Properties

Label 5544.2
Level 5544
Weight 2
Dimension 346450
Nonzero newspaces 120
Sturm bound 3317760

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Defining parameters

Level: \( N \) = \( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(3317760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5544))\).

Total New Old
Modular forms 840960 349690 491270
Cusp forms 817921 346450 471471
Eisenstein series 23039 3240 19799

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5544))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5544.2.a \(\chi_{5544}(1, \cdot)\) 5544.2.a.a 1 1
5544.2.a.b 1
5544.2.a.c 1
5544.2.a.d 1
5544.2.a.e 1
5544.2.a.f 1
5544.2.a.g 1
5544.2.a.h 1
5544.2.a.i 1
5544.2.a.j 1
5544.2.a.k 1
5544.2.a.l 1
5544.2.a.m 1
5544.2.a.n 1
5544.2.a.o 1
5544.2.a.p 1
5544.2.a.q 1
5544.2.a.r 1
5544.2.a.s 1
5544.2.a.t 1
5544.2.a.u 1
5544.2.a.v 1
5544.2.a.w 1
5544.2.a.x 1
5544.2.a.y 1
5544.2.a.z 2
5544.2.a.ba 2
5544.2.a.bb 2
5544.2.a.bc 2
5544.2.a.bd 2
5544.2.a.be 2
5544.2.a.bf 2
5544.2.a.bg 2
5544.2.a.bh 2
5544.2.a.bi 2
5544.2.a.bj 3
5544.2.a.bk 3
5544.2.a.bl 3
5544.2.a.bm 4
5544.2.a.bn 4
5544.2.a.bo 4
5544.2.a.bp 4
5544.2.a.bq 4
5544.2.d \(\chi_{5544}(2575, \cdot)\) None 0 1
5544.2.e \(\chi_{5544}(2771, \cdot)\) n/a 384 1
5544.2.f \(\chi_{5544}(2969, \cdot)\) 5544.2.f.a 36 1
5544.2.f.b 36
5544.2.g \(\chi_{5544}(2773, \cdot)\) n/a 300 1
5544.2.j \(\chi_{5544}(1891, \cdot)\) n/a 360 1
5544.2.k \(\chi_{5544}(1079, \cdot)\) None 0 1
5544.2.p \(\chi_{5544}(3653, \cdot)\) n/a 320 1
5544.2.q \(\chi_{5544}(4465, \cdot)\) n/a 120 1
5544.2.t \(\chi_{5544}(4663, \cdot)\) None 0 1
5544.2.u \(\chi_{5544}(3851, \cdot)\) n/a 240 1
5544.2.v \(\chi_{5544}(881, \cdot)\) 5544.2.v.a 40 1
5544.2.v.b 40
5544.2.w \(\chi_{5544}(1693, \cdot)\) n/a 476 1
5544.2.z \(\chi_{5544}(5347, \cdot)\) n/a 400 1
5544.2.ba \(\chi_{5544}(5543, \cdot)\) None 0 1
5544.2.bf \(\chi_{5544}(197, \cdot)\) n/a 288 1
5544.2.bg \(\chi_{5544}(529, \cdot)\) n/a 480 2
5544.2.bh \(\chi_{5544}(1849, \cdot)\) n/a 360 2
5544.2.bi \(\chi_{5544}(793, \cdot)\) n/a 200 2
5544.2.bj \(\chi_{5544}(4225, \cdot)\) n/a 480 2
5544.2.bk \(\chi_{5544}(2017, \cdot)\) n/a 360 4
5544.2.bl \(\chi_{5544}(4709, \cdot)\) n/a 1920 2
5544.2.bm \(\chi_{5544}(1825, \cdot)\) n/a 576 2
5544.2.br \(\chi_{5544}(571, \cdot)\) n/a 2288 2
