12
9555.2.kg $$\chi_{9555}(194, \cdot)$$ n/a 18720 12
9555.2.kn $$\chi_{9555}(731, \cdot)$$ n/a 12552 12
9555.2.ko $$\chi_{9555}(121, \cdot)$$ n/a 6264 12
9555.2.kr $$\chi_{9555}(101, \cdot)$$ n/a 12552 12
9555.2.ks $$\chi_{9555}(1219, \cdot)$$ n/a 9408 12
9555.2.kt $$\chi_{9555}(419, \cdot)$$ n/a 18720 12
9555.2.ku $$\chi_{9555}(844, \cdot)$$ n/a 9408 12
9555.2.kv $$\chi_{9555}(404, \cdot)$$ n/a 16128 12
9555.2.le $$\chi_{9555}(311, \cdot)$$ n/a 12528 12
9555.2.lf $$\chi_{9555}(251, \cdot)$$ n/a 12528 12
9555.2.lg $$\chi_{9555}(394, \cdot)$$ n/a 9408 12
9555.2.lh $$\chi_{9555}(1004, \cdot)$$ n/a 18720 12
9555.2.lk $$\chi_{9555}(751, \cdot)$$ n/a 6264 12
9555.2.ll $$\chi_{9555}(341, \cdot)$$ n/a 12552 12
9555.2.lq $$\chi_{9555}(1349, \cdot)$$ n/a 18720 12
9555.2.lr $$\chi_{9555}(289, \cdot)$$ n/a 9408 12
9555.2.ls $$\chi_{9555}(457, \cdot)$$ n/a 18816 24
9555.2.lv $$\chi_{9555}(332, \cdot)$$ n/a 37440 24
9555.2.lw $$\chi_{9555}(122, \cdot)$$ n/a 37440 24
9555.2.ly $$\chi_{9555}(232, \cdot)$$ n/a 18816 24
9555.2.ma $$\chi_{9555}(58, \cdot)$$ n/a 18816 24
9555.2.md $$\chi_{9555}(488, \cdot)$$ n/a 37440 24
9555.2.mf $$\chi_{9555}(713, \cdot)$$ n/a 37440 24
9555.2.mh $$\chi_{9555}(697, \cdot)$$ n/a 18816 24
9555.2.mk $$\chi_{9555}(367, \cdot)$$ n/a 18816 24
9555.2.ml $$\chi_{9555}(212, \cdot)$$ n/a 37440 24
9555.2.mq $$\chi_{9555}(53, \cdot)$$ n/a 32256 24
9555.2.mr $$\chi_{9555}(433, \cdot)$$ n/a 18816 24
9555.2.ms $$\chi_{9555}(113, \cdot)$$ n/a 37440 24
9555.2.mt $$\chi_{9555}(103, \cdot)$$ n/a 18816 24
9555.2.mw $$\chi_{9555}(149, \cdot)$$ n/a 37440 24
9555.2.mx $$\chi_{9555}(449, \cdot)$$ n/a 37440 24
9555.2.my $$\chi_{9555}(124, \cdot)$$ n/a 18816 24
9555.2.mz $$\chi_{9555}(349, \cdot)$$ n/a 18816 24
9555.2.ne $$\chi_{9555}(44, \cdot)$$ n/a 37440 24
9555.2.nf $$\chi_{9555}(229, \cdot)$$ n/a 18816 24
9555.2.ng $$\chi_{9555}(346, \cdot)$$ n/a 12576 24
9555.2.nh $$\chi_{9555}(86, \cdot)$$ n/a 25056 24
9555.2.nm $$\chi_{9555}(76, \cdot)$$ n/a 12576 24
9555.2.nn $$\chi_{9555}(661, \cdot)$$ n/a 12528 24
9555.2.no $$\chi_{9555}(71, \cdot)$$ n/a 25056 24
9555.2.np $$\chi_{9555}(11, \cdot)$$ n/a 25104 24
9555.2.ns $$\chi_{9555}(233, \cdot)$$ n/a 37440 24
9555.2.nt $$\chi_{9555}(328, \cdot)$$ n/a 18816 24
9555.2.nu $$\chi_{9555}(218, \cdot)$$ n/a 37440 24
9555.2.nv $$\chi_{9555}(157, \cdot)$$ n/a 16128 24
9555.2.oa $$\chi_{9555}(82, \cdot)$$ n/a 18816 24
9555.2.ob $$\chi_{9555}(737, \cdot)$$ n/a 37440 24
9555.2.og $$\chi_{9555}(712, \cdot)$$ n/a 18816 24
9555.2.oh $$\chi_{9555}(107, \cdot)$$ n/a 37440 24
9555.2.ok $$\chi_{9555}(401, \cdot)$$ n/a 25104 24
9555.2.ol $$\chi_{9555}(136, \cdot)$$ n/a 12528 24
9555.2.om $$\chi_{9555}(409, \cdot)$$ n/a 18816 24
9555.2.on $$\chi_{9555}(674, \cdot)$$ n/a 37440 24
9555.2.oq $$\chi_{9555}(523, \cdot)$$ n/a 18816 24
9555.2.or $$\chi_{9555}(23, \cdot)$$ n/a 37440 24
9555.2.ov $$\chi_{9555}(47, \cdot)$$ n/a 37440 24
9555.2.ox $$\chi_{9555}(163, \cdot)$$ n/a 18816 24
9555.2.oz $$\chi_{9555}(358, \cdot)$$ n/a 18816 24
9555.2.pa $$\chi_{9555}(167, \cdot)$$ n/a 37440 24
9555.2.pc $$\chi_{9555}(353, \cdot)$$ n/a 37440 24
9555.2.pe $$\chi_{9555}(268, \cdot)$$ n/a 18816 24
9555.2.ph $$\chi_{9555}(37, \cdot)$$ n/a 18816 24
9555.2.pi $$\chi_{9555}(782, \cdot)$$ n/a 37440 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9555))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9555)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(455))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1365))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1911))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3185))$$$$^{\oplus 2}$$