# Properties

 Label 2016.2 Level 2016 Weight 2 Dimension 46746 Nonzero newspaces 60 Sturm bound 442368 Trace bound 40

## Defining parameters

 Level: $$N$$ = $$2016 = 2^{5} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$442368$$ Trace bound: $$40$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2016))$$.

Total New Old
Modular forms 113664 47646 66018
Cusp forms 107521 46746 60775
Eisenstein series 6143 900 5243

## Trace form

 $$46746 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 44 q^{5} - 64 q^{6} - 44 q^{7} - 120 q^{8} - 96 q^{9} + O(q^{10})$$ $$46746 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 44 q^{5} - 64 q^{6} - 44 q^{7} - 120 q^{8} - 96 q^{9} - 160 q^{10} - 42 q^{11} - 64 q^{12} - 60 q^{13} - 76 q^{14} - 132 q^{15} - 88 q^{16} - 64 q^{17} - 64 q^{18} - 138 q^{19} - 80 q^{20} - 96 q^{21} - 144 q^{22} - 90 q^{23} - 64 q^{24} - 138 q^{25} - 8 q^{26} - 72 q^{27} - 160 q^{28} - 164 q^{29} - 32 q^{30} - 106 q^{31} - 8 q^{32} - 152 q^{33} - 24 q^{34} - 66 q^{35} - 112 q^{36} - 76 q^{37} + 160 q^{38} - 36 q^{39} + 184 q^{40} + 32 q^{41} - 52 q^{43} + 224 q^{44} + 32 q^{45} + 48 q^{46} + 42 q^{47} + 144 q^{48} - 2 q^{49} + 216 q^{50} + 16 q^{51} + 192 q^{52} + 36 q^{53} + 112 q^{54} - 60 q^{55} + 88 q^{56} - 144 q^{57} + 216 q^{58} + 46 q^{59} + 48 q^{60} - 108 q^{61} + 24 q^{62} - 6 q^{63} - 288 q^{64} - 4 q^{65} - 64 q^{66} - 22 q^{67} + 40 q^{68} + 64 q^{69} - 48 q^{70} + 16 q^{71} - 64 q^{72} - 304 q^{73} - 80 q^{74} + 176 q^{75} - 48 q^{76} - 44 q^{77} - 208 q^{78} + 86 q^{79} - 296 q^{80} + 128 q^{81} - 464 q^{82} + 336 q^{83} - 192 q^{84} - 184 q^{85} - 424 q^{86} + 268 q^{87} - 376 q^{88} + 48 q^{89} - 352 q^{90} + 72 q^{91} - 632 q^{92} - 64 q^{93} - 248 q^{94} + 478 q^{95} - 336 q^{96} + 64 q^{97} - 112 q^{98} + 164 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2016))$$

