## Defining parameters

 Level: $$N$$ = $$25 = 5^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$150$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(25))$$.

Total New Old
Modular forms 64 56 8
Cusp forms 36 36 0
Eisenstein series 28 20 8

## Trace form

 $$36q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 18q^{6} - 10q^{7} - 10q^{8} - 10q^{9} + O(q^{10})$$ $$36q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 18q^{6} - 10q^{7} - 10q^{8} - 10q^{9} - 10q^{10} - 18q^{11} - 10q^{12} - 10q^{13} - 10q^{14} - 10q^{15} + 46q^{16} + 60q^{17} + 140q^{18} + 90q^{19} + 130q^{20} + 42q^{21} + 70q^{22} + 10q^{23} - 40q^{25} - 68q^{26} - 100q^{27} - 250q^{28} - 110q^{29} - 250q^{30} - 158q^{31} - 290q^{32} - 190q^{33} - 260q^{34} - 120q^{35} - 34q^{36} + 50q^{37} + 320q^{38} + 390q^{39} + 440q^{40} + 142q^{41} + 690q^{42} + 230q^{43} + 340q^{44} + 310q^{45} + 162q^{46} + 70q^{47} + 160q^{48} - 100q^{50} - 148q^{51} - 320q^{52} - 190q^{53} - 660q^{54} - 250q^{55} - 310q^{56} - 650q^{57} - 640q^{58} - 260q^{59} - 550q^{60} + 2q^{61} + 60q^{62} - 20q^{63} + 340q^{64} + 360q^{65} + 174q^{66} + 270q^{67} + 710q^{68} + 340q^{69} + 310q^{70} + 102q^{71} + 360q^{72} + 30q^{73} - 90q^{75} - 60q^{76} - 250q^{77} - 500q^{78} - 210q^{79} - 850q^{80} + 26q^{81} + 30q^{82} - 10q^{84} + 600q^{85} + 42q^{86} + 300q^{87} + 190q^{88} - 10q^{89} + 380q^{90} + 282q^{91} - 30q^{92} + 520q^{93} + 790q^{94} + 310q^{95} + 282q^{96} + 270q^{97} + 170q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$

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
25.3.c $$\chi_{25}(7, \cdot)$$ 25.3.c.a 4 2
25.3.f $$\chi_{25}(2, \cdot)$$ 25.3.f.a 32 8