↑

Properties

Label 431.2
Level 431
Weight 2
Dimension 7526
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 30960
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 431 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(30960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(431))\).

Total New Old
Modular forms 7955 7955 0
Cusp forms 7526 7526 0
Eisenstein series 429 429 0

Trace form

\( 7526 q - 212 q^{2} - 211 q^{3} - 208 q^{4} - 209 q^{5} - 203 q^{6} - 207 q^{7} - 200 q^{8} - 202 q^{9} + O(q^{10}) \) \( 7526 q - 212 q^{2} - 211 q^{3} - 208 q^{4} - 209 q^{5} - 203 q^{6} - 207 q^{7} - 200 q^{8} - 202 q^{9} - 197 q^{10} - 203 q^{11} - 187 q^{12} - 201 q^{13} - 191 q^{14} - 191 q^{15} - 184 q^{16} - 197 q^{17} - 176 q^{18} - 195 q^{19} - 173 q^{20} - 183 q^{21} - 179 q^{22} - 191 q^{23} - 155 q^{24} - 184 q^{25} - 173 q^{26} - 175 q^{27} - 159 q^{28} - 185 q^{29} - 143 q^{30} - 183 q^{31} - 152 q^{32} - 167 q^{33} - 161 q^{34} - 167 q^{35} - 124 q^{36} - 177 q^{37} - 155 q^{38} - 159 q^{39} - 125 q^{40} - 173 q^{41} - 119 q^{42} - 171 q^{43} - 131 q^{44} - 137 q^{45} - 143 q^{46} - 167 q^{47} - 91 q^{48} - 158 q^{49} - 122 q^{50} - 143 q^{51} - 117 q^{52} - 161 q^{53} - 95 q^{54} - 143 q^{55} - 95 q^{56} - 135 q^{57} - 125 q^{58} - 155 q^{59} - 47 q^{60} - 153 q^{61} - 119 q^{62} - 111 q^{63} - 88 q^{64} - 131 q^{65} - 71 q^{66} - 147 q^{67} - 89 q^{68} - 119 q^{69} - 71 q^{70} - 143 q^{71} - 20 q^{72} - 141 q^{73} - 101 q^{74} - 91 q^{75} - 75 q^{76} - 119 q^{77} - 47 q^{78} - 135 q^{79} - 29 q^{80} - 94 q^{81} - 89 q^{82} - 131 q^{83} + 9 q^{84} - 107 q^{85} - 83 q^{86} - 95 q^{87} - 35 q^{88} - 125 q^{89} + 19 q^{90} - 103 q^{91} - 47 q^{92} - 87 q^{93} - 71 q^{94} - 95 q^{95} + 37 q^{96} - 117 q^{97} - 44 q^{98} - 59 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(431))\)

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
431.2.a \(\chi_{431}(1, \cdot)\) 431.2.a.a 1 1
431.2.a.b 1
431.2.a.c 3
431.2.a.d 3
431.2.a.e 4
431.2.a.f 24
431.2.c \(\chi_{431}(95, \cdot)\) 431.2.c.a 140 4
431.2.e \(\chi_{431}(2, \cdot)\) 431.2.e.a 1470 42
431.2.g \(\chi_{431}(5, \cdot)\) 431.2.g.a 5880 168