## Defining parameters

 Level: $$N$$ = $$17$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$240$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(17))$$.

Total New Old
Modular forms 116 114 2
Cusp forms 100 100 0
Eisenstein series 16 14 2

## Trace form

 $$100q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} + O(q^{10})$$ $$100q - 8q^{2} - 8q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 8q^{7} - 8q^{8} - 8q^{9} - 30792q^{10} - 30136q^{11} - 448520q^{12} + 188888q^{13} + 485112q^{14} - 483512q^{15} - 1835024q^{16} - 308872q^{17} + 1867248q^{18} + 1110152q^{19} + 2573304q^{20} - 2576552q^{21} - 4872456q^{22} - 1546072q^{23} + 15962728q^{24} + 11840804q^{25} - 26517800q^{26} - 11494880q^{27} + 9370504q^{28} + 14629412q^{29} + 43073848q^{30} + 1635544q^{31} - 29445424q^{32} - 37949488q^{33} - 61465544q^{34} - 2054448q^{35} + 71799480q^{36} + 62997976q^{37} + 11070208q^{38} + 92266680q^{39} - 59333192q^{40} - 141781468q^{41} - 349918040q^{42} - 28756160q^{43} + 300073048q^{44} + 292612772q^{45} + 7112008q^{46} + 80549352q^{47} - 113473312q^{48} - 147967496q^{49} - 350000016q^{50} - 175275208q^{51} - 148045840q^{52} - 129469876q^{53} + 1076768104q^{54} + 603656600q^{55} + 484286992q^{56} - 593808704q^{57} - 762251920q^{58} - 478840296q^{59} - 370566992q^{60} + 432514312q^{61} + 787144208q^{62} + 1496567464q^{63} + 1195591112q^{64} - 286405668q^{65} - 2553133984q^{66} - 644835888q^{67} - 2463221568q^{68} - 383319472q^{69} + 1338707696q^{70} + 511118008q^{71} + 1019013456q^{72} + 328534492q^{73} + 259703656q^{74} + 1064858584q^{75} + 617679776q^{76} - 345339448q^{77} - 2269165696q^{78} - 475417960q^{79} - 220853224q^{80} + 500662400q^{81} + 904295904q^{82} - 319642368q^{83} - 1547731872q^{84} - 1519695380q^{85} + 3356413696q^{86} - 1212935960q^{87} - 2282499656q^{88} - 2724297272q^{89} - 2735441976q^{90} + 2147533336q^{91} + 7534157896q^{92} + 4908431928q^{93} + 6950755288q^{94} + 4494061800q^{95} + 2578069856q^{96} - 2922002216q^{97} - 5864386752q^{98} - 7407555576q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(17))$$

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
17.10.a $$\chi_{17}(1, \cdot)$$ 17.10.a.a 5 1
17.10.a.b 7
17.10.b $$\chi_{17}(16, \cdot)$$ 17.10.b.a 12 1
17.10.c $$\chi_{17}(4, \cdot)$$ 17.10.c.a 24 2
17.10.d $$\chi_{17}(2, \cdot)$$ 17.10.d.a 52 4