Properties

Label 819.2
Level 819
Weight 2
Dimension 17640
Nonzero newspaces 84
Newform subspaces 212
Sturm bound 96768
Trace bound 9

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Defining parameters

Level: \( N \) = \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Newform subspaces: \( 212 \)
Sturm bound: \(96768\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(819))\).

Total New Old
Modular forms 25344 18632 6712
Cusp forms 23041 17640 5401
Eisenstein series 2303 992 1311

Trace form

\( 17640q - 54q^{2} - 72q^{3} - 46q^{4} - 48q^{5} - 72q^{6} - 62q^{7} - 108q^{8} - 72q^{9} + O(q^{10}) \) \( 17640q - 54q^{2} - 72q^{3} - 46q^{4} - 48q^{5} - 72q^{6} - 62q^{7} - 108q^{8} - 72q^{9} - 102q^{10} - 24q^{11} - 96q^{12} - 32q^{13} - 162q^{14} - 216q^{15} - 38q^{16} - 78q^{17} - 120q^{18} - 144q^{19} - 78q^{20} - 132q^{21} - 120q^{22} - 60q^{23} - 192q^{24} - 12q^{25} - 36q^{26} - 204q^{27} - 186q^{28} - 186q^{29} - 252q^{30} - 112q^{31} - 306q^{32} - 192q^{33} - 192q^{34} - 216q^{35} - 504q^{36} - 266q^{37} - 432q^{38} - 216q^{39} - 480q^{40} - 294q^{41} - 300q^{42} - 184q^{43} - 432q^{44} - 288q^{45} - 288q^{46} - 168q^{47} - 192q^{48} - 94q^{49} - 264q^{50} - 120q^{51} + 22q^{52} + 36q^{53} - 12q^{54} + 12q^{55} + 102q^{56} - 96q^{57} + 150q^{58} + 204q^{59} + 12q^{60} + 86q^{61} + 264q^{62} + 24q^{63} - 328q^{64} - 126q^{65} - 324q^{66} - 128q^{67} - 210q^{68} - 168q^{69} - 288q^{70} - 420q^{71} - 276q^{72} - 504q^{73} - 594q^{74} - 336q^{75} - 636q^{76} - 396q^{77} - 708q^{78} - 432q^{79} - 1050q^{80} - 432q^{81} - 798q^{82} - 636q^{83} - 552q^{84} - 642q^{85} - 840q^{86} - 444q^{87} - 888q^{88} - 576q^{89} - 708q^{90} - 462q^{91} - 1104q^{92} - 444q^{93} - 612q^{94} - 420q^{95} - 120q^{96} - 280q^{97} - 330q^{98} - 240q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(819))\)

