# Properties

 Label 5.5 Level 5 Weight 5 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 10 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$5$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

## Trace form

 $$2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8} + O(q^{10})$$ $$2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8} - 10 q^{10} - 16 q^{11} + 168 q^{12} + 278 q^{13} - 420 q^{15} - 328 q^{16} - 2 q^{17} + 18 q^{18} + 420 q^{20} + 624 q^{21} + 16 q^{22} - 332 q^{23} + 350 q^{25} - 556 q^{26} - 1080 q^{27} - 728 q^{28} + 480 q^{30} + 1144 q^{31} + 1288 q^{32} + 96 q^{33} - 260 q^{35} + 252 q^{36} - 502 q^{37} + 360 q^{38} - 2100 q^{40} - 3376 q^{41} - 624 q^{42} + 2948 q^{43} - 270 q^{45} + 664 q^{46} + 4948 q^{47} + 1968 q^{48} + 850 q^{50} + 24 q^{51} - 3892 q^{52} - 6662 q^{53} - 320 q^{55} + 3120 q^{56} - 2160 q^{57} - 960 q^{58} + 840 q^{60} + 3184 q^{61} - 1144 q^{62} + 468 q^{63} + 9730 q^{65} - 192 q^{66} + 1748 q^{67} - 28 q^{68} - 1560 q^{70} - 12136 q^{71} - 540 q^{72} - 1582 q^{73} - 9300 q^{75} + 5040 q^{76} + 416 q^{77} + 3336 q^{78} - 6560 q^{80} + 11502 q^{81} + 3376 q^{82} + 11308 q^{83} - 10 q^{85} - 5896 q^{86} + 5760 q^{87} + 480 q^{88} + 630 q^{90} - 14456 q^{91} + 4648 q^{92} - 6864 q^{93} - 5400 q^{95} - 15456 q^{96} - 13102 q^{97} - 2098 q^{98} + O(q^{100})$$

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

We only show spaces with odd 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
5.5.c $$\chi_{5}(2, \cdot)$$ 5.5.c.a 2 2