# Properties

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

## 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

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