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
819.2.a \(\chi_{819}(1, \cdot)\) 819.2.a.a 1 1
819.2.a.b 1
819.2.a.c 1
819.2.a.d 1
819.2.a.e 1
819.2.a.f 1
819.2.a.g 2
819.2.a.h 2
819.2.a.i 3
819.2.a.j 3
819.2.a.k 4
819.2.a.l 4
819.2.a.m 6
819.2.c \(\chi_{819}(64, \cdot)\) 819.2.c.a 2 1
819.2.c.b 6
819.2.c.c 6
819.2.c.d 8
819.2.c.e 12
819.2.e \(\chi_{819}(755, \cdot)\) 819.2.e.a 32 1
819.2.g \(\chi_{819}(818, \cdot)\) 819.2.g.a 8 1
819.2.g.b 8
819.2.g.c 12
819.2.g.d 12
819.2.i \(\chi_{819}(211, \cdot)\) 819.2.i.a 84 2
819.2.i.b 84
819.2.j \(\chi_{819}(235, \cdot)\) 819.2.j.a 2 2
819.2.j.b 2
819.2.j.c 4
819.2.j.d 6
819.2.j.e 6
819.2.j.f 8
819.2.j.g 10
819.2.j.h 10
819.2.j.i 12
819.2.j.j 20
819.2.k \(\chi_{819}(529, \cdot)\) 819.2.k.a 216 2
819.2.l \(\chi_{819}(373, \cdot)\) 819.2.l.a 216 2
819.2.m \(\chi_{819}(274, \cdot)\) 819.2.m.a 2 2
819.2.m.b 6
819.2.m.c 30
819.2.m.d 34
819.2.m.e 36
819.2.m.f 36
819.2.n \(\chi_{819}(100, \cdot)\) 819.2.n.a 2 2
819.2.n.b 2
819.2.n.c 2
819.2.n.d 12
819.2.n.e 16
819.2.n.f 20
819.2.n.g 36
819.2.o \(\chi_{819}(568, \cdot)\) 819.2.o.a 4 2
819.2.o.b 4
819.2.o.c 4
819.2.o.d 6
819.2.o.e 6
819.2.o.f 6
819.2.o.g 6
819.2.o.h 8
819.2.o.i 12
819.2.o.j 16
819.2.p \(\chi_{819}(16, \cdot)\) 819.2.p.a 216 2
819.2.q \(\chi_{819}(79, \cdot)\) 819.2.q.a 96 2
819.2.q.b 96
819.2.r \(\chi_{819}(625, \cdot)\) 819.2.r.a 96 2
819.2.r.b 96
819.2.s \(\chi_{819}(289, \cdot)\) 819.2.s.a 2 2
819.2.s.b 2
819.2.s.c 2
819.2.s.d 12
819.2.s.e 16
819.2.s.f 20
819.2.s.g 36
819.2.t \(\chi_{819}(22, \cdot)\) 819.2.t.a 84 2
819.2.t.b 84
819.2.u \(\chi_{819}(445, \cdot)\) 819.2.u.a 216 2
819.2.w \(\chi_{819}(8, \cdot)\) 819.2.w.a 28 2
819.2.w.b 28
819.2.y \(\chi_{819}(307, \cdot)\) 819.2.y.a 4 2
819.2.y.b 4
819.2.y.c 4
819.2.y.d 4
819.2.y.e 8
819.2.y.f 12
819.2.y.g 12
819.2.y.h 12
819.2.y.i 32
819.2.z \(\chi_{819}(394, \cdot)\) 819.2.z.a 2 2
819.2.z.b 214
819.2.bb \(\chi_{819}(146, \cdot)\) 819.2.bb.a 2 2
819.2.bb.b 2
819.2.bb.c 212
819.2.be \(\chi_{819}(131, \cdot)\) 819.2.be.a 192 2
819.2.bg \(\chi_{819}(269, \cdot)\) 819.2.bg.a 8 2
819.2.bg.b 68
819.2.bh \(\chi_{819}(589, \cdot)\) 819.2.bh.a 168 2
819.2.bk \(\chi_{819}(25, \cdot)\) 819.2.bk.a 216 2
819.2.bm \(\chi_{819}(478, \cdot)\) 819.2.bm.a 2 2
819.2.bm.b 2
819.2.bm.c 2
819.2.bm.d 4
819.2.bm.e 12
819.2.bm.f 12
819.2.bm.g 20
819.2.bm.h 36
819.2.bn \(\chi_{819}(185, \cdot)\) 819.2.bn.a 216 2
819.2.bq \(\chi_{819}(62, \cdot)\) 819.2.bq.a 72 2
819.2.bs \(\chi_{819}(563, \cdot)\) 819.2.bs.a 216 2
819.2.bt \(\chi_{819}(311, \cdot)\) 819.2.bt.a 216 2
819.2.cc \(\chi_{819}(101, \cdot)\) 819.2.cc.a 216 2
819.2.ce \(\chi_{819}(272, \cdot)\) 819.2.ce.a 216 2
819.2.cf \(\chi_{819}(647, \cdot)\) 819.2.cf.a 76 2
819.2.ch \(\chi_{819}(524, \cdot)\) 819.2.ch.a 216 2
819.2.ci \(\chi_{819}(467, \cdot)\) 819.2.ci.a 72 2
819.2.cm \(\chi_{819}(257, \cdot)\) 819.2.cm.a 216 2
819.2.cq \(\chi_{819}(142, \cdot)\) 819.2.cq.a 216 2
819.2.ct \(\chi_{819}(127, \cdot)\) 819.2.ct.a 12 2
819.2.ct.b 16
819.2.ct.c 16
819.2.ct.d 24
819.2.cv \(\chi_{819}(4, \cdot)\) 819.2.cv.a 2 2
819.2.cv.b 214
819.2.cw \(\chi_{819}(152, \cdot)\) 819.2.cw.a 8 2
