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Properties

Label 503.2
Level 503
Weight 2
Dimension 10292
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 42168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(42168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(503))\).

Total New Old
Modular forms 10793 10793 0
Cusp forms 10292 10292 0
Eisenstein series 501 501 0

Trace form

\( 10292 q - 248 q^{2} - 247 q^{3} - 244 q^{4} - 245 q^{5} - 239 q^{6} - 243 q^{7} - 236 q^{8} - 238 q^{9} + O(q^{10}) \) \( 10292 q - 248 q^{2} - 247 q^{3} - 244 q^{4} - 245 q^{5} - 239 q^{6} - 243 q^{7} - 236 q^{8} - 238 q^{9} - 233 q^{10} - 239 q^{11} - 223 q^{12} - 237 q^{13} - 227 q^{14} - 227 q^{15} - 220 q^{16} - 233 q^{17} - 212 q^{18} - 231 q^{19} - 209 q^{20} - 219 q^{21} - 215 q^{22} - 227 q^{23} - 191 q^{24} - 220 q^{25} - 209 q^{26} - 211 q^{27} - 195 q^{28} - 221 q^{29} - 179 q^{30} - 219 q^{31} - 188 q^{32} - 203 q^{33} - 197 q^{34} - 203 q^{35} - 160 q^{36} - 213 q^{37} - 191 q^{38} - 195 q^{39} - 161 q^{40} - 209 q^{41} - 155 q^{42} - 207 q^{43} - 167 q^{44} - 173 q^{45} - 179 q^{46} - 203 q^{47} - 127 q^{48} - 194 q^{49} - 158 q^{50} - 179 q^{51} - 153 q^{52} - 197 q^{53} - 131 q^{54} - 179 q^{55} - 131 q^{56} - 171 q^{57} - 161 q^{58} - 191 q^{59} - 83 q^{60} - 189 q^{61} - 155 q^{62} - 147 q^{63} - 124 q^{64} - 167 q^{65} - 107 q^{66} - 183 q^{67} - 125 q^{68} - 155 q^{69} - 107 q^{70} - 179 q^{71} - 56 q^{72} - 177 q^{73} - 137 q^{74} - 127 q^{75} - 111 q^{76} - 155 q^{77} - 83 q^{78} - 171 q^{79} - 65 q^{80} - 130 q^{81} - 125 q^{82} - 167 q^{83} - 27 q^{84} - 143 q^{85} - 119 q^{86} - 131 q^{87} - 71 q^{88} - 161 q^{89} - 17 q^{90} - 139 q^{91} - 83 q^{92} - 123 q^{93} - 107 q^{94} - 131 q^{95} + q^{96} - 153 q^{97} - 80 q^{98} - 95 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)

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
503.2.a \(\chi_{503}(1, \cdot)\) 503.2.a.a 1 1
503.2.a.b 1
503.2.a.c 1
503.2.a.d 3
503.2.a.e 10
503.2.a.f 26
503.2.c \(\chi_{503}(2, \cdot)\) 503.2.c.a 10250 250