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Properties

Label 501.2
Level 501
Weight 2
Dimension 6805
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 37184
Trace bound 1

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Defining parameters

Level: \( N \) = \( 501 = 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(37184\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(501))\).

Total New Old
Modular forms 9628 7137 2491
Cusp forms 8965 6805 2160
Eisenstein series 663 332 331

Trace form

\( 6805 q - 3 q^{2} - 84 q^{3} - 173 q^{4} - 6 q^{5} - 86 q^{6} - 174 q^{7} - 15 q^{8} - 84 q^{9} + O(q^{10}) \) \( 6805 q - 3 q^{2} - 84 q^{3} - 173 q^{4} - 6 q^{5} - 86 q^{6} - 174 q^{7} - 15 q^{8} - 84 q^{9} - 184 q^{10} - 12 q^{11} - 90 q^{12} - 180 q^{13} - 24 q^{14} - 89 q^{15} - 197 q^{16} - 18 q^{17} - 86 q^{18} - 186 q^{19} - 42 q^{20} - 91 q^{21} - 202 q^{22} - 24 q^{23} - 98 q^{24} - 197 q^{25} - 42 q^{26} - 84 q^{27} - 222 q^{28} - 30 q^{29} - 101 q^{30} - 198 q^{31} - 63 q^{32} - 95 q^{33} - 220 q^{34} - 48 q^{35} - 90 q^{36} - 204 q^{37} - 60 q^{38} - 97 q^{39} - 256 q^{40} - 42 q^{41} - 107 q^{42} - 210 q^{43} - 84 q^{44} - 89 q^{45} - 238 q^{46} - 48 q^{47} - 114 q^{48} - 223 q^{49} - 93 q^{50} - 101 q^{51} - 264 q^{52} - 54 q^{53} - 86 q^{54} - 238 q^{55} - 120 q^{56} - 103 q^{57} - 256 q^{58} - 60 q^{59} - 125 q^{60} - 228 q^{61} - 96 q^{62} - 91 q^{63} - 293 q^{64} - 84 q^{65} - 119 q^{66} - 234 q^{67} - 126 q^{68} - 107 q^{69} - 310 q^{70} - 72 q^{71} - 98 q^{72} - 240 q^{73} - 114 q^{74} - 114 q^{75} - 306 q^{76} - 96 q^{77} - 125 q^{78} - 246 q^{79} - 186 q^{80} - 84 q^{81} - 292 q^{82} - 84 q^{83} - 139 q^{84} - 274 q^{85} - 132 q^{86} - 113 q^{87} - 346 q^{88} - 90 q^{89} - 101 q^{90} - 278 q^{91} - 168 q^{92} - 115 q^{93} - 310 q^{94} - 120 q^{95} - 146 q^{96} - 264 q^{97} - 171 q^{98} - 95 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)

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
501.2.a \(\chi_{501}(1, \cdot)\) 501.2.a.a 1 1
501.2.a.b 5
501.2.a.c 5
501.2.a.d 8
501.2.a.e 8
501.2.c \(\chi_{501}(500, \cdot)\) 501.2.c.a 22 1
501.2.c.b 32
501.2.e \(\chi_{501}(4, \cdot)\) 501.2.e.a 1148 82
501.2.e.b 1148
501.2.g \(\chi_{501}(5, \cdot)\) 501.2.g.a 4428 82

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(501))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(501)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 2}\)