# Properties

 Label 2736.2 Level 2736 Weight 2 Dimension 91139 Nonzero newspaces 64 Sturm bound 829440 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$64$$ Sturm bound: $$829440$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2736))$$.

Total New Old
Modular forms 211392 92515 118877
Cusp forms 203329 91139 112190
Eisenstein series 8063 1376 6687

## Trace form

 $$91139 q - 96 q^{2} - 96 q^{3} - 100 q^{4} - 125 q^{5} - 128 q^{6} - 83 q^{7} - 108 q^{8} - 40 q^{9} + O(q^{10})$$ $$91139 q - 96 q^{2} - 96 q^{3} - 100 q^{4} - 125 q^{5} - 128 q^{6} - 83 q^{7} - 108 q^{8} - 40 q^{9} - 292 q^{10} - 99 q^{11} - 128 q^{12} - 137 q^{13} - 60 q^{14} - 102 q^{15} - 52 q^{16} - 199 q^{17} - 88 q^{18} - 233 q^{19} - 104 q^{20} - 134 q^{21} - 4 q^{22} - 31 q^{23} - 64 q^{24} + 29 q^{25} + 20 q^{26} - 60 q^{27} - 212 q^{28} - 61 q^{29} - 88 q^{30} - 47 q^{31} - 36 q^{32} - 246 q^{33} - 76 q^{34} + 75 q^{35} - 120 q^{36} - 386 q^{37} - 148 q^{38} - 90 q^{39} - 212 q^{40} + 3 q^{41} - 208 q^{42} + 45 q^{43} - 268 q^{44} - 114 q^{45} - 412 q^{46} + 69 q^{47} - 232 q^{48} - 283 q^{49} - 264 q^{50} - 32 q^{51} - 220 q^{52} - 103 q^{53} - 216 q^{54} - 87 q^{55} - 300 q^{56} - 56 q^{57} - 280 q^{58} - 23 q^{59} - 344 q^{60} - 109 q^{61} - 300 q^{62} - 102 q^{63} - 148 q^{64} - 477 q^{65} - 368 q^{66} - 203 q^{67} - 268 q^{68} - 310 q^{69} - 20 q^{70} - 263 q^{71} - 352 q^{72} - 149 q^{73} - 212 q^{74} - 200 q^{75} - 68 q^{76} - 452 q^{77} - 344 q^{78} - 289 q^{79} - 364 q^{80} - 440 q^{81} - 308 q^{82} - 333 q^{83} - 416 q^{84} - 131 q^{85} - 388 q^{86} - 234 q^{87} - 244 q^{88} - 135 q^{89} - 416 q^{90} - 455 q^{91} - 292 q^{92} - 78 q^{93} - 292 q^{94} - 181 q^{95} - 408 q^{96} - 193 q^{97} - 280 q^{98} - 126 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2736))$$