5544.2.bs \(\chi_{5544}(1607, \cdot)\) None 0 2
5544.2.bv \(\chi_{5544}(65, \cdot)\) n/a 576 2
5544.2.bw \(\chi_{5544}(1453, \cdot)\) n/a 1920 2
5544.2.bx \(\chi_{5544}(2047, \cdot)\) None 0 2
5544.2.by \(\chi_{5544}(3827, \cdot)\) n/a 2288 2
5544.2.cd \(\chi_{5544}(901, \cdot)\) n/a 952 2
5544.2.ce \(\chi_{5544}(89, \cdot)\) n/a 160 2
5544.2.cf \(\chi_{5544}(683, \cdot)\) n/a 640 2
5544.2.cg \(\chi_{5544}(1495, \cdot)\) None 0 2
5544.2.cj \(\chi_{5544}(1847, \cdot)\) None 0 2
5544.2.ck \(\chi_{5544}(1651, \cdot)\) n/a 1920 2
5544.2.cn \(\chi_{5544}(4421, \cdot)\) n/a 2288 2
5544.2.cs \(\chi_{5544}(2903, \cdot)\) None 0 2
5544.2.ct \(\chi_{5544}(859, \cdot)\) n/a 1920 2
5544.2.cw \(\chi_{5544}(2045, \cdot)\) n/a 1728 2
5544.2.cz \(\chi_{5544}(155, \cdot)\) n/a 1440 2
5544.2.da \(\chi_{5544}(967, \cdot)\) None 0 2
5544.2.dd \(\chi_{5544}(2749, \cdot)\) n/a 2288 2
5544.2.de \(\chi_{5544}(353, \cdot)\) n/a 480 2
5544.2.df \(\chi_{5544}(2531, \cdot)\) n/a 1920 2
5544.2.dg \(\chi_{5544}(1759, \cdot)\) None 0 2
5544.2.dj \(\chi_{5544}(3541, \cdot)\) n/a 2288 2
5544.2.dk \(\chi_{5544}(2729, \cdot)\) n/a 480 2
5544.2.dn \(\chi_{5544}(989, \cdot)\) n/a 768 2
5544.2.ds \(\chi_{5544}(3167, \cdot)\) None 0 2
5544.2.dt \(\chi_{5544}(2971, \cdot)\) n/a 800 2
5544.2.dw \(\chi_{5544}(3565, \cdot)\) n/a 800 2
5544.2.dx \(\chi_{5544}(3761, \cdot)\) n/a 192 2
5544.2.dy \(\chi_{5544}(395, \cdot)\) n/a 768 2
5544.2.dz \(\chi_{5544}(199, \cdot)\) None 0 2
5544.2.ec \(\chi_{5544}(2927, \cdot)\) None 0 2
5544.2.ed \(\chi_{5544}(43, \cdot)\) n/a 1728 2
5544.2.eg \(\chi_{5544}(241, \cdot)\) n/a 576 2
5544.2.eh \(\chi_{5544}(1013, \cdot)\) n/a 1920 2
5544.2.em \(\chi_{5544}(23, \cdot)\) None 0 2
5544.2.en \(\chi_{5544}(2419, \cdot)\) n/a 2288 2
5544.2.eq \(\chi_{5544}(769, \cdot)\) n/a 576 2
5544.2.er \(\chi_{5544}(1805, \cdot)\) n/a 1920 2
5544.2.eu \(\chi_{5544}(923, \cdot)\) n/a 2288 2
5544.2.ev \(\chi_{5544}(727, \cdot)\) None 0 2
5544.2.ey \(\chi_{5544}(3301, \cdot)\) n/a 1920 2
5544.2.ez \(\chi_{5544}(1649, \cdot)\) n/a 576 2
5544.2.fa \(\chi_{5544}(131, \cdot)\) n/a 2288 2
5544.2.fb \(\chi_{5544}(3631, \cdot)\) None 0 2
5544.2.fe \(\chi_{5544}(925, \cdot)\) n/a 1440 2
5544.2.ff \(\chi_{5544}(1121, \cdot)\) n/a 432 2
5544.2.fi \(\chi_{5544}(2089, \cdot)\) n/a 240 2
