## Defining parameters

 Level: $$N$$ = $$289 = 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$24$$ Sturm bound: $$13872$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(289))$$.

Total New Old
Modular forms 3668 3628 40
Cusp forms 3269 3259 10
Eisenstein series 399 369 30

## Trace form

 $$3259 q - 123 q^{2} - 124 q^{3} - 127 q^{4} - 126 q^{5} - 132 q^{6} - 128 q^{7} - 135 q^{8} - 133 q^{9} + O(q^{10})$$ $$3259 q - 123 q^{2} - 124 q^{3} - 127 q^{4} - 126 q^{5} - 132 q^{6} - 128 q^{7} - 135 q^{8} - 133 q^{9} - 130 q^{10} - 116 q^{11} - 100 q^{12} - 118 q^{13} - 112 q^{14} - 96 q^{15} - 79 q^{16} - 120 q^{17} - 207 q^{18} - 124 q^{19} - 106 q^{20} - 104 q^{21} - 124 q^{22} - 128 q^{23} - 100 q^{24} - 95 q^{25} - 90 q^{26} - 112 q^{27} - 80 q^{28} - 110 q^{29} - 64 q^{30} - 88 q^{31} - 71 q^{32} - 88 q^{33} - 64 q^{34} - 216 q^{35} - 51 q^{36} - 94 q^{37} - 84 q^{38} - 80 q^{39} - 18 q^{40} - 74 q^{41} - 24 q^{42} - 84 q^{43} - 12 q^{44} - 94 q^{45} - 96 q^{46} - 88 q^{47} - 36 q^{48} - 113 q^{49} - 85 q^{50} - 96 q^{51} - 202 q^{52} - 86 q^{53} - 64 q^{55} - 8 q^{57} - 34 q^{58} - 52 q^{59} + 48 q^{60} - 54 q^{61} - 8 q^{62} + 16 q^{63} - 23 q^{64} - 52 q^{65} - 8 q^{66} - 108 q^{67} - 28 q^{68} - 104 q^{69} + 8 q^{70} - 96 q^{71} + 77 q^{72} + 6 q^{73} - 66 q^{74} + 12 q^{75} - 20 q^{76} - 56 q^{77} + 48 q^{78} - 72 q^{79} + 46 q^{80} - 33 q^{81} - 30 q^{82} - 76 q^{83} + 24 q^{84} - 36 q^{85} - 140 q^{86} - 48 q^{87} + 20 q^{88} - 66 q^{89} + 102 q^{90} - 8 q^{91} + 96 q^{92} - 56 q^{93} + 56 q^{94} - 16 q^{95} + 156 q^{96} - 90 q^{97} + 53 q^{98} + 28 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$

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
289.2.a $$\chi_{289}(1, \cdot)$$ 289.2.a.a 1 1
289.2.a.b 2
289.2.a.c 2
289.2.a.d 3
289.2.a.e 3
289.2.a.f 4
289.2.b $$\chi_{289}(288, \cdot)$$ 289.2.b.a 2 1
289.2.b.b 4
289.2.b.c 4
289.2.b.d 6
289.2.c $$\chi_{289}(38, \cdot)$$ 289.2.c.a 4 2
289.2.c.b 8
289.2.c.c 8
289.2.c.d 12
289.2.d $$\chi_{289}(110, \cdot)$$ 289.2.d.a 4 4
289.2.d.b 4
289.2.d.c 4
289.2.d.d 8
289.2.d.e 16
289.2.d.f 24
289.2.f $$\chi_{289}(18, \cdot)$$ 289.2.f.a 384 16
289.2.g $$\chi_{289}(16, \cdot)$$ 289.2.g.a 384 16
289.2.h $$\chi_{289}(4, \cdot)$$ 289.2.h.a 768 32
289.2.i $$\chi_{289}(2, \cdot)$$ 289.2.i.a 1600 64

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(289))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(289)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$