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
2016.2.a $$\chi_{2016}(1, \cdot)$$ 2016.2.a.a 1 1
2016.2.a.b 1
2016.2.a.c 1
2016.2.a.d 1
2016.2.a.e 1
2016.2.a.f 1
2016.2.a.g 1
2016.2.a.h 1
2016.2.a.i 1
2016.2.a.j 1
2016.2.a.k 1
2016.2.a.l 1
2016.2.a.m 1
2016.2.a.n 1
2016.2.a.o 2
2016.2.a.p 2
2016.2.a.q 2
2016.2.a.r 2
2016.2.a.s 2
2016.2.a.t 2
2016.2.a.u 2
2016.2.a.v 2
2016.2.b $$\chi_{2016}(1567, \cdot)$$ 2016.2.b.a 8 1
2016.2.b.b 8
2016.2.b.c 8
2016.2.b.d 16
2016.2.c $$\chi_{2016}(1009, \cdot)$$ 2016.2.c.a 2 1
2016.2.c.b 4
2016.2.c.c 4
2016.2.c.d 4
2016.2.c.e 8
2016.2.c.f 8
2016.2.h $$\chi_{2016}(575, \cdot)$$ 2016.2.h.a 4 1
2016.2.h.b 4
2016.2.h.c 4
2016.2.h.d 4
2016.2.h.e 8
2016.2.i $$\chi_{2016}(881, \cdot)$$ 2016.2.i.a 8 1
2016.2.i.b 24
2016.2.j $$\chi_{2016}(1583, \cdot)$$ 2016.2.j.a 24 1
2016.2.k $$\chi_{2016}(1889, \cdot)$$ 2016.2.k.a 16 1
2016.2.k.b 16
2016.2.p $$\chi_{2016}(559, \cdot)$$ 2016.2.p.a 2 1
2016.2.p.b 4
2016.2.p.c 4
2016.2.p.d 4
2016.2.p.e 4
2016.2.p.f 4
2016.2.p.g 16
2016.2.q $$\chi_{2016}(1537, \cdot)$$ n/a 192 2
2016.2.r $$\chi_{2016}(673, \cdot)$$ n/a 144 2
2016.2.s $$\chi_{2016}(289, \cdot)$$ 2016.2.s.a 2 2
2016.2.s.b 2
2016.2.s.c 2
2016.2.s.d 2
2016.2.s.e 2
2016.2.s.f 2
2016.2.s.g 2
2016.2.s.h 2
2016.2.s.i 2
2016.2.s.j 2
2016.2.s.k 2
2016.2.s.l 2
2016.2.s.m 2
2016.2.s.n 2
2016.2.s.o 4
2016.2.s.p 4
2016.2.s.q 4
2016.2.s.r 4
2016.2.s.s 4
2016.2.s.t 4
2016.2.s.u 6
2016.2.s.v 6
2016.2.s.w 8
2016.2.s.x 8
2016.2.t $$\chi_{2016}(193, \cdot)$$ n/a 192 2
2016.2.v $$\chi_{2016}(71, \cdot)$$ None 0 2
2016.2.x $$\chi_{2016}(55, \cdot)$$ None 0 2
2016.2.z $$\chi_{2016}(505, \cdot)$$ None 0 2
2016.2.bb $$\chi_{2016}(377, \cdot)$$ None 0 2
2016.2.be $$\chi_{2016}(1201, \cdot)$$ n/a 184 2
2016.2.bf $$\chi_{2016}(31, \cdot)$$ n/a 192 2
2016.2.bg $$\chi_{2016}(689, \cdot)$$ n/a 184 2
2016.2.bh $$\chi_{2016}(95, \cdot)$$ n/a 192 2
2016.2.bm $$\chi_{2016}(1231, \cdot)$$ n/a 184 2
2016.2.bn $$\chi_{2016}(367, \cdot)$$ n/a 184 2
2016.2.bs $$\chi_{2016}(271, \cdot)$$ 2016.2.bs.a 12 2
2016.2.bs.b 32
2016.2.bs.c 32
2016.2.bt $$\chi_{2016}(1025, \cdot)$$ 2016.2.bt.a 32 2
2016.2.bt.b 32
2016.2.bu $$\chi_{2016}(431, \cdot)$$ 2016.2.bu.a 8 2
2016.2.bu.b 8
2016.2.bu.c 48
2016.2.bz $$\chi_{2016}(239, \cdot)$$ n/a 144 2
2016.2.ca $$\chi_{2016}(257, \cdot)$$ n/a 192 2
2016.2.cb $$\chi_{2016}(527, \cdot)$$ n/a 184 2
2016.2.cc $$\chi_{2016}(545, \cdot)$$ n/a 192 2
2016.2.ch $$\chi_{2016}(1247, \cdot)$$ n/a 144 2
2016.2.ci $$\chi_{2016}(1265, \cdot)$$ n/a 184 2
2016.2.cj $$\chi_{2016}(767, \cdot)$$ n/a 192 2
2016.2.ck $$\chi_{2016}(209, \cdot)$$ n/a 184 2
