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Properties

Label 2016.3
Level 2016
Weight 3
Dimension 93942
Nonzero newspaces 60
Sturm bound 663552
Trace bound 40

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(663552\)
Trace bound: \(40\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2016))\).

Total New Old
Modular forms 224256 94842 129414
Cusp forms 218112 93942 124170
Eisenstein series 6144 900 5244

Trace form

\( 93942 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 56 q^{5} - 64 q^{6} - 44 q^{7} - 120 q^{8} - 96 q^{9} + O(q^{10}) \) \( 93942 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 56 q^{5} - 64 q^{6} - 44 q^{7} - 120 q^{8} - 96 q^{9} - 64 q^{10} + 2 q^{11} - 64 q^{12} + 8 q^{13} - 44 q^{14} - 84 q^{15} - 88 q^{16} + 88 q^{17} - 64 q^{18} - 46 q^{19} - 208 q^{20} - 48 q^{21} - 416 q^{22} + 86 q^{23} - 64 q^{24} - 170 q^{25} - 248 q^{26} - 144 q^{27} - 240 q^{28} - 448 q^{29} - 128 q^{30} - 298 q^{31} - 8 q^{32} - 392 q^{33} + 40 q^{34} - 342 q^{35} - 688 q^{36} - 664 q^{37} - 1280 q^{38} - 276 q^{39} - 1032 q^{40} - 696 q^{41} - 480 q^{42} - 364 q^{43} - 736 q^{44} - 256 q^{45} - 336 q^{46} + 222 q^{47} + 144 q^{48} + 218 q^{49} + 504 q^{50} + 40 q^{51} + 384 q^{52} + 1256 q^{53} + 1168 q^{54} + 88 q^{55} + 824 q^{56} - 48 q^{57} + 1704 q^{58} - 350 q^{59} + 1392 q^{60} + 680 q^{61} + 1080 q^{62} - 282 q^{63} + 96 q^{64} - 476 q^{65} - 64 q^{66} + 106 q^{67} + 1192 q^{68} - 320 q^{69} + 600 q^{70} + 236 q^{71} - 64 q^{72} - 392 q^{73} + 1008 q^{74} - 64 q^{75} + 976 q^{76} - 28 q^{77} + 656 q^{78} - 1818 q^{79} + 3160 q^{80} + 800 q^{81} + 2736 q^{82} - 3088 q^{83} + 1152 q^{84} - 912 q^{85} + 2312 q^{86} - 1484 q^{87} + 840 q^{88} - 728 q^{89} + 1376 q^{90} - 1392 q^{91} + 8 q^{92} - 64 q^{93} - 2328 q^{94} - 294 q^{95} - 336 q^{96} - 968 q^{97} - 2672 q^{98} + 1484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2016))\)

