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Properties

Label 463.2
Level 463
Weight 2
Dimension 8702
Nonzero newspaces 8
Newform subspaces 9
Sturm bound 35728
Trace bound 1

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Defining parameters

Level: \( N \) = \( 463 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 9 \)
Sturm bound: \(35728\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(463))\).

Total New Old
Modular forms 9163 9163 0
Cusp forms 8702 8702 0
Eisenstein series 461 461 0

Trace form

\( 8702 q - 228 q^{2} - 227 q^{3} - 224 q^{4} - 225 q^{5} - 219 q^{6} - 223 q^{7} - 216 q^{8} - 218 q^{9} + O(q^{10}) \) \( 8702 q - 228 q^{2} - 227 q^{3} - 224 q^{4} - 225 q^{5} - 219 q^{6} - 223 q^{7} - 216 q^{8} - 218 q^{9} - 213 q^{10} - 219 q^{11} - 203 q^{12} - 217 q^{13} - 207 q^{14} - 207 q^{15} - 200 q^{16} - 213 q^{17} - 192 q^{18} - 211 q^{19} - 189 q^{20} - 199 q^{21} - 195 q^{22} - 207 q^{23} - 171 q^{24} - 200 q^{25} - 189 q^{26} - 191 q^{27} - 175 q^{28} - 201 q^{29} - 159 q^{30} - 199 q^{31} - 168 q^{32} - 183 q^{33} - 177 q^{34} - 183 q^{35} - 140 q^{36} - 193 q^{37} - 171 q^{38} - 175 q^{39} - 141 q^{40} - 189 q^{41} - 135 q^{42} - 187 q^{43} - 147 q^{44} - 153 q^{45} - 159 q^{46} - 183 q^{47} - 107 q^{48} - 174 q^{49} - 138 q^{50} - 159 q^{51} - 133 q^{52} - 177 q^{53} - 111 q^{54} - 159 q^{55} - 111 q^{56} - 151 q^{57} - 141 q^{58} - 171 q^{59} - 63 q^{60} - 169 q^{61} - 135 q^{62} - 127 q^{63} - 104 q^{64} - 147 q^{65} - 87 q^{66} - 163 q^{67} - 105 q^{68} - 135 q^{69} - 87 q^{70} - 159 q^{71} - 36 q^{72} - 157 q^{73} - 117 q^{74} - 107 q^{75} - 91 q^{76} - 135 q^{77} - 63 q^{78} - 151 q^{79} - 45 q^{80} - 110 q^{81} - 105 q^{82} - 147 q^{83} - 7 q^{84} - 123 q^{85} - 99 q^{86} - 111 q^{87} - 51 q^{88} - 141 q^{89} + 3 q^{90} - 119 q^{91} - 63 q^{92} - 103 q^{93} - 87 q^{94} - 111 q^{95} + 21 q^{96} - 133 q^{97} - 60 q^{98} - 75 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(463))\)

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
463.2.a \(\chi_{463}(1, \cdot)\) 463.2.a.a 16 1
463.2.a.b 22
463.2.c \(\chi_{463}(21, \cdot)\) 463.2.c.a 76 2
463.2.e \(\chi_{463}(34, \cdot)\) 463.2.e.a 222 6
463.2.f \(\chi_{463}(15, \cdot)\) 463.2.f.a 370 10
463.2.h \(\chi_{463}(33, \cdot)\) 463.2.h.a 456 12
463.2.j \(\chi_{463}(36, \cdot)\) 463.2.j.a 760 20
463.2.m \(\chi_{463}(8, \cdot)\) 463.2.m.a 2220 60
463.2.o \(\chi_{463}(2, \cdot)\) 463.2.o.a 4560 120