# Properties

 Label 2015.2 Level 2015 Weight 2 Dimension 143867 Nonzero newspaces 100 Sturm bound 645120 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2015 = 5 \cdot 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$645120$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2015))$$.

Total New Old
Modular forms 164160 147691 16469
Cusp forms 158401 143867 14534
Eisenstein series 5759 3824 1935

## Trace form

 $$143867q - 267q^{2} - 264q^{3} - 255q^{4} - 411q^{5} - 792q^{6} - 260q^{7} - 267q^{8} - 269q^{9} + O(q^{10})$$ $$143867q - 267q^{2} - 264q^{3} - 255q^{4} - 411q^{5} - 792q^{6} - 260q^{7} - 267q^{8} - 269q^{9} - 435q^{10} - 816q^{11} - 296q^{12} - 327q^{13} - 588q^{14} - 426q^{15} - 815q^{16} - 258q^{17} - 291q^{18} - 296q^{19} - 459q^{20} - 856q^{21} - 408q^{22} - 312q^{23} - 576q^{24} - 443q^{25} - 1017q^{26} - 816q^{27} - 628q^{28} - 414q^{29} - 672q^{30} - 973q^{31} - 1011q^{32} - 420q^{33} - 546q^{34} - 534q^{35} - 1211q^{36} - 410q^{37} - 384q^{38} - 396q^{39} - 1137q^{40} - 942q^{41} - 468q^{42} - 348q^{43} - 336q^{44} - 525q^{45} - 948q^{46} - 300q^{47} - 324q^{48} - 457q^{49} - 717q^{50} - 1188q^{51} - 431q^{52} - 666q^{53} - 696q^{54} - 486q^{55} - 1176q^{56} - 452q^{57} - 510q^{58} - 240q^{59} - 588q^{60} - 1194q^{61} - 483q^{62} - 800q^{63} - 459q^{64} - 492q^{65} - 2448q^{66} - 224q^{67} - 450q^{68} - 324q^{69} - 600q^{70} - 996q^{71} - 519q^{72} - 302q^{73} - 510q^{74} - 596q^{75} - 1180q^{76} - 504q^{77} - 660q^{78} - 656q^{79} - 843q^{80} - 1025q^{81} - 558q^{82} - 756q^{83} - 908q^{84} - 666q^{85} - 1416q^{86} - 636q^{87} - 1152q^{88} - 690q^{89} - 1191q^{90} - 1224q^{91} - 1464q^{92} - 784q^{93} - 960q^{94} - 810q^{95} - 1956q^{96} - 562q^{97} - 1059q^{98} - 708q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2015))$$