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
2736.2.a $$\chi_{2736}(1, \cdot)$$ 2736.2.a.a 1 1
2736.2.a.b 1
2736.2.a.c 1
2736.2.a.d 1
2736.2.a.e 1
2736.2.a.f 1
2736.2.a.g 1
2736.2.a.h 1
2736.2.a.i 1
2736.2.a.j 1
2736.2.a.k 1
2736.2.a.l 1
2736.2.a.m 1
2736.2.a.n 1
2736.2.a.o 1
2736.2.a.p 1
2736.2.a.q 1
2736.2.a.r 1
2736.2.a.s 1
2736.2.a.t 1
2736.2.a.u 1
2736.2.a.v 1
2736.2.a.w 1
2736.2.a.x 1
2736.2.a.y 2
2736.2.a.z 2
2736.2.a.ba 2
2736.2.a.bb 2
2736.2.a.bc 3
2736.2.a.bd 3
2736.2.a.be 3
2736.2.a.bf 4
2736.2.d $$\chi_{2736}(2015, \cdot)$$ 2736.2.d.a 12 1
2736.2.d.b 24
2736.2.e $$\chi_{2736}(1063, \cdot)$$ None 0 1
2736.2.f $$\chi_{2736}(1025, \cdot)$$ 2736.2.f.a 2 1
2736.2.f.b 2
2736.2.f.c 2
2736.2.f.d 2
2736.2.f.e 4
2736.2.f.f 4
2736.2.f.g 8
2736.2.f.h 8
2736.2.f.i 8
2736.2.g $$\chi_{2736}(1369, \cdot)$$ None 0 1
2736.2.j $$\chi_{2736}(647, \cdot)$$ None 0 1
2736.2.k $$\chi_{2736}(2431, \cdot)$$ 2736.2.k.a 2 1
2736.2.k.b 2
2736.2.k.c 2
2736.2.k.d 2
2736.2.k.e 2
2736.2.k.f 2
2736.2.k.g 2
2736.2.k.h 2
2736.2.k.i 2
2736.2.k.j 4
2736.2.k.k 4
2736.2.k.l 4
2736.2.k.m 4
2736.2.k.n 4
2736.2.k.o 4
2736.2.k.p 8
2736.2.p $$\chi_{2736}(2393, \cdot)$$ None 0 1
2736.2.q $$\chi_{2736}(913, \cdot)$$ n/a 216 2
2736.2.r $$\chi_{2736}(49, \cdot)$$ n/a 236 2
2736.2.s $$\chi_{2736}(577, \cdot)$$ 2736.2.s.a 2 2
2736.2.s.b 2
2736.2.s.c 2
2736.2.s.d 2
2736.2.s.e 2
2736.2.s.f 2
2736.2.s.g 2
2736.2.s.h 2
2736.2.s.i 2
2736.2.s.j 2
2736.2.s.k 2
2736.2.s.l 2
2736.2.s.m 2
2736.2.s.n 2
2736.2.s.o 2
2736.2.s.p 2
2736.2.s.q 2
2736.2.s.r 2
2736.2.s.s 4
2736.2.s.t 4
2736.2.s.u 4
2736.2.s.v 4
2736.2.s.w 4
2736.2.s.x 6
2736.2.s.y 6
2736.2.s.z 6
2736.2.s.ba 8
2736.2.s.bb 8
2736.2.s.bc 8
2736.2.t $$\chi_{2736}(961, \cdot)$$ n/a 236 2
2736.2.u $$\chi_{2736}(341, \cdot)$$ n/a 320 2
2736.2.x $$\chi_{2736}(685, \cdot)$$ n/a 360 2
2736.2.y $$\chi_{2736}(1331, \cdot)$$ n/a 288 2
2736.2.bb $$\chi_{2736}(379, \cdot)$$ n/a 396 2
2736.2.be $$\chi_{2736}(121, \cdot)$$ None 0 2
2736.2.bf $$\chi_{2736}(65, \cdot)$$ n/a 236 2
2736.2.bg $$\chi_{2736}(1015, \cdot)$$ None 0 2
2736.2.bh $$\chi_{2736}(1679, \cdot)$$ n/a 240 2
2736.2.bm $$\chi_{2736}(559, \cdot)$$ 2736.2.bm.a 2 2
2736.2.bm.b 2
2736.2.bm.c 2
2736.2.bm.d 2
2736.2.bm.e 2
2736.2.bm.f 2
2736.2.bm.g 2
2736.2.bm.h 2
2736.2.bm.i 4
2736.2.bm.j 4
2736.2.bm.k 4
2736.2.bm.l 6
2736.2.bm.m 6
2736.2.bm.n 6
2736.2.bm.o 6
2736.2.bm.p 8
2736.2.bm.q 8
2736.2.bm.r 8
2736.2.bm.s 8
2736.2.bm.t 16
2736.2.bn $$\chi_{2736}(1223, \cdot)$$ None 0 2
2736.2.bq $$\chi_{2736}(569, \cdot)$$ None 0 2
2736.2.bt $$\chi_{2736}(2345, \cdot)$$ None 0 2
2736.2.bu $$\chi_{2736}(943, \cdot)$$ n/a 240 2
2736.2.bv $$\chi_{2736}(1607, \cdot)$$ None 0 2
2736.2.by $$\chi_{2736}(1559, \cdot)$$ None 0 2
2736.2.bz $$\chi_{2736}(607, \cdot)$$ n/a 240 2
2736.2.cc $$\chi_{2736}(521, \cdot)$$ None 0 2
2736.2.cf $$\chi_{2736}(487, \cdot)$$ None 0 2
2736.2.cg $$\chi_{2736}(1151, \cdot)$$ 2736.2.cg.a 24 2
2736.2.cg.b 24
2736.2.cg.c 32
2736.2.cj $$\chi_{2736}(1033, \cdot)$$ None 0 2
2736.2.ck $$\chi_{2736}(977, \cdot)$$ n/a 236 2
2736.2.cn $$\chi_{2736}(113, \cdot)$$ n/a 236 2
2736.2.co $$\chi_{2736}(457, \cdot)$$ None 0 2
2736.2.ct $$\chi_{2736}(191, \cdot)$$ n/a 216 2
