# Properties

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

## 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

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

## 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 the 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