Properties

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

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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

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

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

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