# Properties

 Label 3744.2 Level 3744 Weight 2 Dimension 169326 Nonzero newspaces 100 Sturm bound 1548288 Trace bound 77

## Defining parameters

 Level: $$N$$ = $$3744 = 2^{5} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$1548288$$ Trace bound: $$77$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3744))$$.

Total New Old
Modular forms 393216 171306 221910
Cusp forms 380929 169326 211603
Eisenstein series 12287 1980 10307

## Trace form

 $$169326 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 116 q^{5} - 160 q^{6} - 88 q^{7} - 120 q^{8} - 240 q^{9} + O(q^{10})$$ $$169326 q - 120 q^{2} - 120 q^{3} - 120 q^{4} - 116 q^{5} - 160 q^{6} - 88 q^{7} - 120 q^{8} - 240 q^{9} - 376 q^{10} - 96 q^{11} - 160 q^{12} - 138 q^{13} - 296 q^{14} - 132 q^{15} - 160 q^{16} - 100 q^{17} - 160 q^{18} - 300 q^{19} - 152 q^{20} - 192 q^{21} - 144 q^{22} - 144 q^{23} - 160 q^{24} - 246 q^{25} - 112 q^{26} - 288 q^{27} - 320 q^{28} - 164 q^{29} - 128 q^{30} - 160 q^{31} - 80 q^{32} - 392 q^{33} - 96 q^{34} - 132 q^{35} - 112 q^{36} - 292 q^{37} + 88 q^{38} - 126 q^{39} - 32 q^{40} - 76 q^{41} - 40 q^{43} + 152 q^{44} - 64 q^{45} - 168 q^{46} + 24 q^{47} + 48 q^{48} + 78 q^{49} + 216 q^{50} - 56 q^{51} - 12 q^{52} - 132 q^{53} + 16 q^{54} - 180 q^{55} + 176 q^{56} - 144 q^{57} + 144 q^{58} + 40 q^{59} - 48 q^{60} - 132 q^{61} - 48 q^{62} - 12 q^{63} - 288 q^{64} - 248 q^{65} - 352 q^{66} - 40 q^{67} - 32 q^{68} - 32 q^{69} - 96 q^{70} + 28 q^{71} - 160 q^{72} - 628 q^{73} - 152 q^{74} + 104 q^{75} - 120 q^{76} - 88 q^{77} - 200 q^{78} - 76 q^{79} - 368 q^{80} + 80 q^{81} - 680 q^{82} + 264 q^{83} - 384 q^{84} - 208 q^{85} - 496 q^{86} + 196 q^{87} - 448 q^{88} - 156 q^{89} - 448 q^{90} - 228 q^{91} - 800 q^{92} - 160 q^{93} - 464 q^{94} + 268 q^{95} - 432 q^{96} - 308 q^{97} - 560 q^{98} + 164 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3744))$$

