## Defining parameters

 Level: $$N$$ = $$102 = 2 \cdot 3 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$5$$ Newform subspaces: $$9$$ Sturm bound: $$1152$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(102))$$.

Total New Old
Modular forms 352 73 279
Cusp forms 225 73 152
Eisenstein series 127 0 127

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$

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
102.2.a $$\chi_{102}(1, \cdot)$$ 102.2.a.a 1 1
102.2.a.b 1
102.2.a.c 1
102.2.b $$\chi_{102}(67, \cdot)$$ 102.2.b.a 2 1
102.2.f $$\chi_{102}(13, \cdot)$$ 102.2.f.a 4 2
102.2.h $$\chi_{102}(19, \cdot)$$ 102.2.h.a 8 4
102.2.h.b 8
102.2.i $$\chi_{102}(5, \cdot)$$ 102.2.i.a 24 8
102.2.i.b 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(102))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(102)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 2}$$