5544.2.fj \(\chi_{5544}(1277, \cdot)\) n/a 640 2
5544.2.fo \(\chi_{5544}(1871, \cdot)\) None 0 2
5544.2.fp \(\chi_{5544}(2683, \cdot)\) n/a 952 2
5544.2.fq \(\chi_{5544}(725, \cdot)\) n/a 2288 2
5544.2.fv \(\chi_{5544}(2707, \cdot)\) n/a 1920 2
5544.2.fw \(\chi_{5544}(1055, \cdot)\) None 0 2
5544.2.fz \(\chi_{5544}(1937, \cdot)\) n/a 480 2
5544.2.ga \(\chi_{5544}(1165, \cdot)\) n/a 2288 2
5544.2.gb \(\chi_{5544}(3343, \cdot)\) None 0 2
5544.2.gc \(\chi_{5544}(947, \cdot)\) n/a 1920 2
5544.2.gf \(\chi_{5544}(701, \cdot)\) n/a 1152 4
5544.2.gk \(\chi_{5544}(1819, \cdot)\) n/a 1904 4
5544.2.gl \(\chi_{5544}(503, \cdot)\) None 0 4
5544.2.go \(\chi_{5544}(377, \cdot)\) n/a 384 4
5544.2.gp \(\chi_{5544}(2197, \cdot)\) n/a 1904 4
5544.2.gq \(\chi_{5544}(127, \cdot)\) None 0 4
5544.2.gr \(\chi_{5544}(323, \cdot)\) n/a 1152 4
5544.2.gu \(\chi_{5544}(125, \cdot)\) n/a 1536 4
5544.2.gv \(\chi_{5544}(937, \cdot)\) n/a 480 4
5544.2.ha \(\chi_{5544}(2395, \cdot)\) n/a 1440 4
5544.2.hb \(\chi_{5544}(71, \cdot)\) None 0 4
5544.2.he \(\chi_{5544}(953, \cdot)\) n/a 288 4
5544.2.hf \(\chi_{5544}(757, \cdot)\) n/a 1440 4
5544.2.hg \(\chi_{5544}(559, \cdot)\) None 0 4
5544.2.hh \(\chi_{5544}(755, \cdot)\) n/a 1536 4
5544.2.hk \(\chi_{5544}(697, \cdot)\) n/a 2304 8
5544.2.hl \(\chi_{5544}(289, \cdot)\) n/a 960 8
5544.2.hm \(\chi_{5544}(169, \cdot)\) n/a 1728 8
5544.2.hn \(\chi_{5544}(25, \cdot)\) n/a 2304 8
5544.2.hq \(\chi_{5544}(79, \cdot)\) None 0 8
5544.2.hr \(\chi_{5544}(443, \cdot)\) n/a 9152 8
5544.2.hs \(\chi_{5544}(185, \cdot)\) n/a 2304 8
5544.2.ht \(\chi_{5544}(61, \cdot)\) n/a 9152 8
5544.2.hw \(\chi_{5544}(691, \cdot)\) n/a 9152 8
5544.2.hx \(\chi_{5544}(1559, \cdot)\) None 0 8
5544.2.ic \(\chi_{5544}(821, \cdot)\) n/a 9152 8
5544.2.id \(\chi_{5544}(863, \cdot)\) None 0 8
5544.2.ie \(\chi_{5544}(667, \cdot)\) n/a 3808 8
5544.2.ij \(\chi_{5544}(73, \cdot)\) n/a 960 8
5544.2.ik \(\chi_{5544}(269, \cdot)\) n/a 3072 8
5544.2.in \(\chi_{5544}(421, \cdot)\) n/a 6912 8
5544.2.io \(\chi_{5544}(281, \cdot)\) n/a 1728 8
5544.2.ir \(\chi_{5544}(227, \cdot)\) n/a 9152 8
5544.2.is \(\chi_{5544}(103, \cdot)\) None 0 8
5544.2.it \(\chi_{5544}(1285, \cdot)\) n/a 9152 8
5544.2.iu \(\chi_{5544}(2153, \cdot)\) n/a 2304 8
5544.2.ix \(\chi_{5544}(83, \cdot)\) n/a 9152 8
