## Defining parameters

 Level: $$N$$ = $$25 = 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$100$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(25))$$.

Total New Old
Modular forms 39 33 6
Cusp forms 12 12 0
Eisenstein series 27 21 6

## Trace form

 $$12 q - 7 q^{2} - 6 q^{3} - 3 q^{4} - 5 q^{5} - 6 q^{6} - 2 q^{7} + 5 q^{8} + 3 q^{9} + O(q^{10})$$ $$12 q - 7 q^{2} - 6 q^{3} - 3 q^{4} - 5 q^{5} - 6 q^{6} - 2 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} - 6 q^{11} + 18 q^{12} + 4 q^{13} + 14 q^{14} + 10 q^{15} - 3 q^{16} - 2 q^{17} + 4 q^{18} - 10 q^{19} - 10 q^{20} - 6 q^{21} - 14 q^{22} - 6 q^{23} - 20 q^{24} - 15 q^{25} - 6 q^{26} - 14 q^{28} + 10 q^{30} - 6 q^{31} + 18 q^{32} + 18 q^{33} + 19 q^{34} + 20 q^{35} + 17 q^{36} + 23 q^{37} + 20 q^{38} + 6 q^{39} + 15 q^{40} + 4 q^{41} - 14 q^{42} - 6 q^{43} + 4 q^{44} - 25 q^{45} - 6 q^{46} - 2 q^{47} - 36 q^{48} - 8 q^{49} - 25 q^{50} - 16 q^{51} - 22 q^{52} - q^{53} - 20 q^{54} + 10 q^{55} + 10 q^{56} - 10 q^{57} + 10 q^{58} - 10 q^{60} + 4 q^{61} - 24 q^{62} + 4 q^{63} + 7 q^{64} + 5 q^{65} + 18 q^{66} + 18 q^{67} - 4 q^{68} + 16 q^{69} + 30 q^{70} + 14 q^{71} + 15 q^{72} + 24 q^{73} - 6 q^{74} + 10 q^{75} + 6 q^{77} + 28 q^{78} + 30 q^{79} + 5 q^{80} + 27 q^{81} - 4 q^{82} - 36 q^{83} + 14 q^{84} - 35 q^{85} - 6 q^{86} - 20 q^{87} - 30 q^{88} - 45 q^{89} - 25 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} - 26 q^{94} + 10 q^{95} + 14 q^{96} - 52 q^{97} + q^{98} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$

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
25.2.a $$\chi_{25}(1, \cdot)$$ None 0 1
25.2.b $$\chi_{25}(24, \cdot)$$ None 0 1
25.2.d $$\chi_{25}(6, \cdot)$$ 25.2.d.a 4 4
25.2.e $$\chi_{25}(4, \cdot)$$ 25.2.e.a 8 4