## Defining parameters

 Level: $$N$$ = $$17$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(17))$$.

Total New Old
Modular forms 44 42 2
Cusp forms 28 28 0
Eisenstein series 16 14 2

## Trace form

 $$28 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10})$$ $$28 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 112 q^{10} - 120 q^{11} - 104 q^{12} + 24 q^{13} + 152 q^{14} + 328 q^{15} + 432 q^{16} + 120 q^{17} + 432 q^{18} + 72 q^{19} + 104 q^{20} - 104 q^{21} - 232 q^{22} - 216 q^{23} - 1880 q^{24} - 1236 q^{25} - 1040 q^{26} - 224 q^{27} + 136 q^{28} + 252 q^{29} + 1336 q^{30} + 856 q^{31} + 1168 q^{32} + 1040 q^{33} + 2104 q^{34} + 976 q^{35} + 1656 q^{36} + 664 q^{37} - 336 q^{38} - 1224 q^{39} - 2504 q^{40} - 1428 q^{41} - 2936 q^{42} - 1472 q^{43} - 1960 q^{44} - 1348 q^{45} - 1016 q^{46} + 1512 q^{47} + 3296 q^{48} + 1528 q^{49} + 2784 q^{50} + 1592 q^{51} + 3056 q^{52} - 316 q^{53} - 2696 q^{54} - 1896 q^{55} - 1008 q^{56} - 2096 q^{57} - 1488 q^{58} - 872 q^{59} - 1424 q^{60} + 232 q^{61} - 1872 q^{62} + 1960 q^{63} - 2104 q^{64} + 1092 q^{65} + 5168 q^{66} + 2128 q^{67} + 3632 q^{68} + 3728 q^{69} + 1264 q^{70} + 184 q^{71} + 48 q^{72} + 292 q^{73} + 256 q^{74} + 856 q^{75} + 480 q^{76} - 216 q^{77} - 1792 q^{78} - 360 q^{79} - 872 q^{80} - 2992 q^{81} - 424 q^{82} - 5504 q^{83} - 8352 q^{84} - 4316 q^{85} - 8512 q^{86} - 1496 q^{87} + 1720 q^{88} - 1112 q^{89} - 1056 q^{90} + 1432 q^{91} + 3464 q^{92} + 2232 q^{93} + 3928 q^{94} + 3880 q^{95} + 5984 q^{96} + 280 q^{97} + 8568 q^{98} - 2616 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(17))$$

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
17.4.a $$\chi_{17}(1, \cdot)$$ 17.4.a.a 1 1
17.4.a.b 3
17.4.b $$\chi_{17}(16, \cdot)$$ 17.4.b.a 4 1
17.4.c $$\chi_{17}(4, \cdot)$$ 17.4.c.a 8 2
17.4.d $$\chi_{17}(2, \cdot)$$ 17.4.d.a 12 4