Properties

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

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Defining parameters

Level: \( N \) = \( 501 = 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 10 \)
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

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

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 the 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

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