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Properties

Label 2736.3
Level 2736
Weight 3
Dimension 182965
Nonzero newspaces 64
Sturm bound 1244160
Trace bound 33

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Defining parameters

Level: \( N \) = \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1244160\)
Trace bound: \(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2736))\).

Total New Old
Modular forms 418752 184343 234409
Cusp forms 410688 182965 227723
Eisenstein series 8064 1378 6686

Trace form

\( 182965 q - 96 q^{2} - 96 q^{3} - 84 q^{4} - 105 q^{5} - 128 q^{6} - 35 q^{7} - 108 q^{8} - 16 q^{9} + O(q^{10}) \) \( 182965 q - 96 q^{2} - 96 q^{3} - 84 q^{4} - 105 q^{5} - 128 q^{6} - 35 q^{7} - 108 q^{8} - 16 q^{9} - 364 q^{10} - 43 q^{11} - 128 q^{12} - 173 q^{13} - 188 q^{14} - 162 q^{15} - 244 q^{16} - 447 q^{17} - 328 q^{18} - 325 q^{19} - 376 q^{20} - 242 q^{21} - 92 q^{22} - 215 q^{23} - 64 q^{24} + 131 q^{25} + 92 q^{26} - 240 q^{27} + 76 q^{28} + 119 q^{29} + 296 q^{30} + 133 q^{31} + 604 q^{32} - 174 q^{33} + 404 q^{34} - 273 q^{35} + 264 q^{36} - 500 q^{37} + 360 q^{38} - 474 q^{39} + 716 q^{40} - 57 q^{41} + 272 q^{42} - 647 q^{43} + 388 q^{44} + 162 q^{45} - 284 q^{46} + 369 q^{47} - 232 q^{48} - 9 q^{49} - 752 q^{50} + 532 q^{51} - 940 q^{52} + 113 q^{53} - 744 q^{54} + 649 q^{55} - 812 q^{56} + 280 q^{57} - 1680 q^{58} + 1093 q^{59} + 904 q^{60} + 203 q^{61} + 324 q^{62} + 570 q^{63} - 1428 q^{64} + 595 q^{65} + 1072 q^{66} + 921 q^{67} - 268 q^{68} + 26 q^{69} - 164 q^{70} + 671 q^{71} - 352 q^{72} + 427 q^{73} - 252 q^{74} + 16 q^{75} + 324 q^{76} - 832 q^{77} - 1208 q^{78} + 541 q^{79} + 276 q^{80} - 1616 q^{81} + 2764 q^{82} + 53 q^{83} - 1184 q^{84} - 1471 q^{85} + 36 q^{86} + 30 q^{87} + 1580 q^{88} - 1887 q^{89} - 704 q^{90} - 1679 q^{91} + 892 q^{92} - 1314 q^{93} + 60 q^{94} - 795 q^{95} - 408 q^{96} - 1101 q^{97} - 1784 q^{98} - 1602 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2736))\)