2016.2.cp $$\chi_{2016}(17, \cdot)$$ 2016.2.cp.a 8 2
2016.2.cp.b 56
2016.2.cq $$\chi_{2016}(863, \cdot)$$ 2016.2.cq.a 8 2
2016.2.cq.b 8
2016.2.cq.c 8
2016.2.cq.d 8
2016.2.cq.e 32
2016.2.cr $$\chi_{2016}(1297, \cdot)$$ 2016.2.cr.a 8 2
2016.2.cr.b 8
2016.2.cr.c 12
2016.2.cr.d 16
2016.2.cr.e 32
2016.2.cs $$\chi_{2016}(703, \cdot)$$ 2016.2.cs.a 16 2
2016.2.cs.b 16
2016.2.cs.c 16
2016.2.cs.d 32
2016.2.cx $$\chi_{2016}(223, \cdot)$$ n/a 192 2
2016.2.cy $$\chi_{2016}(529, \cdot)$$ n/a 184 2
2016.2.cz $$\chi_{2016}(607, \cdot)$$ n/a 192 2
2016.2.da $$\chi_{2016}(337, \cdot)$$ n/a 144 2
2016.2.df $$\chi_{2016}(929, \cdot)$$ n/a 192 2
2016.2.dg $$\chi_{2016}(1103, \cdot)$$ n/a 184 2
2016.2.dh $$\chi_{2016}(943, \cdot)$$ n/a 184 2
2016.2.dk $$\chi_{2016}(125, \cdot)$$ n/a 512 4
2016.2.dm $$\chi_{2016}(253, \cdot)$$ n/a 480 4
2016.2.do $$\chi_{2016}(323, \cdot)$$ n/a 384 4
2016.2.dq $$\chi_{2016}(307, \cdot)$$ n/a 632 4
2016.2.ds $$\chi_{2016}(391, \cdot)$$ None 0 4
2016.2.du $$\chi_{2016}(407, \cdot)$$ None 0 4
2016.2.dw $$\chi_{2016}(457, \cdot)$$ None 0 4
2016.2.dz $$\chi_{2016}(761, \cdot)$$ None 0 4
2016.2.ea $$\chi_{2016}(89, \cdot)$$ None 0 4
2016.2.ec $$\chi_{2016}(361, \cdot)$$ None 0 4
2016.2.ef $$\chi_{2016}(25, \cdot)$$ None 0 4
2016.2.eg $$\chi_{2016}(185, \cdot)$$ None 0 4
2016.2.ei $$\chi_{2016}(599, \cdot)$$ None 0 4
2016.2.ek $$\chi_{2016}(199, \cdot)$$ None 0 4
2016.2.en $$\chi_{2016}(103, \cdot)$$ None 0 4
2016.2.ep $$\chi_{2016}(23, \cdot)$$ None 0 4
2016.2.eq $$\chi_{2016}(359, \cdot)$$ None 0 4
2016.2.es $$\chi_{2016}(439, \cdot)$$ None 0 4
2016.2.eu $$\chi_{2016}(41, \cdot)$$ None 0 4
2016.2.ew $$\chi_{2016}(169, \cdot)$$ None 0 4
2016.2.ez $$\chi_{2016}(85, \cdot)$$ n/a 2304 8
2016.2.fb $$\chi_{2016}(293, \cdot)$$ n/a 3040 8
2016.2.fc $$\chi_{2016}(11, \cdot)$$ n/a 3040 8
2016.2.fg $$\chi_{2016}(19, \cdot)$$ n/a 1264 8
2016.2.fh $$\chi_{2016}(187, \cdot)$$ n/a 3040 8
2016.2.fk $$\chi_{2016}(347, \cdot)$$ n/a 3040 8
2016.2.fl $$\chi_{2016}(107, \cdot)$$ n/a 1024 8
2016.2.fm $$\chi_{2016}(115, \cdot)$$ n/a 3040 8
2016.2.fo $$\chi_{2016}(5, \cdot)$$ n/a 3040 8
2016.2.fs $$\chi_{2016}(205, \cdot)$$ n/a 3040 8
2016.2.ft $$\chi_{2016}(37, \cdot)$$ n/a 1264 8
2016.2.fw $$\chi_{2016}(269, \cdot)$$ n/a 1024 8
2016.2.fx $$\chi_{2016}(173, \cdot)$$ n/a 3040 8
2016.2.fy $$\chi_{2016}(277, \cdot)$$ n/a 3040 8
2016.2.gb $$\chi_{2016}(139, \cdot)$$ n/a 3040 8
2016.2.gd $$\chi_{2016}(155, \cdot)$$ n/a 2304 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2016))$$ into lower level spaces

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