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
2016.3.d \(\chi_{2016}(449, \cdot)\) 2016.3.d.a 4 1
2016.3.d.b 4
2016.3.d.c 4
2016.3.d.d 12
2016.3.d.e 12
2016.3.d.f 12
2016.3.e \(\chi_{2016}(1007, \cdot)\) 2016.3.e.a 8 1
2016.3.e.b 8
2016.3.e.c 48
2016.3.f \(\chi_{2016}(1441, \cdot)\) 2016.3.f.a 8 1
2016.3.f.b 8
2016.3.f.c 8
2016.3.f.d 8
2016.3.f.e 16
2016.3.f.f 16
2016.3.f.g 16
2016.3.g \(\chi_{2016}(1135, \cdot)\) 2016.3.g.a 4 1
2016.3.g.b 8
2016.3.g.c 24
2016.3.g.d 24
2016.3.l \(\chi_{2016}(433, \cdot)\) 2016.3.l.a 2 1
2016.3.l.b 2
2016.3.l.c 2
2016.3.l.d 4
2016.3.l.e 4
2016.3.l.f 8
2016.3.l.g 24
2016.3.l.h 32
2016.3.m \(\chi_{2016}(127, \cdot)\) 2016.3.m.a 4 1
2016.3.m.b 8
2016.3.m.c 8
2016.3.m.d 12
2016.3.m.e 12
2016.3.m.f 16
2016.3.n \(\chi_{2016}(1457, \cdot)\) 2016.3.n.a 48 1
2016.3.o \(\chi_{2016}(2015, \cdot)\) 2016.3.o.a 32 1
2016.3.o.b 32
2016.3.u \(\chi_{2016}(937, \cdot)\) None 0 2
2016.3.w \(\chi_{2016}(953, \cdot)\) None 0 2
2016.3.y \(\chi_{2016}(503, \cdot)\) None 0 2
2016.3.ba \(\chi_{2016}(631, \cdot)\) None 0 2
2016.3.bc \(\chi_{2016}(47, \cdot)\) n/a 376 2
2016.3.bd \(\chi_{2016}(65, \cdot)\) n/a 384 2
2016.3.bi \(\chi_{2016}(79, \cdot)\) n/a 376 2
2016.3.bj \(\chi_{2016}(1825, \cdot)\) n/a 384 2
2016.3.bk \(\chi_{2016}(1151, \cdot)\) n/a 128 2
2016.3.bl \(\chi_{2016}(305, \cdot)\) n/a 128 2
2016.3.bo \(\chi_{2016}(113, \cdot)\) n/a 288 2
2016.3.bp \(\chi_{2016}(383, \cdot)\) n/a 384 2
2016.3.bq \(\chi_{2016}(401, \cdot)\) n/a 376 2
2016.3.br \(\chi_{2016}(671, \cdot)\) n/a 384 2
2016.3.bv \(\chi_{2016}(1105, \cdot)\) n/a 376 2
2016.3.bw \(\chi_{2016}(1663, \cdot)\) n/a 384 2
2016.3.bx \(\chi_{2016}(241, \cdot)\) n/a 376 2
2016.3.by \(\chi_{2016}(799, \cdot)\) n/a 288 2
2016.3.cd \(\chi_{2016}(415, \cdot)\) n/a 160 2
2016.3.ce \(\chi_{2016}(145, \cdot)\) n/a 156 2
2016.3.cf \(\chi_{2016}(1423, \cdot)\) n/a 156 2
2016.3.cg \(\chi_{2016}(577, \cdot)\) n/a 160 2
2016.3.cl \(\chi_{2016}(97, \cdot)\) n/a 384 2
2016.3.cm \(\chi_{2016}(655, \cdot)\) n/a 376 2
2016.3.cn \(\chi_{2016}(481, \cdot)\) n/a 384 2
2016.3.co \(\chi_{2016}(463, \cdot)\) n/a 288 2
2016.3.ct \(\chi_{2016}(1121, \cdot)\) n/a 288 2
2016.3.cu \(\chi_{2016}(1391, \cdot)\) n/a 376 2
2016.3.cv \(\chi_{2016}(641, \cdot)\) n/a 384 2
2016.3.cw \(\chi_{2016}(335, \cdot)\) n/a 376 2
2016.3.db \(\chi_{2016}(143, \cdot)\) n/a 128 2
2016.3.dc \(\chi_{2016}(737, \cdot)\) n/a 128 2
2016.3.dd \(\chi_{2016}(319, \cdot)\) n/a 384 2
2016.3.de \(\chi_{2016}(817, \cdot)\) n/a 376 2
2016.3.di \(\chi_{2016}(1055, \cdot)\) n/a 384 2
2016.3.dj \(\chi_{2016}(977, \cdot)\) n/a 376 2
2016.3.dl \(\chi_{2016}(379, \cdot)\) n/a 960 4
2016.3.dn \(\chi_{2016}(251, \cdot)\) n/a 1024 4
2016.3.dp \(\chi_{2016}(181, \cdot)\) n/a 1272 4
2016.3.dr \(\chi_{2016}(197, \cdot)\) n/a 768 4
2016.3.dt \(\chi_{2016}(281, \cdot)\) None 0 4
2016.3.dv \(\chi_{2016}(265, \cdot)\) None 0 4
2016.3.dx \(\chi_{2016}(311, \cdot)\) None 0 4
2016.3.dy \(\chi_{2016}(151, \cdot)\) None 0 4
2016.3.eb \(\chi_{2016}(487, \cdot)\) None 0 4
2016.3.ed \(\chi_{2016}(215, \cdot)\) None 0 4
2016.3.ee \(\chi_{2016}(887, \cdot)\) None 0 4
2016.3.eh \(\chi_{2016}(583, \cdot)\) None 0 4
2016.3.ej \(\chi_{2016}(313, \cdot)\) None 0 4
2016.3.el \(\chi_{2016}(233, \cdot)\) None 0 4
2016.3.em \(\chi_{2016}(137, \cdot)\) None 0 4
2016.3.eo \(\chi_{2016}(745, \cdot)\) None 0 4
2016.3.er \(\chi_{2016}(73, \cdot)\) None 0 4
2016.3.et \(\chi_{2016}(473, \cdot)\) None 0 4
2016.3.ev \(\chi_{2016}(295, \cdot)\) None 0 4
2016.3.ex \(\chi_{2016}(167, \cdot)\) None 0 4
2016.3.ey \(\chi_{2016}(83, \cdot)\) n/a 6112 8
2016.3.fa \(\chi_{2016}(43, \cdot)\) n/a 4608 8
2016.3.fd \(\chi_{2016}(229, \cdot)\) n/a 6112 8
2016.3.fe \(\chi_{2016}(221, \cdot)\) n/a 6112 8
2016.3.ff \(\chi_{2016}(53, \cdot)\) n/a 2048 8
2016.3.fi \(\chi_{2016}(325, \cdot)\) n/a 2544 8
2016.3.fj \(\chi_{2016}(61, \cdot)\) n/a 6112 8
2016.3.fn \(\chi_{2016}(149, \cdot)\) n/a 6112 8
2016.3.fp \(\chi_{2016}(403, \cdot)\) n/a 6112 8
2016.3.fq \(\chi_{2016}(395, \cdot)\) n/a 2048 8
2016.3.fr \(\chi_{2016}(59, \cdot)\) n/a 6112 8
2016.3.fu \(\chi_{2016}(67, \cdot)\) n/a 6112 8
2016.3.fv \(\chi_{2016}(163, \cdot)\) n/a 2544 8
2016.3.fz \(\chi_{2016}(131, \cdot)\) n/a 6112 8
2016.3.ga \(\chi_{2016}(29, \cdot)\) n/a 4608 8
2016.3.gc \(\chi_{2016}(13, \cdot)\) n/a 6112 8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2016))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2016)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)