Properties

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

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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

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