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Properties

Label 455.2
Level 455
Weight 2
Dimension 6675
Nonzero newspaces 50
Newform subspaces 94
Sturm bound 32256
Trace bound 9

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Defining parameters

Level: \( N \) = \( 455 = 5 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 50 \)
Newform subspaces: \( 94 \)
Sturm bound: \(32256\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(455))\).

Total New Old
Modular forms 8640 7331 1309
Cusp forms 7489 6675 814
Eisenstein series 1151 656 495

Trace form

\( 6675 q - 27 q^{2} - 28 q^{3} - 31 q^{4} - 57 q^{5} - 108 q^{6} - 53 q^{7} - 123 q^{8} - 69 q^{9} + O(q^{10}) \) \( 6675 q - 27 q^{2} - 28 q^{3} - 31 q^{4} - 57 q^{5} - 108 q^{6} - 53 q^{7} - 123 q^{8} - 69 q^{9} - 105 q^{10} - 132 q^{11} - 156 q^{12} - 85 q^{13} - 159 q^{14} - 192 q^{15} - 207 q^{16} - 78 q^{17} - 195 q^{18} - 124 q^{19} - 177 q^{20} - 236 q^{21} - 228 q^{22} - 96 q^{23} - 228 q^{24} - 85 q^{25} - 219 q^{26} - 184 q^{27} - 131 q^{28} - 162 q^{29} - 156 q^{30} - 184 q^{31} - 207 q^{32} - 120 q^{33} - 150 q^{34} - 105 q^{35} - 499 q^{36} - 58 q^{37} - 156 q^{38} - 108 q^{39} - 255 q^{40} - 270 q^{41} - 228 q^{42} - 252 q^{43} - 324 q^{44} - 243 q^{45} - 456 q^{46} - 216 q^{47} - 244 q^{48} - 249 q^{49} - 441 q^{50} - 384 q^{51} - 159 q^{52} - 222 q^{53} - 120 q^{54} - 96 q^{55} - 315 q^{56} - 112 q^{57} - 6 q^{58} - 12 q^{59} + 192 q^{60} - 146 q^{61} + 48 q^{62} - 41 q^{63} + 5 q^{64} - 15 q^{65} - 240 q^{66} + 68 q^{67} + 30 q^{68} + 120 q^{69} + 93 q^{70} - 384 q^{71} + 453 q^{72} - 10 q^{73} - 6 q^{74} - 12 q^{75} + 164 q^{76} + 60 q^{77} - 84 q^{78} + 184 q^{79} + 51 q^{80} - 81 q^{81} + 246 q^{82} - 108 q^{83} + 316 q^{84} - 168 q^{85} - 300 q^{86} - 72 q^{87} + 300 q^{88} - 90 q^{89} - 111 q^{90} - 77 q^{91} - 72 q^{92} - 208 q^{93} + 168 q^{94} - 108 q^{95} - 132 q^{96} + 134 q^{97} + 45 q^{98} - 204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(455))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
455.2.a \(\chi_{455}(1, \cdot)\) 455.2.a.a 1 1
455.2.a.b 1
455.2.a.c 4
455.2.a.d 4
455.2.a.e 6
455.2.a.f 7
455.2.c \(\chi_{455}(274, \cdot)\) 455.2.c.a 2 1
455.2.c.b 14
455.2.c.c 20
455.2.d \(\chi_{455}(246, \cdot)\) 455.2.d.a 10 1
455.2.d.b 18
455.2.f \(\chi_{455}(64, \cdot)\) 455.2.f.a 22 1
455.2.f.b 22
455.2.i \(\chi_{455}(211, \cdot)\) 455.2.i.a 2 2
455.2.i.b 2
455.2.i.c 2
455.2.i.d 2
455.2.i.e 10
455.2.i.f 10
455.2.i.g 14
455.2.i.h 14
455.2.j \(\chi_{455}(261, \cdot)\) 455.2.j.a 2 2
455.2.j.b 2
455.2.j.c 2
455.2.j.d 8
455.2.j.e 14
455.2.j.f 16
455.2.j.g 20
455.2.k \(\chi_{455}(81, \cdot)\) 455.2.k.a 38 2
455.2.k.b 38
