# 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

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

## 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

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