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Properties

Label 429.2
Level 429
Weight 2
Dimension 4703
Nonzero newspaces 24
Newform subspaces 53
Sturm bound 26880
Trace bound 4

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Defining parameters

Level: \( N \) = \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 53 \)
Sturm bound: \(26880\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(429))\).

Total New Old
Modular forms 7200 5095 2105
Cusp forms 6241 4703 1538
Eisenstein series 959 392 567

Trace form

\( 4703 q + 9 q^{2} - 35 q^{3} - 55 q^{4} + 18 q^{5} - 39 q^{6} - 80 q^{7} - 31 q^{8} - 59 q^{9} + O(q^{10}) \) \( 4703 q + 9 q^{2} - 35 q^{3} - 55 q^{4} + 18 q^{5} - 39 q^{6} - 80 q^{7} - 31 q^{8} - 59 q^{9} - 142 q^{10} - 9 q^{11} - 159 q^{12} - 117 q^{13} - 36 q^{14} - 84 q^{15} - 183 q^{16} - 42 q^{17} - 107 q^{18} - 156 q^{19} - 106 q^{20} - 116 q^{21} - 199 q^{22} - 16 q^{23} - 115 q^{24} - 147 q^{25} - 89 q^{26} - 125 q^{27} - 176 q^{28} - 10 q^{29} - 42 q^{30} - 68 q^{31} + 29 q^{32} - 7 q^{33} - 190 q^{34} + 16 q^{35} + 33 q^{36} - 54 q^{37} + 80 q^{38} - 9 q^{39} - 218 q^{40} - 78 q^{41} - 72 q^{42} - 212 q^{43} - 119 q^{44} - 136 q^{45} - 360 q^{46} - 92 q^{47} - 167 q^{48} - 301 q^{49} - 169 q^{50} - 202 q^{51} - 327 q^{52} - 170 q^{53} - 155 q^{54} - 242 q^{55} - 240 q^{56} - 116 q^{57} - 286 q^{58} - 48 q^{59} - 166 q^{60} - 218 q^{61} - 96 q^{62} - 36 q^{63} - 243 q^{64} - 78 q^{65} - 31 q^{66} - 200 q^{67} - 2 q^{68} + 2 q^{69} - 208 q^{70} + 48 q^{71} + 29 q^{72} - 114 q^{73} + 6 q^{74} - 39 q^{75} - 260 q^{76} - 68 q^{77} + 41 q^{78} - 336 q^{79} - 138 q^{80} + 13 q^{81} - 122 q^{82} - 80 q^{83} - 100 q^{84} - 192 q^{85} - 76 q^{86} - 126 q^{87} - 267 q^{88} - 130 q^{89} - 174 q^{90} - 276 q^{91} - 172 q^{92} - 226 q^{93} - 376 q^{94} - 276 q^{95} - 207 q^{96} - 286 q^{97} - 239 q^{98} - 159 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)

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
429.2.a \(\chi_{429}(1, \cdot)\) 429.2.a.a 1 1
429.2.a.b 1
429.2.a.c 2
429.2.a.d 2
429.2.a.e 3
429.2.a.f 3
429.2.a.g 3
429.2.a.h 4
429.2.b \(\chi_{429}(298, \cdot)\) 429.2.b.a 10 1
429.2.b.b 14
429.2.e \(\chi_{429}(428, \cdot)\) 429.2.e.a 8 1
429.2.e.b 8
429.2.e.c 16
429.2.e.d 20
429.2.f \(\chi_{429}(131, \cdot)\) 429.2.f.a 48 1
429.2.i \(\chi_{429}(100, \cdot)\) 429.2.i.a 2 2
429.2.i.b 2
429.2.i.c 10
429.2.i.d 10
429.2.i.e 10
429.2.i.f 10
429.2.j \(\chi_{429}(122, \cdot)\) 429.2.j.a 96 2
429.2.m \(\chi_{429}(109, \cdot)\) 429.2.m.a 28 2
429.2.m.b 28
429.2.n \(\chi_{429}(157, \cdot)\) 429.2.n.a 12 4
429.2.n.b 20
429.2.n.c 28
429.2.n.d 36
429.2.p \(\chi_{429}(230, \cdot)\) 429.2.p.a 8 2
429.2.p.b 96
429.2.s \(\chi_{429}(166, \cdot)\) 429.2.s.a 24 2
429.2.s.b 28
429.2.t \(\chi_{429}(296, \cdot)\) 429.2.t.a 104 2
429.2.x \(\chi_{429}(248, \cdot)\) 429.2.x.a 192 4
429.2.y \(\chi_{429}(116, \cdot)\) 429.2.y.a 32 4
429.2.y.b 176
429.2.bb \(\chi_{429}(25, \cdot)\) 429.2.bb.a 56 4
429.2.bb.b 56
429.2.bd \(\chi_{429}(76, \cdot)\) 429.2.bd.a 56 4
429.2.bd.b 56
429.2.be \(\chi_{429}(89, \cdot)\) 429.2.be.a 184 4
429.2.bg \(\chi_{429}(16, \cdot)\) 429.2.bg.a 112 8
429.2.bg.b 112
429.2.bi \(\chi_{429}(5, \cdot)\) 429.2.bi.a 416 8
429.2.bj \(\chi_{429}(73, \cdot)\) 429.2.bj.a 112 8
429.2.bj.b 112
429.2.bm \(\chi_{429}(17, \cdot)\) 429.2.bm.a 416 8
429.2.bn \(\chi_{429}(4, \cdot)\) 429.2.bn.a 112 8
429.2.bn.b 112
429.2.bq \(\chi_{429}(29, \cdot)\) 429.2.bq.a 416 8
429.2.bs \(\chi_{429}(7, \cdot)\) 429.2.bs.a 224 16
429.2.bs.b 224
429.2.bv \(\chi_{429}(20, \cdot)\) 429.2.bv.a 832 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(429))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(429)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)