## 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

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

## 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