Properties

Label 855.2
Level 855
Weight 2
Dimension 18246
Nonzero newspaces 48
Newform subspaces 126
Sturm bound 103680
Trace bound 11

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Defining parameters

Level: \( N \) = \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Newform subspaces: \( 126 \)
Sturm bound: \(103680\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(855))\).

Total New Old
Modular forms 27072 19166 7906
Cusp forms 24769 18246 6523
Eisenstein series 2303 920 1383

Trace form

\( 18246q - 40q^{2} - 56q^{3} - 32q^{4} - 63q^{5} - 184q^{6} - 30q^{7} - 48q^{8} - 64q^{9} + O(q^{10}) \) \( 18246q - 40q^{2} - 56q^{3} - 32q^{4} - 63q^{5} - 184q^{6} - 30q^{7} - 48q^{8} - 64q^{9} - 213q^{10} - 154q^{11} - 88q^{12} - 26q^{13} - 42q^{14} - 116q^{15} - 76q^{16} - 40q^{17} - 104q^{18} - 100q^{19} - 176q^{20} - 216q^{21} - 16q^{22} - 60q^{23} - 144q^{24} - 69q^{25} - 154q^{26} - 104q^{27} - 100q^{28} - 62q^{29} - 172q^{30} - 110q^{31} + 10q^{32} - 88q^{33} + 8q^{34} - 29q^{35} - 224q^{36} - 112q^{37} + 88q^{38} - 80q^{39} + 46q^{40} - 26q^{41} + 64q^{43} + 10q^{44} - 106q^{45} - 532q^{46} - 100q^{47} - 244q^{48} - 150q^{49} - 208q^{50} - 364q^{51} - 454q^{52} - 274q^{53} - 280q^{54} - 375q^{55} - 912q^{56} - 268q^{57} - 376q^{58} - 412q^{59} - 364q^{60} - 370q^{61} - 456q^{62} - 336q^{63} - 512q^{64} - 286q^{65} - 680q^{66} - 84q^{67} - 446q^{68} - 300q^{69} - 201q^{70} - 380q^{71} - 228q^{72} - 14q^{73} - 14q^{74} - 92q^{75} - 18q^{76} + 78q^{77} + 8q^{78} + 102q^{79} - 209q^{80} - 136q^{81} + 96q^{82} + 108q^{83} + 72q^{84} - 105q^{85} + 92q^{86} + 16q^{87} - 90q^{88} + 132q^{89} + 10q^{90} - 366q^{91} + 84q^{92} + 48q^{93} - 280q^{94} - 230q^{95} - 608q^{96} - 328q^{97} - 626q^{98} - 284q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)