We only show spaces with odd 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
2736.3.b \(\chi_{2736}(2735, \cdot)\) 2736.3.b.a 8 1
2736.3.b.b 8
2736.3.b.c 16
2736.3.b.d 16
2736.3.b.e 32
2736.3.c \(\chi_{2736}(343, \cdot)\) None 0 1
2736.3.h \(\chi_{2736}(305, \cdot)\) 2736.3.h.a 4 1
2736.3.h.b 8
2736.3.h.c 12
2736.3.h.d 12
2736.3.h.e 16
2736.3.h.f 20
2736.3.i \(\chi_{2736}(2089, \cdot)\) None 0 1
2736.3.l \(\chi_{2736}(1367, \cdot)\) None 0 1
2736.3.m \(\chi_{2736}(1711, \cdot)\) 2736.3.m.a 6 1
2736.3.m.b 12
2736.3.m.c 12
2736.3.m.d 12
2736.3.m.e 12
2736.3.m.f 12
2736.3.m.g 24
2736.3.n \(\chi_{2736}(1673, \cdot)\) None 0 1
2736.3.o \(\chi_{2736}(721, \cdot)\) 2736.3.o.a 1 1
2736.3.o.b 2
2736.3.o.c 2
2736.3.o.d 2
2736.3.o.e 2
2736.3.o.f 2
2736.3.o.g 2
2736.3.o.h 2
2736.3.o.i 2
2736.3.o.j 4
2736.3.o.k 4
2736.3.o.l 4
2736.3.o.m 6
2736.3.o.n 8
2736.3.o.o 8
2736.3.o.p 8
2736.3.o.q 20
2736.3.o.r 20
2736.3.v \(\chi_{2736}(989, \cdot)\) n/a 576 2
2736.3.w \(\chi_{2736}(37, \cdot)\) n/a 796 2
2736.3.z \(\chi_{2736}(683, \cdot)\) n/a 640 2
2736.3.ba \(\chi_{2736}(1027, \cdot)\) n/a 720 2
2736.3.bc \(\chi_{2736}(2041, \cdot)\) None 0 2
2736.3.bd \(\chi_{2736}(353, \cdot)\) n/a 476 2
2736.3.bi \(\chi_{2736}(1303, \cdot)\) None 0 2
2736.3.bj \(\chi_{2736}(1247, \cdot)\) n/a 480 2
2736.3.bk \(\chi_{2736}(847, \cdot)\) n/a 200 2
2736.3.bl \(\chi_{2736}(791, \cdot)\) None 0 2
2736.3.bo \(\chi_{2736}(1969, \cdot)\) n/a 476 2
2736.3.bp \(\chi_{2736}(425, \cdot)\) None 0 2
2736.3.br \(\chi_{2736}(761, \cdot)\) None 0 2
2736.3.bs \(\chi_{2736}(1633, \cdot)\) n/a 476 2
2736.3.bw \(\chi_{2736}(455, \cdot)\) None 0 2
2736.3.bx \(\chi_{2736}(799, \cdot)\) n/a 432 2
2736.3.ca \(\chi_{2736}(1375, \cdot)\) n/a 480 2
2736.3.cb \(\chi_{2736}(1319, \cdot)\) None 0 2
2736.3.cd \(\chi_{2736}(145, \cdot)\) n/a 198 2
2736.3.ce \(\chi_{2736}(809, \cdot)\) None 0 2
2736.3.ch \(\chi_{2736}(919, \cdot)\) None 0 2
2736.3.ci \(\chi_{2736}(863, \cdot)\) n/a 160 2
2736.3.cl \(\chi_{2736}(1217, \cdot)\) n/a 432 2
2736.3.cm \(\chi_{2736}(265, \cdot)\) None 0 2
2736.3.cp \(\chi_{2736}(601, \cdot)\) None 0 2
2736.3.cq \(\chi_{2736}(1265, \cdot)\) n/a 476 2
2736.3.cr \(\chi_{2736}(7, \cdot)\) None 0 2
2736.3.cs \(\chi_{2736}(335, \cdot)\) n/a 480 2
2736.3.cv \(\chi_{2736}(911, \cdot)\) n/a 480 2
2736.3.cw \(\chi_{2736}(1255, \cdot)\) None 0 2
2736.3.cz \(\chi_{2736}(217, \cdot)\) None 0 2
2736.3.da \(\chi_{2736}(881, \cdot)\) n/a 160 2
2736.3.de \(\chi_{2736}(673, \cdot)\) n/a 476 2
2736.3.df \(\chi_{2736}(1337, \cdot)\) None 0 2
2736.3.dg \(\chi_{2736}(463, \cdot)\) n/a 480 2
2736.3.dh \(\chi_{2736}(407, \cdot)\) None 0 2
