## 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

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

## 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