455.2.l \(\chi_{455}(16, \cdot)\) 455.2.l.a 38 2
455.2.l.b 38
455.2.m \(\chi_{455}(148, \cdot)\) 455.2.m.a 4 2
455.2.m.b 38
455.2.m.c 42
455.2.p \(\chi_{455}(216, \cdot)\) 455.2.p.a 80 2
455.2.r \(\chi_{455}(27, \cdot)\) 455.2.r.a 8 2
455.2.r.b 88
455.2.s \(\chi_{455}(272, \cdot)\) 455.2.s.a 8 2
455.2.s.b 8
455.2.s.c 8
455.2.s.d 8
455.2.s.e 72
455.2.u \(\chi_{455}(34, \cdot)\) 455.2.u.a 8 2
455.2.u.b 96
455.2.x \(\chi_{455}(8, \cdot)\) 455.2.x.a 4 2
455.2.x.b 38
455.2.x.c 42
455.2.z \(\chi_{455}(186, \cdot)\) 455.2.z.a 76 2
455.2.ba \(\chi_{455}(74, \cdot)\) 455.2.ba.a 104 2
455.2.bc \(\chi_{455}(179, \cdot)\) 455.2.bc.a 104 2
455.2.bh \(\chi_{455}(324, \cdot)\) 455.2.bh.a 104 2
455.2.bj \(\chi_{455}(134, \cdot)\) 455.2.bj.a 44 2
455.2.bj.b 44
455.2.bm \(\chi_{455}(9, \cdot)\) 455.2.bm.a 104 2
455.2.bo \(\chi_{455}(51, \cdot)\) 455.2.bo.a 72 2
455.2.bq \(\chi_{455}(36, \cdot)\) 455.2.bq.a 20 2
455.2.bq.b 36
455.2.br \(\chi_{455}(29, \cdot)\) 455.2.br.a 4 2
455.2.br.b 76
455.2.bt \(\chi_{455}(79, \cdot)\) 455.2.bt.a 96 2
455.2.bv \(\chi_{455}(121, \cdot)\) 455.2.bv.a 76 2
455.2.bz \(\chi_{455}(4, \cdot)\) 455.2.bz.a 104 2
455.2.cb \(\chi_{455}(37, \cdot)\) 455.2.cb.a 208 4
455.2.cd \(\chi_{455}(67, \cdot)\) 455.2.cd.a 208 4
455.2.ce \(\chi_{455}(162, \cdot)\) 455.2.ce.a 4 4
455.2.ce.b 80
455.2.ce.c 84
455.2.cg \(\chi_{455}(268, \cdot)\) 455.2.cg.a 208 4
455.2.ci \(\chi_{455}(171, \cdot)\) 455.2.ci.a 152 4
455.2.cl \(\chi_{455}(54, \cdot)\) 455.2.cl.a 208 4
455.2.cn \(\chi_{455}(279, \cdot)\) 455.2.cn.a 16 4
455.2.cn.b 192
455.2.co \(\chi_{455}(164, \cdot)\) 455.2.co.a 208 4
455.2.cr \(\chi_{455}(17, \cdot)\) 455.2.cr.a 208 4
455.2.cs \(\chi_{455}(68, \cdot)\) 455.2.cs.a 208 4
455.2.cu \(\chi_{455}(157, \cdot)\) 455.2.cu.a 192 4
455.2.cw \(\chi_{455}(82, \cdot)\) 455.2.cw.a 208 4
455.2.cz \(\chi_{455}(62, \cdot)\) 455.2.cz.a 8 4
455.2.cz.b 8
455.2.cz.c 192
455.2.db \(\chi_{455}(3, \cdot)\) 455.2.db.a 208 4
455.2.dc \(\chi_{455}(48, \cdot)\) 455.2.dc.a 208 4
455.2.df \(\chi_{455}(12, \cdot)\) 455.2.df.a 208 4
455.2.dg \(\chi_{455}(136, \cdot)\) 455.2.dg.a 152 4
455.2.dj \(\chi_{455}(31, \cdot)\) 455.2.dj.a 144 4
455.2.dk \(\chi_{455}(6, \cdot)\) 455.2.dk.a 144 4
455.2.dn \(\chi_{455}(19, \cdot)\) 455.2.dn.a 208 4
455.2.do \(\chi_{455}(58, \cdot)\) 455.2.do.a 208 4
455.2.dr \(\chi_{455}(18, \cdot)\) 455.2.dr.a 208 4
455.2.dt \(\chi_{455}(232, \cdot)\) 455.2.dt.a 4 4
455.2.dt.b 80
455.2.dt.c 84
455.2.du \(\chi_{455}(2, \cdot)\) 455.2.du.a 208 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(455))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(455)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)