## 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

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

## 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