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
855.2.a \(\chi_{855}(1, \cdot)\) 855.2.a.a 1 1
855.2.a.b 1
855.2.a.c 1
855.2.a.d 2
855.2.a.e 2
855.2.a.f 2
855.2.a.g 2
855.2.a.h 3
855.2.a.i 3
855.2.a.j 3
855.2.a.k 3
855.2.a.l 3
855.2.a.m 4
855.2.b \(\chi_{855}(854, \cdot)\) 855.2.b.a 4 1
855.2.b.b 4
855.2.b.c 8
855.2.b.d 24
855.2.c \(\chi_{855}(514, \cdot)\) 855.2.c.a 2 1
855.2.c.b 2
855.2.c.c 2
855.2.c.d 6
855.2.c.e 6
855.2.c.f 12
855.2.c.g 14
855.2.h \(\chi_{855}(341, \cdot)\) 855.2.h.a 24 1
855.2.i \(\chi_{855}(286, \cdot)\) 855.2.i.a 26 2
855.2.i.b 30
855.2.i.c 42
855.2.i.d 46
855.2.j \(\chi_{855}(106, \cdot)\) 855.2.j.a 80 2
855.2.j.b 80
855.2.k \(\chi_{855}(406, \cdot)\) 855.2.k.a 2 2
855.2.k.b 2
855.2.k.c 2
855.2.k.d 2
855.2.k.e 4
855.2.k.f 4
855.2.k.g 6
855.2.k.h 8
855.2.k.i 10
855.2.k.j 12
855.2.k.k 12
855.2.l \(\chi_{855}(391, \cdot)\) 855.2.l.a 80 2
855.2.l.b 80
855.2.n \(\chi_{855}(647, \cdot)\) 855.2.n.a 4 2
855.2.n.b 4
855.2.n.c 8
855.2.n.d 20
855.2.n.e 36
855.2.p \(\chi_{855}(37, \cdot)\) 855.2.p.a 4 2
855.2.p.b 4
855.2.p.c 4
855.2.p.d 4
855.2.p.e 8
855.2.p.f 12
855.2.p.g 24
855.2.p.h 36
855.2.s \(\chi_{855}(49, \cdot)\) 855.2.s.a 232 2
855.2.t \(\chi_{855}(164, \cdot)\) 855.2.t.a 232 2
855.2.w \(\chi_{855}(56, \cdot)\) 855.2.w.a 160 2
855.2.x \(\chi_{855}(221, \cdot)\) 855.2.x.a 160 2
855.2.bc \(\chi_{855}(521, \cdot)\) 855.2.bc.a 48 2
855.2.bd \(\chi_{855}(179, \cdot)\) 855.2.bd.a 16 2
855.2.bd.b 64
855.2.be \(\chi_{855}(64, \cdot)\) 855.2.be.a 4 2
855.2.be.b 8
855.2.be.c 8
855.2.be.d 12
855.2.be.e 24
855.2.be.f 40
855.2.bj \(\chi_{855}(229, \cdot)\) 855.2.bj.a 108 2
855.2.bj.b 108
855.2.bk \(\chi_{855}(619, \cdot)\) 855.2.bk.a 232 2
855.2.bl \(\chi_{855}(284, \cdot)\) 855.2.bl.a 32 2
855.2.bl.b 200
855.2.bm \(\chi_{855}(734, \cdot)\) 855.2.bm.a 232 2
855.2.bp \(\chi_{855}(506, \cdot)\) 855.2.bp.a 160 2
855.2.bs \(\chi_{855}(226, \cdot)\) 855.2.bs.a 12 6
855.2.bs.b 18
855.2.bs.c 18
855.2.bs.d 18
855.2.bs.e 24
855.2.bs.f 30
855.2.bs.g 42
855.2.bs.h 42
855.2.bt \(\chi_{855}(61, \cdot)\) 855.2.bt.a 240 6
855.2.bt.b 240
855.2.bu \(\chi_{855}(16, \cdot)\) 855.2.bu.a 240 6
855.2.bu.b 240
855.2.bv \(\chi_{855}(88, \cdot)\) 855.2.bv.a 464 4
855.2.bx \(\chi_{855}(68, \cdot)\) 855.2.bx.a 464 4
855.2.bz \(\chi_{855}(197, \cdot)\) 855.2.bz.a 160 4
855.2.cc \(\chi_{855}(322, \cdot)\) 855.2.cc.a 464 4
855.2.ce \(\chi_{855}(202, \cdot)\) 855.2.ce.a 464 4
855.2.cg \(\chi_{855}(77, \cdot)\) 855.2.cg.a 4 4
855.2.cg.b 4
855.2.cg.c 208
855.2.cg.d 216
855.2.ci \(\chi_{855}(182, \cdot)\) 855.2.ci.a 464 4
855.2.cj \(\chi_{855}(217, \cdot)\) 855.2.cj.a 4 4
855.2.cj.b 4
855.2.cj.c 4
855.2.cj.d 4
855.2.cj.e 24
855.2.cj.f 72
855.2.cj.g 80
855.2.cn \(\chi_{855}(4, \cdot)\) 855.2.cn.a 696 6
855.2.co \(\chi_{855}(299, \cdot)\) 855.2.co.a 696 6
855.2.cp \(\chi_{855}(41, \cdot)\) 855.2.cp.a 480 6
855.2.cq \(\chi_{855}(71, \cdot)\) 855.2.cq.a 168 6
855.2.cz \(\chi_{855}(14, \cdot)\) 855.2.cz.a 696 6
855.2.da \(\chi_{855}(199, \cdot)\) 855.2.da.a 24 6
855.2.da.b 48
855.2.da.c 96
855.2.da.d 120
855.2.db \(\chi_{855}(89, \cdot)\) 855.2.db.a 240 6
855.2.dc \(\chi_{855}(454, \cdot)\) 855.2.dc.a 696 6
855.2.dd \(\chi_{855}(86, \cdot)\) 855.2.dd.a 480 6
855.2.dh \(\chi_{855}(47, \cdot)\) 855.2.dh.a 1392 12
855.2.dk \(\chi_{855}(13, \cdot)\) 855.2.dk.a 1392 12
855.2.dl \(\chi_{855}(127, \cdot)\) 855.2.dl.a 96 12
855.2.dl.b 240
855.2.dl.c 240
855.2.dm \(\chi_{855}(23, \cdot)\) 855.2.dm.a 1392 12
855.2.dn \(\chi_{855}(17, \cdot)\) 855.2.dn.a 480 12
855.2.dq \(\chi_{855}(22, \cdot)\) 855.2.dq.a 1392 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(855))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(855)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)