# Properties

 Label 169.2 Level 169 Weight 2 Dimension 1066 Nonzero newspaces 8 Newform subspaces 14 Sturm bound 4732 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$169 = 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$14$$ Sturm bound: $$4732$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(169))$$.

Total New Old
Modular forms 1297 1271 26
Cusp forms 1070 1066 4
Eisenstein series 227 205 22

## Trace form

 $$1066 q - 69 q^{2} - 70 q^{3} - 73 q^{4} - 72 q^{5} - 78 q^{6} - 70 q^{7} - 63 q^{8} - 63 q^{9} + O(q^{10})$$ $$1066 q - 69 q^{2} - 70 q^{3} - 73 q^{4} - 72 q^{5} - 78 q^{6} - 70 q^{7} - 63 q^{8} - 63 q^{9} - 54 q^{10} - 66 q^{11} - 42 q^{12} - 60 q^{13} - 126 q^{14} - 66 q^{15} - 57 q^{16} - 66 q^{17} - 39 q^{18} - 46 q^{19} - 42 q^{20} - 46 q^{21} - 42 q^{22} - 66 q^{23} - 6 q^{24} - 55 q^{25} - 42 q^{26} - 94 q^{27} - 22 q^{28} - 42 q^{29} + 6 q^{30} - 46 q^{31} + 3 q^{32} - 30 q^{33} - 24 q^{34} - 30 q^{35} + 11 q^{36} - 70 q^{37} - 42 q^{38} - 40 q^{39} - 72 q^{40} - 18 q^{41} + 18 q^{42} - 18 q^{43} + 6 q^{44} + 6 q^{45} + 30 q^{46} - 30 q^{47} + 26 q^{48} - 7 q^{49} + 27 q^{50} + 18 q^{51} + 11 q^{52} - 84 q^{53} + 18 q^{54} - 6 q^{55} + 42 q^{56} + 2 q^{57} - 6 q^{58} - 42 q^{59} + 90 q^{60} - 14 q^{61} + 6 q^{62} + 26 q^{63} + 53 q^{64} + 9 q^{65} - 6 q^{66} - 22 q^{67} + 54 q^{68} - 6 q^{69} + 66 q^{70} - 18 q^{71} + 111 q^{72} - 4 q^{73} + 66 q^{74} + 54 q^{75} + 74 q^{76} + 18 q^{77} + 102 q^{78} - 86 q^{79} + 138 q^{80} + 21 q^{81} + 30 q^{82} + 6 q^{83} + 146 q^{84} + 12 q^{85} + 54 q^{86} + 54 q^{87} + 102 q^{88} + 36 q^{89} + 144 q^{90} + 26 q^{91} - 6 q^{92} + 74 q^{93} + 78 q^{94} + 30 q^{95} + 174 q^{96} - 4 q^{97} + 51 q^{98} + 78 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$

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
169.2.a $$\chi_{169}(1, \cdot)$$ 169.2.a.a 2 1
169.2.a.b 3
169.2.a.c 3
169.2.b $$\chi_{169}(168, \cdot)$$ 169.2.b.a 2 1
169.2.b.b 6
169.2.c $$\chi_{169}(22, \cdot)$$ 169.2.c.a 4 2
169.2.c.b 6
169.2.c.c 6
169.2.e $$\chi_{169}(23, \cdot)$$ 169.2.e.a 2 2
169.2.e.b 12
169.2.g $$\chi_{169}(14, \cdot)$$ 169.2.g.a 156 12
169.2.h $$\chi_{169}(12, \cdot)$$ 169.2.h.a 168 12
169.2.i $$\chi_{169}(3, \cdot)$$ 169.2.i.a 336 24
169.2.k $$\chi_{169}(4, \cdot)$$ 169.2.k.a 360 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(169))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(169)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$