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
2015.2.a $$\chi_{2015}(1, \cdot)$$ 2015.2.a.a 1 1
2015.2.a.b 1
2015.2.a.c 1
2015.2.a.d 3
2015.2.a.e 6
2015.2.a.f 7
2015.2.a.g 8
2015.2.a.h 8
2015.2.a.i 20
2015.2.a.j 20
2015.2.a.k 22
2015.2.a.l 22
2015.2.c $$\chi_{2015}(404, \cdot)$$ n/a 180 1
2015.2.d $$\chi_{2015}(311, \cdot)$$ n/a 140 1
2015.2.f $$\chi_{2015}(714, \cdot)$$ n/a 212 1
2015.2.i $$\chi_{2015}(776, \cdot)$$ n/a 280 2
2015.2.j $$\chi_{2015}(191, \cdot)$$ n/a 300 2
2015.2.k $$\chi_{2015}(1121, \cdot)$$ n/a 300 2
2015.2.l $$\chi_{2015}(521, \cdot)$$ n/a 256 2
2015.2.m $$\chi_{2015}(993, \cdot)$$ n/a 420 2
2015.2.o $$\chi_{2015}(216, \cdot)$$ n/a 304 2
2015.2.q $$\chi_{2015}(92, \cdot)$$ n/a 384 2
2015.2.t $$\chi_{2015}(402, \cdot)$$ n/a 440 2
2015.2.u $$\chi_{2015}(619, \cdot)$$ n/a 440 2
2015.2.w $$\chi_{2015}(187, \cdot)$$ n/a 420 2
2015.2.y $$\chi_{2015}(66, \cdot)$$ n/a 512 4
2015.2.ba $$\chi_{2015}(831, \cdot)$$ n/a 296 2
2015.2.bb $$\chi_{2015}(924, \cdot)$$ n/a 384 2
2015.2.be $$\chi_{2015}(439, \cdot)$$ n/a 440 2
2015.2.bh $$\chi_{2015}(1369, \cdot)$$ n/a 440 2
2015.2.bk $$\chi_{2015}(1024, \cdot)$$ n/a 424 2
2015.2.bm $$\chi_{2015}(1524, \cdot)$$ n/a 440 2
2015.2.bo $$\chi_{2015}(966, \cdot)$$ n/a 300 2
2015.2.br $$\chi_{2015}(621, \cdot)$$ n/a 280 2
2015.2.bs $$\chi_{2015}(94, \cdot)$$ n/a 416 2
2015.2.bv $$\chi_{2015}(594, \cdot)$$ n/a 440 2
2015.2.bx $$\chi_{2015}(36, \cdot)$$ n/a 300 2
2015.2.ca $$\chi_{2015}(129, \cdot)$$ n/a 440 2
2015.2.cd $$\chi_{2015}(64, \cdot)$$ n/a 880 4
2015.2.cf $$\chi_{2015}(376, \cdot)$$ n/a 608 4
2015.2.cg $$\chi_{2015}(469, \cdot)$$ n/a 768 4
2015.2.ci $$\chi_{2015}(242, \cdot)$$ n/a 880 4
2015.2.cl $$\chi_{2015}(98, \cdot)$$ n/a 880 4
2015.2.cn $$\chi_{2015}(67, \cdot)$$ n/a 880 4
2015.2.cp $$\chi_{2015}(32, \cdot)$$ n/a 840 4
2015.2.cr $$\chi_{2015}(6, \cdot)$$ n/a 600 4
2015.2.cs $$\chi_{2015}(99, \cdot)$$ n/a 880 4
2015.2.cv $$\chi_{2015}(154, \cdot)$$ n/a 880 4
2015.2.cx $$\chi_{2015}(1029, \cdot)$$ n/a 880 4
2015.2.cy $$\chi_{2015}(688, \cdot)$$ n/a 880 4
2015.2.db $$\chi_{2015}(378, \cdot)$$ n/a 768 4
2015.2.dc $$\chi_{2015}(68, \cdot)$$ n/a 880 4
2015.2.de $$\chi_{2015}(88, \cdot)$$ n/a 880 4
2015.2.dg $$\chi_{2015}(433, \cdot)$$ n/a 880 4
2015.2.dj $$\chi_{2015}(347, \cdot)$$ n/a 880 4
2015.2.dl $$\chi_{2015}(588, \cdot)$$ n/a 880 4
2015.2.dn $$\chi_{2015}(192, \cdot)$$ n/a 880 4
2015.2.do $$\chi_{2015}(161, \cdot)$$ n/a 592 4
2015.2.dr $$\chi_{2015}(626, \cdot)$$ n/a 600 4
2015.2.dt $$\chi_{2015}(371, \cdot)$$ n/a 592 4
2015.2.dv $$\chi_{2015}(119, \cdot)$$ n/a 880 4
