# Properties

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

## 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

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

## 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

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