## Defining parameters

 Level: $$N$$ = $$1503 = 3^{2} \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$334656$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1503))$$.

Total New Old
Modular forms 84992 66971 18021
Cusp forms 82337 65487 16850
Eisenstein series 2655 1484 1171

## Trace form

 $$65487q - 249q^{2} - 332q^{3} - 249q^{4} - 249q^{5} - 332q^{6} - 249q^{7} - 249q^{8} - 332q^{9} + O(q^{10})$$ $$65487q - 249q^{2} - 332q^{3} - 249q^{4} - 249q^{5} - 332q^{6} - 249q^{7} - 249q^{8} - 332q^{9} - 747q^{10} - 249q^{11} - 332q^{12} - 249q^{13} - 249q^{14} - 332q^{15} - 249q^{16} - 249q^{17} - 332q^{18} - 747q^{19} - 249q^{20} - 332q^{21} - 249q^{22} - 249q^{23} - 332q^{24} - 249q^{25} - 249q^{26} - 332q^{27} - 747q^{28} - 249q^{29} - 332q^{30} - 249q^{31} - 249q^{32} - 332q^{33} - 249q^{34} - 249q^{35} - 332q^{36} - 747q^{37} - 249q^{38} - 332q^{39} - 249q^{40} - 249q^{41} - 332q^{42} - 249q^{43} - 249q^{44} - 332q^{45} - 747q^{46} - 249q^{47} - 332q^{48} - 249q^{49} - 249q^{50} - 332q^{51} - 249q^{52} - 249q^{53} - 332q^{54} - 747q^{55} - 249q^{56} - 332q^{57} - 249q^{58} - 249q^{59} - 332q^{60} - 249q^{61} - 249q^{62} - 332q^{63} - 747q^{64} - 249q^{65} - 332q^{66} - 249q^{67} - 249q^{68} - 332q^{69} - 249q^{70} - 249q^{71} - 332q^{72} - 747q^{73} - 249q^{74} - 332q^{75} - 249q^{76} - 249q^{77} - 332q^{78} - 249q^{79} - 249q^{80} - 332q^{81} - 747q^{82} - 249q^{83} - 332q^{84} - 249q^{85} - 249q^{86} - 332q^{87} - 249q^{88} - 249q^{89} - 332q^{90} - 747q^{91} - 249q^{92} - 332q^{93} - 249q^{94} - 249q^{95} - 332q^{96} - 249q^{97} - 249q^{98} - 332q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1503))$$

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
1503.2.a $$\chi_{1503}(1, \cdot)$$ 1503.2.a.a 1 1
1503.2.a.b 2
1503.2.a.c 5
1503.2.a.d 5
1503.2.a.e 8
1503.2.a.f 8
1503.2.a.g 12
1503.2.a.h 14
1503.2.a.i 14
1503.2.c $$\chi_{1503}(1502, \cdot)$$ 1503.2.c.a 56 1
1503.2.e $$\chi_{1503}(502, \cdot)$$ n/a 332 2
1503.2.g $$\chi_{1503}(500, \cdot)$$ n/a 332 2
1503.2.i $$\chi_{1503}(19, \cdot)$$ n/a 5658 82
1503.2.k $$\chi_{1503}(17, \cdot)$$ n/a 4592 82
1503.2.m $$\chi_{1503}(4, \cdot)$$ n/a 27224 164
1503.2.o $$\chi_{1503}(5, \cdot)$$ n/a 27224 164

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1503))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1503)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(501))$$$$^{\oplus 2}$$