2015.2.dx $$\chi_{2015}(397, \cdot)$$ n/a 880 4
2015.2.dz $$\chi_{2015}(838, \cdot)$$ n/a 840 4
2015.2.eb $$\chi_{2015}(253, \cdot)$$ n/a 880 4
2015.2.ec $$\chi_{2015}(707, \cdot)$$ n/a 880 4
2015.2.ee $$\chi_{2015}(131, \cdot)$$ n/a 1024 8
2015.2.ef $$\chi_{2015}(386, \cdot)$$ n/a 1200 8
2015.2.eg $$\chi_{2015}(16, \cdot)$$ n/a 1184 8
2015.2.eh $$\chi_{2015}(81, \cdot)$$ n/a 1200 8
2015.2.ej $$\chi_{2015}(8, \cdot)$$ n/a 1760 8
2015.2.el $$\chi_{2015}(294, \cdot)$$ n/a 1760 8
2015.2.en $$\chi_{2015}(27, \cdot)$$ n/a 1536 8
2015.2.eo $$\chi_{2015}(77, \cdot)$$ n/a 1760 8
2015.2.er $$\chi_{2015}(151, \cdot)$$ n/a 1216 8
2015.2.et $$\chi_{2015}(47, \cdot)$$ n/a 1760 8
2015.2.eu $$\chi_{2015}(324, \cdot)$$ n/a 1760 8
2015.2.ex $$\chi_{2015}(121, \cdot)$$ n/a 1200 8
2015.2.fa $$\chi_{2015}(159, \cdot)$$ n/a 1760 8
2015.2.fb $$\chi_{2015}(9, \cdot)$$ n/a 1760 8
2015.2.fe $$\chi_{2015}(231, \cdot)$$ n/a 1200 8
2015.2.ff $$\chi_{2015}(101, \cdot)$$ n/a 1184 8
2015.2.fi $$\chi_{2015}(289, \cdot)$$ n/a 1760 8
2015.2.fl $$\chi_{2015}(134, \cdot)$$ n/a 1760 8
2015.2.fm $$\chi_{2015}(4, \cdot)$$ n/a 1760 8
2015.2.fq $$\chi_{2015}(49, \cdot)$$ n/a 1760 8
2015.2.ft $$\chi_{2015}(14, \cdot)$$ n/a 1536 8
2015.2.fu $$\chi_{2015}(51, \cdot)$$ n/a 1184 8
2015.2.fx $$\chi_{2015}(138, \cdot)$$ n/a 3520 16
2015.2.fy $$\chi_{2015}(28, \cdot)$$ n/a 3520 16
2015.2.ga $$\chi_{2015}(188, \cdot)$$ n/a 3520 16
2015.2.gc $$\chi_{2015}(7, \cdot)$$ n/a 3520 16
2015.2.ge $$\chi_{2015}(189, \cdot)$$ n/a 3520 16
2015.2.gg $$\chi_{2015}(46, \cdot)$$ n/a 2368 16
2015.2.gi $$\chi_{2015}(141, \cdot)$$ n/a 2400 16
2015.2.gl $$\chi_{2015}(21, \cdot)$$ n/a 2368 16
2015.2.gn $$\chi_{2015}(3, \cdot)$$ n/a 3520 16
2015.2.gp $$\chi_{2015}(23, \cdot)$$ n/a 3520 16
2015.2.gr $$\chi_{2015}(17, \cdot)$$ n/a 3520 16
2015.2.gs $$\chi_{2015}(178, \cdot)$$ n/a 3520 16
2015.2.gu $$\chi_{2015}(42, \cdot)$$ n/a 3520 16
2015.2.gw $$\chi_{2015}(127, \cdot)$$ n/a 3520 16
2015.2.gz $$\chi_{2015}(12, \cdot)$$ n/a 3520 16
2015.2.ha $$\chi_{2015}(53, \cdot)$$ n/a 3072 16
2015.2.hc $$\chi_{2015}(24, \cdot)$$ n/a 3520 16
2015.2.he $$\chi_{2015}(54, \cdot)$$ n/a 3520 16
2015.2.hh $$\chi_{2015}(34, \cdot)$$ n/a 3520 16
2015.2.hi $$\chi_{2015}(11, \cdot)$$ n/a 2400 16
2015.2.hk $$\chi_{2015}(2, \cdot)$$ n/a 3520 16
2015.2.hm $$\chi_{2015}(162, \cdot)$$ n/a 3520 16
2015.2.ho $$\chi_{2015}(193, \cdot)$$ n/a 3520 16
2015.2.hr $$\chi_{2015}(18, \cdot)$$ n/a 3520 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2015))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2015)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(403))$$$$^{\oplus 2}$$