819.2.cw.b 68
819.2.cz \(\chi_{819}(698, \cdot)\) 819.2.cz.a 216 2
819.2.db \(\chi_{819}(209, \cdot)\) 819.2.db.a 192 2
819.2.dd \(\chi_{819}(68, \cdot)\) 819.2.dd.a 216 2
819.2.de \(\chi_{819}(419, \cdot)\) 819.2.de.a 2 2
819.2.de.b 2
819.2.de.c 212
819.2.df \(\chi_{819}(404, \cdot)\) 819.2.df.a 64 2
819.2.dj \(\chi_{819}(277, \cdot)\) 819.2.dj.a 2 2
819.2.dj.b 214
819.2.dk \(\chi_{819}(43, \cdot)\) 819.2.dk.a 168 2
819.2.dl \(\chi_{819}(298, \cdot)\) 819.2.dl.a 2 2
819.2.dl.b 2
819.2.dl.c 2
819.2.dl.d 2
819.2.dl.e 16
819.2.dl.f 16
819.2.dl.g 16
819.2.dl.h 32
819.2.do \(\chi_{819}(361, \cdot)\) 819.2.do.a 2 2
819.2.do.b 2
819.2.do.c 2
819.2.do.d 4
819.2.do.e 12
819.2.do.f 12
819.2.do.g 20
819.2.do.h 36
819.2.dr \(\chi_{819}(88, \cdot)\) 819.2.dr.a 2 2
819.2.dr.b 214
819.2.dt \(\chi_{819}(337, \cdot)\) 819.2.dt.a 168 2
819.2.du \(\chi_{819}(248, \cdot)\) 819.2.du.a 192 2
819.2.dx \(\chi_{819}(503, \cdot)\) 819.2.dx.a 72 2
819.2.dz \(\chi_{819}(614, \cdot)\) 819.2.dz.a 216 2
819.2.ea \(\chi_{819}(173, \cdot)\) 819.2.ea.a 216 2
819.2.eg \(\chi_{819}(38, \cdot)\) 819.2.eg.a 216 2
819.2.ei \(\chi_{819}(17, \cdot)\) 819.2.ei.a 76 2
819.2.ej \(\chi_{819}(335, \cdot)\) 819.2.ej.a 216 2
819.2.em \(\chi_{819}(158, \cdot)\) 819.2.em.a 432 4
819.2.ep \(\chi_{819}(229, \cdot)\) 819.2.ep.a 432 4
819.2.eq \(\chi_{819}(202, \cdot)\) 819.2.eq.a 432 4
819.2.et \(\chi_{819}(136, \cdot)\) 819.2.et.a 4 4
819.2.et.b 28
819.2.et.c 36
819.2.et.d 40
819.2.et.e 72
819.2.ev \(\chi_{819}(86, \cdot)\) 819.2.ev.a 432 4
819.2.ew \(\chi_{819}(176, \cdot)\) 819.2.ew.a 336 4
819.2.ez \(\chi_{819}(305, \cdot)\) 819.2.ez.a 152 4
819.2.fa \(\chi_{819}(124, \cdot)\) 819.2.fa.a 432 4
819.2.fd \(\chi_{819}(422, \cdot)\) 819.2.fd.a 152 4
819.2.fe \(\chi_{819}(11, \cdot)\) 819.2.fe.a 432 4
819.2.fh \(\chi_{819}(239, \cdot)\) 819.2.fh.a 336 4
819.2.fk \(\chi_{819}(31, \cdot)\) 819.2.fk.a 432 4
819.2.fl \(\chi_{819}(76, \cdot)\) 819.2.fl.a 432 4
819.2.fm \(\chi_{819}(370, \cdot)\) 819.2.fm.a 4 4
819.2.fm.b 4
819.2.fm.c 4
819.2.fm.d 4
819.2.fm.e 32
819.2.fm.f 32
819.2.fm.g 32
819.2.fm.h 64
819.2.fn \(\chi_{819}(73, \cdot)\) 819.2.fn.a 4 4
819.2.fn.b 4
819.2.fn.c 8
819.2.fn.d 8
819.2.fn.e 32
819.2.fn.f 36
819.2.fn.g 36
819.2.fn.h 48
819.2.fs \(\chi_{819}(241, \cdot)\) 819.2.fs.a 432 4
819.2.ft \(\chi_{819}(409, \cdot)\) 819.2.ft.a 432 4
819.2.fw \(\chi_{819}(71, \cdot)\) 819.2.fw.a 56 4
819.2.fw.b 56
819.2.fx \(\chi_{819}(317, \cdot)\) 819.2.fx.a 432 4
819.2.fy \(\chi_{819}(50, \cdot)\) 819.2.fy.a 336 4
819.2.fz \(\chi_{819}(44, \cdot)\) 819.2.fz.a 144 4
819.2.ge \(\chi_{819}(137, \cdot)\) 819.2.ge.a 432 4
819.2.gf \(\chi_{819}(2, \cdot)\) 819.2.gf.a 432 4
819.2.gh \(\chi_{819}(19, \cdot)\) 819.2.gh.a 4 4
819.2.gh.b 28
819.2.gh.c 36
819.2.gh.d 40
819.2.gh.e 72
819.2.gi \(\chi_{819}(115, \cdot)\) 819.2.gi.a 432 4
819.2.gl \(\chi_{819}(34, \cdot)\) 819.2.gl.a 4 4
819.2.gl.b 4
819.2.gl.c 4
819.2.gl.d 4
819.2.gl.e 416

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(819))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(819)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)