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Properties

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

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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

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