## Defining parameters

 Level: $$N$$ = $$5$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(5))$$.

Total New Old
Modular forms 5 3 2
Cusp forms 1 1 0
Eisenstein series 4 2 2

## Trace form

 $$q - 4q^{2} + 2q^{3} + 8q^{4} - 5q^{5} - 8q^{6} + 6q^{7} - 23q^{9} + O(q^{10})$$ $$q - 4q^{2} + 2q^{3} + 8q^{4} - 5q^{5} - 8q^{6} + 6q^{7} - 23q^{9} + 20q^{10} + 32q^{11} + 16q^{12} - 38q^{13} - 24q^{14} - 10q^{15} - 64q^{16} + 26q^{17} + 92q^{18} + 100q^{19} - 40q^{20} + 12q^{21} - 128q^{22} - 78q^{23} + 25q^{25} + 152q^{26} - 100q^{27} + 48q^{28} - 50q^{29} + 40q^{30} - 108q^{31} + 256q^{32} + 64q^{33} - 104q^{34} - 30q^{35} - 184q^{36} + 266q^{37} - 400q^{38} - 76q^{39} + 22q^{41} - 48q^{42} + 442q^{43} + 256q^{44} + 115q^{45} + 312q^{46} - 514q^{47} - 128q^{48} - 307q^{49} - 100q^{50} + 52q^{51} - 304q^{52} + 2q^{53} + 400q^{54} - 160q^{55} + 200q^{57} + 200q^{58} + 500q^{59} - 80q^{60} - 518q^{61} + 432q^{62} - 138q^{63} - 512q^{64} + 190q^{65} - 256q^{66} + 126q^{67} + 208q^{68} - 156q^{69} + 120q^{70} + 412q^{71} - 878q^{73} - 1064q^{74} + 50q^{75} + 800q^{76} + 192q^{77} + 304q^{78} + 600q^{79} + 320q^{80} + 421q^{81} - 88q^{82} + 282q^{83} + 96q^{84} - 130q^{85} - 1768q^{86} - 100q^{87} - 150q^{89} - 460q^{90} - 228q^{91} - 624q^{92} - 216q^{93} + 2056q^{94} - 500q^{95} + 512q^{96} + 386q^{97} + 1228q^{98} - 736q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$

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
5.4.a $$\chi_{5}(1, \cdot)$$ 5.4.a.a 1 1
5.4.b $$\chi_{5}(4, \cdot)$$ None 0 1