2736.2.cu $$\chi_{2736}(151, \cdot)$$ None 0 2
2736.2.cx $$\chi_{2736}(103, \cdot)$$ None 0 2
2736.2.cy $$\chi_{2736}(239, \cdot)$$ n/a 240 2
2736.2.db $$\chi_{2736}(505, \cdot)$$ None 0 2
2736.2.dc $$\chi_{2736}(449, \cdot)$$ 2736.2.dc.a 4 2
2736.2.dc.b 4
2736.2.dc.c 16
2736.2.dc.d 16
2736.2.dc.e 20
2736.2.dc.f 20
2736.2.dd $$\chi_{2736}(905, \cdot)$$ None 0 2
2736.2.di $$\chi_{2736}(31, \cdot)$$ n/a 240 2
2736.2.dj $$\chi_{2736}(311, \cdot)$$ None 0 2
2736.2.dk $$\chi_{2736}(289, \cdot)$$ n/a 294 6
2736.2.dl $$\chi_{2736}(625, \cdot)$$ n/a 708 6
2736.2.dm $$\chi_{2736}(385, \cdot)$$ n/a 708 6
2736.2.do $$\chi_{2736}(1189, \cdot)$$ n/a 792 4
2736.2.dp $$\chi_{2736}(1133, \cdot)$$ n/a 640 4
2736.2.ds $$\chi_{2736}(419, \cdot)$$ n/a 1728 4
2736.2.dt $$\chi_{2736}(331, \cdot)$$ n/a 1904 4
2736.2.dv $$\chi_{2736}(259, \cdot)$$ n/a 1904 4
2736.2.dy $$\chi_{2736}(83, \cdot)$$ n/a 1904 4
2736.2.ea $$\chi_{2736}(11, \cdot)$$ n/a 1904 4
2736.2.eb $$\chi_{2736}(835, \cdot)$$ n/a 1904 4
2736.2.ee $$\chi_{2736}(797, \cdot)$$ n/a 1904 4
2736.2.ef $$\chi_{2736}(349, \cdot)$$ n/a 1904 4
2736.2.eh $$\chi_{2736}(277, \cdot)$$ n/a 1904 4
2736.2.ek $$\chi_{2736}(221, \cdot)$$ n/a 1904 4
2736.2.em $$\chi_{2736}(293, \cdot)$$ n/a 1904 4
2736.2.en $$\chi_{2736}(229, \cdot)$$ n/a 1728 4
2736.2.eq $$\chi_{2736}(1171, \cdot)$$ n/a 792 4
2736.2.er $$\chi_{2736}(467, \cdot)$$ n/a 640 4
2736.2.eu $$\chi_{2736}(439, \cdot)$$ None 0 6
2736.2.ew $$\chi_{2736}(671, \cdot)$$ n/a 720 6
2736.2.ex $$\chi_{2736}(79, \cdot)$$ n/a 720 6
2736.2.ez $$\chi_{2736}(23, \cdot)$$ None 0 6
2736.2.fb $$\chi_{2736}(401, \cdot)$$ n/a 708 6
2736.2.fd $$\chi_{2736}(25, \cdot)$$ None 0 6
2736.2.fh $$\chi_{2736}(89, \cdot)$$ None 0 6
2736.2.fi $$\chi_{2736}(73, \cdot)$$ None 0 6
2736.2.fk $$\chi_{2736}(737, \cdot)$$ n/a 240 6
2736.2.fn $$\chi_{2736}(41, \cdot)$$ None 0 6
2736.2.fp $$\chi_{2736}(1031, \cdot)$$ None 0 6
2736.2.fr $$\chi_{2736}(895, \cdot)$$ n/a 720 6
2736.2.fu $$\chi_{2736}(775, \cdot)$$ None 0 6
2736.2.fw $$\chi_{2736}(575, \cdot)$$ n/a 240 6
2736.2.fx $$\chi_{2736}(127, \cdot)$$ n/a 300 6
2736.2.fz $$\chi_{2736}(215, \cdot)$$ None 0 6
2736.2.gc $$\chi_{2736}(47, \cdot)$$ n/a 720 6
2736.2.ge $$\chi_{2736}(295, \cdot)$$ None 0 6
2736.2.gh $$\chi_{2736}(857, \cdot)$$ None 0 6
2736.2.gi $$\chi_{2736}(169, \cdot)$$ None 0 6
2736.2.gk $$\chi_{2736}(257, \cdot)$$ n/a 708 6
2736.2.gm $$\chi_{2736}(85, \cdot)$$ n/a 5712 12
2736.2.go $$\chi_{2736}(173, \cdot)$$ n/a 5712 12
2736.2.gq $$\chi_{2736}(131, \cdot)$$ n/a 5712 12
2736.2.gt $$\chi_{2736}(91, \cdot)$$ n/a 2376 12
2736.2.gv $$\chi_{2736}(35, \cdot)$$ n/a 1920 12
2736.2.gw $$\chi_{2736}(211, \cdot)$$ n/a 5712 12
2736.2.gz $$\chi_{2736}(29, \cdot)$$ n/a 5712 12
2736.2.ha $$\chi_{2736}(253, \cdot)$$ n/a 2376 12
2736.2.hc $$\chi_{2736}(53, \cdot)$$ n/a 1920 12
2736.2.hf $$\chi_{2736}(61, \cdot)$$ n/a 5712 12
2736.2.hh $$\chi_{2736}(67, \cdot)$$ n/a 5712 12
2736.2.hj $$\chi_{2736}(275, \cdot)$$ n/a 5712 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2736))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2736)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(684))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1368))$$$$^{\oplus 2}$$