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Properties

Label 471.2
Level 471
Weight 2
Dimension 6005
Nonzero newspaces 12
Newform subspaces 26
Sturm bound 32864
Trace bound 1

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Defining parameters

Level: \( N \) = \( 471 = 3 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 26 \)
Sturm bound: \(32864\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(471))\).

Total New Old
Modular forms 8528 6317 2211
Cusp forms 7905 6005 1900
Eisenstein series 623 312 311

Trace form

\( 6005 q - 3 q^{2} - 79 q^{3} - 163 q^{4} - 6 q^{5} - 81 q^{6} - 164 q^{7} - 15 q^{8} - 79 q^{9} + O(q^{10}) \) \( 6005 q - 3 q^{2} - 79 q^{3} - 163 q^{4} - 6 q^{5} - 81 q^{6} - 164 q^{7} - 15 q^{8} - 79 q^{9} - 174 q^{10} - 12 q^{11} - 85 q^{12} - 170 q^{13} - 24 q^{14} - 84 q^{15} - 187 q^{16} - 18 q^{17} - 81 q^{18} - 176 q^{19} - 42 q^{20} - 86 q^{21} - 192 q^{22} - 24 q^{23} - 93 q^{24} - 187 q^{25} - 42 q^{26} - 79 q^{27} - 212 q^{28} - 30 q^{29} - 96 q^{30} - 188 q^{31} - 63 q^{32} - 90 q^{33} - 210 q^{34} - 48 q^{35} - 85 q^{36} - 194 q^{37} - 60 q^{38} - 92 q^{39} - 246 q^{40} - 42 q^{41} - 102 q^{42} - 200 q^{43} - 84 q^{44} - 84 q^{45} - 228 q^{46} - 48 q^{47} - 109 q^{48} - 213 q^{49} - 93 q^{50} - 96 q^{51} - 254 q^{52} - 54 q^{53} - 81 q^{54} - 228 q^{55} - 120 q^{56} - 98 q^{57} - 246 q^{58} - 60 q^{59} - 120 q^{60} - 218 q^{61} - 96 q^{62} - 86 q^{63} - 283 q^{64} - 84 q^{65} - 114 q^{66} - 224 q^{67} - 126 q^{68} - 102 q^{69} - 300 q^{70} - 72 q^{71} - 93 q^{72} - 230 q^{73} - 114 q^{74} - 109 q^{75} - 296 q^{76} - 96 q^{77} - 120 q^{78} - 236 q^{79} - 186 q^{80} - 79 q^{81} - 282 q^{82} - 84 q^{83} - 134 q^{84} - 264 q^{85} - 132 q^{86} - 108 q^{87} - 336 q^{88} - 90 q^{89} - 96 q^{90} - 268 q^{91} - 168 q^{92} - 110 q^{93} - 300 q^{94} - 120 q^{95} - 141 q^{96} - 254 q^{97} - 171 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(471))\)

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
471.2.a \(\chi_{471}(1, \cdot)\) 471.2.a.a 1 1
471.2.a.b 2
471.2.a.c 3
471.2.a.d 9
471.2.a.e 12
471.2.b \(\chi_{471}(313, \cdot)\) 471.2.b.a 12 1
471.2.b.b 14
471.2.e \(\chi_{471}(169, \cdot)\) 471.2.e.a 4 2
471.2.e.b 22
471.2.e.c 28
471.2.f \(\chi_{471}(185, \cdot)\) 471.2.f.a 100 2
471.2.h \(\chi_{471}(13, \cdot)\) 471.2.h.a 24 2
471.2.h.b 26
471.2.l \(\chi_{471}(50, \cdot)\) 471.2.l.a 4 4
471.2.l.b 200
471.2.m \(\chi_{471}(16, \cdot)\) 471.2.m.a 156 12
471.2.m.b 180
471.2.p \(\chi_{471}(4, \cdot)\) 471.2.p.a 144 12
471.2.p.b 168
471.2.q \(\chi_{471}(19, \cdot)\) 471.2.q.a 312 24
471.2.q.b 336
471.2.s \(\chi_{471}(2, \cdot)\) 471.2.s.a 1200 24
471.2.v \(\chi_{471}(10, \cdot)\) 471.2.v.a 288 24
471.2.v.b 312
471.2.w \(\chi_{471}(5, \cdot)\) 471.2.w.a 48 48
471.2.w.b 2400

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(471))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(471)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(157))\)\(^{\oplus 2}\)