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
3744.2.a $$\chi_{3744}(1, \cdot)$$ 3744.2.a.a 1 1
3744.2.a.b 1
3744.2.a.c 1
3744.2.a.d 1
3744.2.a.e 1
3744.2.a.f 1
3744.2.a.g 1
3744.2.a.h 1
3744.2.a.i 1
3744.2.a.j 1
3744.2.a.k 1
3744.2.a.l 1
3744.2.a.m 1
3744.2.a.n 1
3744.2.a.o 1
3744.2.a.p 1
3744.2.a.q 2
3744.2.a.r 2
3744.2.a.s 2
3744.2.a.t 2
3744.2.a.u 2
3744.2.a.v 2
3744.2.a.w 2
3744.2.a.x 2
3744.2.a.y 2
3744.2.a.z 3
3744.2.a.ba 3
3744.2.a.bb 4
3744.2.a.bc 4
3744.2.a.bd 4
3744.2.a.be 4
3744.2.a.bf 4
3744.2.c $$\chi_{3744}(3457, \cdot)$$ 3744.2.c.a 2 1
3744.2.c.b 2
3744.2.c.c 2
3744.2.c.d 2
3744.2.c.e 2
3744.2.c.f 4
3744.2.c.g 4
3744.2.c.h 4
3744.2.c.i 4
3744.2.c.j 4
3744.2.c.k 4
3744.2.c.l 6
3744.2.c.m 6
3744.2.c.n 8
3744.2.c.o 8
3744.2.c.p 8
3744.2.d $$\chi_{3744}(287, \cdot)$$ 3744.2.d.a 4 1
3744.2.d.b 4
3744.2.d.c 8
3744.2.d.d 8
3744.2.d.e 12
3744.2.d.f 12
3744.2.g $$\chi_{3744}(1873, \cdot)$$ 3744.2.g.a 2 1
3744.2.g.b 4
3744.2.g.c 6
3744.2.g.d 8
3744.2.g.e 16
3744.2.g.f 24
3744.2.h $$\chi_{3744}(1871, \cdot)$$ 3744.2.h.a 56 1
3744.2.j $$\chi_{3744}(2159, \cdot)$$ 3744.2.j.a 48 1
3744.2.m $$\chi_{3744}(1585, \cdot)$$ 3744.2.m.a 2 1
3744.2.m.b 2
3744.2.m.c 2
3744.2.m.d 2
3744.2.m.e 4
3744.2.m.f 8
3744.2.m.g 8
3744.2.m.h 16
3744.2.m.i 24
3744.2.n $$\chi_{3744}(3743, \cdot)$$ 3744.2.n.a 28 1
3744.2.n.b 28
3744.2.q $$\chi_{3744}(1249, \cdot)$$ n/a 288 2
3744.2.r $$\chi_{3744}(1537, \cdot)$$ n/a 336 2
3744.2.s $$\chi_{3744}(2401, \cdot)$$ n/a 336 2
3744.2.t $$\chi_{3744}(289, \cdot)$$ n/a 140 2
3744.2.u $$\chi_{3744}(343, \cdot)$$ None 0 2
3744.2.x $$\chi_{3744}(2969, \cdot)$$ None 0 2
3744.2.y $$\chi_{3744}(935, \cdot)$$ None 0 2
3744.2.ba $$\chi_{3744}(937, \cdot)$$ None 0 2
3744.2.be $$\chi_{3744}(1711, \cdot)$$ n/a 136 2
3744.2.bf $$\chi_{3744}(1279, \cdot)$$ n/a 140 2
3744.2.bi $$\chi_{3744}(161, \cdot)$$ n/a 112 2
3744.2.bj $$\chi_{3744}(593, \cdot)$$ n/a 112 2
3744.2.bk $$\chi_{3744}(1223, \cdot)$$ None 0 2
3744.2.bm $$\chi_{3744}(649, \cdot)$$ None 0 2
3744.2.bp $$\chi_{3744}(1097, \cdot)$$ None 0 2
3744.2.bq $$\chi_{3744}(2215, \cdot)$$ None 0 2
3744.2.bt $$\chi_{3744}(719, \cdot)$$ n/a 112 2
3744.2.bu $$\chi_{3744}(2161, \cdot)$$ n/a 136 2
3744.2.bx $$\chi_{3744}(575, \cdot)$$ n/a 112 2
3744.2.by $$\chi_{3744}(2305, \cdot)$$ n/a 140 2
3744.2.ca $$\chi_{3744}(49, \cdot)$$ n/a 328 2
3744.2.cd $$\chi_{3744}(2063, \cdot)$$ n/a 328 2
3744.2.cf $$\chi_{3744}(95, \cdot)$$ n/a 336 2
3744.2.ch $$\chi_{3744}(1247, \cdot)$$ n/a 336 2
3744.2.cl $$\chi_{3744}(815, \cdot)$$ n/a 328 2
3744.2.cn $$\chi_{3744}(337, \cdot)$$ n/a 328 2
3744.2.co $$\chi_{3744}(911, \cdot)$$ n/a 288 2
3744.2.cq $$\chi_{3744}(2545, \cdot)$$ n/a 328 2
