# Properties

 Label 102.2 Level 102 Weight 2 Dimension 73 Nonzero newspaces 5 Newform subspaces 9 Sturm bound 1152 Trace bound 1

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(102)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 1}$$