5544.2.iy \(\chi_{5544}(223, \cdot)\) None 0 8
5544.2.jb \(\chi_{5544}(601, \cdot)\) n/a 2304 8
5544.2.jc \(\chi_{5544}(797, \cdot)\) n/a 9152 8
5544.2.jf \(\chi_{5544}(1775, \cdot)\) None 0 8
5544.2.jg \(\chi_{5544}(403, \cdot)\) n/a 9152 8
5544.2.jl \(\chi_{5544}(481, \cdot)\) n/a 2304 8
5544.2.jm \(\chi_{5544}(5, \cdot)\) n/a 9152 8
5544.2.jp \(\chi_{5544}(911, \cdot)\) None 0 8
5544.2.jq \(\chi_{5544}(211, \cdot)\) n/a 6912 8
5544.2.jt \(\chi_{5544}(899, \cdot)\) n/a 3072 8
5544.2.ju \(\chi_{5544}(775, \cdot)\) None 0 8
5544.2.jv \(\chi_{5544}(37, \cdot)\) n/a 3808 8
5544.2.jw \(\chi_{5544}(233, \cdot)\) n/a 768 8
5544.2.jz \(\chi_{5544}(215, \cdot)\) None 0 8
5544.2.ka \(\chi_{5544}(955, \cdot)\) n/a 3808 8
5544.2.kf \(\chi_{5544}(557, \cdot)\) n/a 3072 8
5544.2.ki \(\chi_{5544}(13, \cdot)\) n/a 9152 8
5544.2.kj \(\chi_{5544}(713, \cdot)\) n/a 2304 8
5544.2.km \(\chi_{5544}(515, \cdot)\) n/a 9152 8
5544.2.kn \(\chi_{5544}(151, \cdot)\) None 0 8
5544.2.ko \(\chi_{5544}(733, \cdot)\) n/a 9152 8
5544.2.kp \(\chi_{5544}(257, \cdot)\) n/a 2304 8
5544.2.ks \(\chi_{5544}(995, \cdot)\) n/a 6912 8
5544.2.kt \(\chi_{5544}(799, \cdot)\) None 0 8
5544.2.kw \(\chi_{5544}(29, \cdot)\) n/a 6912 8
5544.2.kz \(\chi_{5544}(479, \cdot)\) None 0 8
5544.2.la \(\chi_{5544}(115, \cdot)\) n/a 9152 8
5544.2.lf \(\chi_{5544}(149, \cdot)\) n/a 9152 8
5544.2.li \(\chi_{5544}(167, \cdot)\) None 0 8
5544.2.lj \(\chi_{5544}(643, \cdot)\) n/a 9152 8
5544.2.lm \(\chi_{5544}(179, \cdot)\) n/a 3072 8
5544.2.ln \(\chi_{5544}(415, \cdot)\) None 0 8
5544.2.lo \(\chi_{5544}(325, \cdot)\) n/a 3808 8
5544.2.lp \(\chi_{5544}(521, \cdot)\) n/a 768 8
5544.2.lu \(\chi_{5544}(31, \cdot)\) None 0 8
5544.2.lv \(\chi_{5544}(299, \cdot)\) n/a 9152 8
5544.2.lw \(\chi_{5544}(569, \cdot)\) n/a 2304 8
5544.2.lx \(\chi_{5544}(445, \cdot)\) n/a 9152 8
5544.2.ma \(\chi_{5544}(1075, \cdot)\) n/a 9152 8
5544.2.mb \(\chi_{5544}(191, \cdot)\) None 0 8
5544.2.mg \(\chi_{5544}(1181, \cdot)\) n/a 9152 8
5544.2.mh \(\chi_{5544}(409, \cdot)\) n/a 2304 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5544))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5544)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1386))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2772))\)\(^{\oplus 2}\)