3744.2.cu $$\chi_{3744}(959, \cdot)$$ n/a 336 2
3744.2.cw $$\chi_{3744}(191, \cdot)$$ n/a 336 2
3744.2.cx $$\chi_{3744}(1921, \cdot)$$ n/a 336 2
3744.2.cz $$\chi_{3744}(1777, \cdot)$$ n/a 328 2
3744.2.db $$\chi_{3744}(623, \cdot)$$ n/a 328 2
3744.2.de $$\chi_{3744}(625, \cdot)$$ n/a 288 2
3744.2.dg $$\chi_{3744}(335, \cdot)$$ n/a 328 2
3744.2.dh $$\chi_{3744}(673, \cdot)$$ n/a 336 2
3744.2.dj $$\chi_{3744}(1535, \cdot)$$ n/a 288 2
3744.2.dm $$\chi_{3744}(961, \cdot)$$ n/a 336 2
3744.2.do $$\chi_{3744}(2687, \cdot)$$ n/a 336 2
3744.2.dq $$\chi_{3744}(2831, \cdot)$$ n/a 328 2
3744.2.dr $$\chi_{3744}(529, \cdot)$$ n/a 328 2
3744.2.dv $$\chi_{3744}(2591, \cdot)$$ n/a 112 2
3744.2.dw $$\chi_{3744}(433, \cdot)$$ n/a 136 2
3744.2.dz $$\chi_{3744}(2447, \cdot)$$ n/a 112 2
3744.2.eb $$\chi_{3744}(125, \cdot)$$ n/a 896 4
3744.2.ed $$\chi_{3744}(1243, \cdot)$$ n/a 1112 4
3744.2.ee $$\chi_{3744}(181, \cdot)$$ n/a 1112 4
3744.2.eg $$\chi_{3744}(469, \cdot)$$ n/a 960 4
3744.2.ej $$\chi_{3744}(755, \cdot)$$ n/a 768 4
3744.2.el $$\chi_{3744}(467, \cdot)$$ n/a 896 4
3744.2.em $$\chi_{3744}(1061, \cdot)$$ n/a 896 4
3744.2.eo $$\chi_{3744}(307, \cdot)$$ n/a 1112 4
3744.2.eq $$\chi_{3744}(665, \cdot)$$ None 0 4
3744.2.et $$\chi_{3744}(1783, \cdot)$$ None 0 4
3744.2.eu $$\chi_{3744}(617, \cdot)$$ None 0 4
3744.2.ew $$\chi_{3744}(151, \cdot)$$ None 0 4
3744.2.ey $$\chi_{3744}(1735, \cdot)$$ None 0 4
3744.2.fb $$\chi_{3744}(41, \cdot)$$ None 0 4
3744.2.fd $$\chi_{3744}(281, \cdot)$$ None 0 4
3744.2.ff $$\chi_{3744}(1159, \cdot)$$ None 0 4
3744.2.fg $$\chi_{3744}(1465, \cdot)$$ None 0 4
3744.2.fi $$\chi_{3744}(23, \cdot)$$ None 0 4
3744.2.fl $$\chi_{3744}(599, \cdot)$$ None 0 4
3744.2.fo $$\chi_{3744}(361, \cdot)$$ None 0 4
3744.2.fp $$\chi_{3744}(121, \cdot)$$ None 0 4
3744.2.fs $$\chi_{3744}(503, \cdot)$$ None 0 4
3744.2.ft $$\chi_{3744}(263, \cdot)$$ None 0 4
3744.2.fv $$\chi_{3744}(25, \cdot)$$ None 0 4
3744.2.fw $$\chi_{3744}(31, \cdot)$$ n/a 672 4
3744.2.fx $$\chi_{3744}(463, \cdot)$$ n/a 656 4
3744.2.gc $$\chi_{3744}(305, \cdot)$$ n/a 224 4
3744.2.gd $$\chi_{3744}(449, \cdot)$$ n/a 224 4
3744.2.ge $$\chi_{3744}(353, \cdot)$$ n/a 672 4
3744.2.gf $$\chi_{3744}(1553, \cdot)$$ n/a 656 4
3744.2.gk $$\chi_{3744}(401, \cdot)$$ n/a 656 4
3744.2.gl $$\chi_{3744}(929, \cdot)$$ n/a 672 4
3744.2.go $$\chi_{3744}(1567, \cdot)$$ n/a 280 4
3744.2.gp $$\chi_{3744}(271, \cdot)$$ n/a 272 4
3744.2.gq $$\chi_{3744}(175, \cdot)$$ n/a 656 4
3744.2.gr $$\chi_{3744}(223, \cdot)$$ n/a 672 4
3744.2.gw $$\chi_{3744}(799, \cdot)$$ n/a 672 4
3744.2.gx $$\chi_{3744}(943, \cdot)$$ n/a 656 4
3744.2.gy $$\chi_{3744}(785, \cdot)$$ n/a 656 4
3744.2.gz $$\chi_{3744}(1217, \cdot)$$ n/a 672 4
