## Defining parameters

 Level: $$N$$ = $$1502 = 2 \cdot 751$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$282000$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1502))$$.

Total New Old
Modular forms 71250 23499 47751
Cusp forms 69751 23499 46252
Eisenstein series 1499 0 1499

## Trace form

 $$23499q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10})$$ $$23499q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 32q^{21} - 12q^{22} - 24q^{23} - 4q^{24} - 31q^{25} - 14q^{26} - 40q^{27} - 8q^{28} - 30q^{29} - 24q^{30} - 32q^{31} - q^{32} - 48q^{33} - 18q^{34} - 48q^{35} - 13q^{36} - 38q^{37} - 20q^{38} - 56q^{39} - 6q^{40} - 42q^{41} - 32q^{42} - 44q^{43} - 12q^{44} - 78q^{45} - 24q^{46} - 48q^{47} - 4q^{48} - 57q^{49} - 31q^{50} - 72q^{51} - 14q^{52} - 54q^{53} - 40q^{54} - 72q^{55} - 8q^{56} - 80q^{57} - 30q^{58} - 60q^{59} - 24q^{60} - 62q^{61} - 32q^{62} - 104q^{63} - q^{64} - 84q^{65} - 48q^{66} - 68q^{67} - 18q^{68} - 96q^{69} - 48q^{70} - 72q^{71} - 13q^{72} - 74q^{73} - 38q^{74} - 124q^{75} - 20q^{76} - 96q^{77} - 56q^{78} - 80q^{79} - 6q^{80} - 121q^{81} - 42q^{82} - 84q^{83} - 32q^{84} - 108q^{85} - 44q^{86} - 120q^{87} - 12q^{88} - 90q^{89} - 78q^{90} - 112q^{91} - 24q^{92} - 128q^{93} - 48q^{94} - 120q^{95} - 4q^{96} - 98q^{97} - 57q^{98} - 156q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1502))$$

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
1502.2.a $$\chi_{1502}(1, \cdot)$$ 1502.2.a.a 1 1
1502.2.a.b 1
1502.2.a.c 2
1502.2.a.d 2
1502.2.a.e 11
1502.2.a.f 11
1502.2.a.g 16
1502.2.a.h 19
1502.2.c $$\chi_{1502}(823, \cdot)$$ n/a 124 2
1502.2.d $$\chi_{1502}(569, \cdot)$$ n/a 256 4
1502.2.g $$\chi_{1502}(215, \cdot)$$ n/a 496 8
1502.2.h $$\chi_{1502}(51, \cdot)$$ n/a 1280 20
1502.2.k $$\chi_{1502}(61, \cdot)$$ n/a 2480 40
1502.2.l $$\chi_{1502}(43, \cdot)$$ n/a 6400 100
1502.2.o $$\chi_{1502}(5, \cdot)$$ n/a 12400 200

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1502))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1502)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(751))$$$$^{\oplus 2}$$