2736.3.dn \(\chi_{2736}(829, \cdot)\) n/a 1592 4
2736.3.dq \(\chi_{2736}(125, \cdot)\) n/a 1280 4
2736.3.dr \(\chi_{2736}(227, \cdot)\) n/a 3824 4
2736.3.du \(\chi_{2736}(619, \cdot)\) n/a 3824 4
2736.3.dw \(\chi_{2736}(691, \cdot)\) n/a 3824 4
2736.3.dx \(\chi_{2736}(635, \cdot)\) n/a 3824 4
2736.3.dz \(\chi_{2736}(563, \cdot)\) n/a 3824 4
2736.3.ec \(\chi_{2736}(115, \cdot)\) n/a 3456 4
2736.3.ed \(\chi_{2736}(77, \cdot)\) n/a 3456 4
2736.3.eg \(\chi_{2736}(445, \cdot)\) n/a 3824 4
2736.3.ei \(\chi_{2736}(373, \cdot)\) n/a 3824 4
2736.3.ej \(\chi_{2736}(653, \cdot)\) n/a 3824 4
2736.3.el \(\chi_{2736}(581, \cdot)\) n/a 3824 4
2736.3.eo \(\chi_{2736}(493, \cdot)\) n/a 3824 4
2736.3.ep \(\chi_{2736}(163, \cdot)\) n/a 1592 4
2736.3.es \(\chi_{2736}(107, \cdot)\) n/a 1280 4
2736.3.et \(\chi_{2736}(1199, \cdot)\) n/a 1440 6
2736.3.ev \(\chi_{2736}(727, \cdot)\) None 0 6
2736.3.ey \(\chi_{2736}(167, \cdot)\) None 0 6
2736.3.fa \(\chi_{2736}(175, \cdot)\) n/a 1440 6
2736.3.fc \(\chi_{2736}(553, \cdot)\) None 0 6
2736.3.fe \(\chi_{2736}(689, \cdot)\) n/a 1428 6
2736.3.ff \(\chi_{2736}(233, \cdot)\) None 0 6
2736.3.fg \(\chi_{2736}(433, \cdot)\) n/a 594 6
2736.3.fj \(\chi_{2736}(17, \cdot)\) n/a 480 6
2736.3.fl \(\chi_{2736}(649, \cdot)\) None 0 6
2736.3.fm \(\chi_{2736}(193, \cdot)\) n/a 1428 6
2736.3.fo \(\chi_{2736}(137, \cdot)\) None 0 6
2736.3.fq \(\chi_{2736}(367, \cdot)\) n/a 1440 6
2736.3.fs \(\chi_{2736}(743, \cdot)\) None 0 6
2736.3.ft \(\chi_{2736}(143, \cdot)\) n/a 480 6
2736.3.fv \(\chi_{2736}(55, \cdot)\) None 0 6
2736.3.fy \(\chi_{2736}(71, \cdot)\) None 0 6
2736.3.ga \(\chi_{2736}(271, \cdot)\) n/a 600 6
2736.3.gb \(\chi_{2736}(967, \cdot)\) None 0 6
2736.3.gd \(\chi_{2736}(383, \cdot)\) n/a 1440 6
2736.3.gf \(\chi_{2736}(329, \cdot)\) None 0 6
2736.3.gg \(\chi_{2736}(97, \cdot)\) n/a 1428 6
2736.3.gj \(\chi_{2736}(929, \cdot)\) n/a 1428 6
2736.3.gl \(\chi_{2736}(409, \cdot)\) None 0 6
2736.3.gn \(\chi_{2736}(245, \cdot)\) n/a 11472 12
2736.3.gp \(\chi_{2736}(13, \cdot)\) n/a 11472 12
2736.3.gr \(\chi_{2736}(283, \cdot)\) n/a 11472 12
2736.3.gs \(\chi_{2736}(395, \cdot)\) n/a 3840 12
2736.3.gu \(\chi_{2736}(595, \cdot)\) n/a 4776 12
2736.3.gx \(\chi_{2736}(59, \cdot)\) n/a 11472 12
2736.3.gy \(\chi_{2736}(205, \cdot)\) n/a 11472 12
2736.3.hb \(\chi_{2736}(557, \cdot)\) n/a 3840 12
2736.3.hd \(\chi_{2736}(109, \cdot)\) n/a 4776 12
2736.3.he \(\chi_{2736}(5, \cdot)\) n/a 11472 12
2736.3.hg \(\chi_{2736}(155, \cdot)\) n/a 11472 12
2736.3.hi \(\chi_{2736}(43, \cdot)\) n/a 11472 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2736))\) into lower level spaces

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