3744.2.hd $$\chi_{3744}(311, \cdot)$$ None 0 4
3744.2.hg $$\chi_{3744}(217, \cdot)$$ None 0 4
3744.2.hh $$\chi_{3744}(601, \cdot)$$ None 0 4
3744.2.hk $$\chi_{3744}(647, \cdot)$$ None 0 4
3744.2.hl $$\chi_{3744}(1031, \cdot)$$ None 0 4
3744.2.hn $$\chi_{3744}(313, \cdot)$$ None 0 4
3744.2.ho $$\chi_{3744}(745, \cdot)$$ None 0 4
3744.2.hq $$\chi_{3744}(887, \cdot)$$ None 0 4
3744.2.ht $$\chi_{3744}(583, \cdot)$$ None 0 4
3744.2.hv $$\chi_{3744}(137, \cdot)$$ None 0 4
3744.2.hx $$\chi_{3744}(473, \cdot)$$ None 0 4
3744.2.hy $$\chi_{3744}(1591, \cdot)$$ None 0 4
3744.2.ia $$\chi_{3744}(7, \cdot)$$ None 0 4
3744.2.ic $$\chi_{3744}(713, \cdot)$$ None 0 4
3744.2.if $$\chi_{3744}(487, \cdot)$$ None 0 4
3744.2.ig $$\chi_{3744}(89, \cdot)$$ None 0 4
3744.2.ij $$\chi_{3744}(67, \cdot)$$ n/a 5344 8
3744.2.il $$\chi_{3744}(605, \cdot)$$ n/a 5344 8
3744.2.in $$\chi_{3744}(317, \cdot)$$ n/a 5344 8
3744.2.iq $$\chi_{3744}(115, \cdot)$$ n/a 5344 8
3744.2.ir $$\chi_{3744}(163, \cdot)$$ n/a 2224 8
3744.2.iu $$\chi_{3744}(917, \cdot)$$ n/a 1792 8
3744.2.iv $$\chi_{3744}(245, \cdot)$$ n/a 5344 8
3744.2.ix $$\chi_{3744}(187, \cdot)$$ n/a 5344 8
3744.2.iz $$\chi_{3744}(157, \cdot)$$ n/a 4608 8
3744.2.jb $$\chi_{3744}(493, \cdot)$$ n/a 5344 8
3744.2.jd $$\chi_{3744}(35, \cdot)$$ n/a 1792 8
3744.2.je $$\chi_{3744}(491, \cdot)$$ n/a 5344 8
3744.2.jg $$\chi_{3744}(563, \cdot)$$ n/a 5344 8
3744.2.ji $$\chi_{3744}(419, \cdot)$$ n/a 5344 8
3744.2.jk $$\chi_{3744}(347, \cdot)$$ n/a 5344 8
3744.2.jn $$\chi_{3744}(179, \cdot)$$ n/a 1792 8
3744.2.jo $$\chi_{3744}(829, \cdot)$$ n/a 2224 8
3744.2.jr $$\chi_{3744}(61, \cdot)$$ n/a 5344 8
3744.2.jt $$\chi_{3744}(133, \cdot)$$ n/a 5344 8
3744.2.jv $$\chi_{3744}(277, \cdot)$$ n/a 5344 8
3744.2.jx $$\chi_{3744}(205, \cdot)$$ n/a 5344 8
3744.2.jy $$\chi_{3744}(685, \cdot)$$ n/a 2224 8
3744.2.ka $$\chi_{3744}(155, \cdot)$$ n/a 5344 8
3744.2.kc $$\chi_{3744}(131, \cdot)$$ n/a 4608 8
3744.2.ke $$\chi_{3744}(5, \cdot)$$ n/a 5344 8
3744.2.kg $$\chi_{3744}(643, \cdot)$$ n/a 5344 8
3744.2.kh $$\chi_{3744}(19, \cdot)$$ n/a 2224 8
3744.2.kk $$\chi_{3744}(197, \cdot)$$ n/a 1792 8
3744.2.kl $$\chi_{3744}(149, \cdot)$$ n/a 5344 8
3744.2.ko $$\chi_{3744}(499, \cdot)$$ n/a 5344 8
3744.2.kq $$\chi_{3744}(331, \cdot)$$ n/a 5344 8
3744.2.ks $$\chi_{3744}(461, \cdot)$$ n/a 5344 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3744))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3744)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(936))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1248))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1872))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3744))$$$$^{\oplus 1}$$