# Properties

 Label 125.2.a Level $125$ Weight $2$ Character orbit 125.a Rep. character $\chi_{125}(1,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $3$ Sturm bound $25$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$125 = 5^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 125.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$25$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(125))$$.

Total New Old
Modular forms 17 8 9
Cusp forms 8 8 0
Eisenstein series 9 0 9

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$5$$Dim.
$$+$$$$2$$
$$-$$$$6$$

## Trace form

 $$8 q + 6 q^{4} - 4 q^{6} + 4 q^{9} + O(q^{10})$$ $$8 q + 6 q^{4} - 4 q^{6} + 4 q^{9} - 4 q^{11} - 8 q^{14} - 2 q^{16} + 10 q^{19} + 6 q^{21} - 20 q^{24} - 14 q^{26} - 10 q^{29} + 6 q^{31} - 18 q^{34} - 22 q^{36} - 2 q^{39} - 14 q^{41} + 22 q^{44} + 26 q^{46} + 6 q^{49} + 26 q^{51} + 10 q^{54} + 10 q^{56} + 30 q^{59} - 4 q^{61} + 16 q^{64} + 2 q^{66} - 32 q^{69} - 24 q^{71} + 12 q^{74} + 20 q^{76} + 40 q^{79} - 32 q^{81} - 8 q^{84} + 56 q^{86} - 30 q^{89} + 46 q^{91} + 2 q^{94} - 34 q^{96} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(125))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
125.2.a.a $2$ $0.998$ $$\Q(\sqrt{5})$$ None $$-1$$ $$-3$$ $$0$$ $$-6$$ $+$ $$q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$$
125.2.a.b $2$ $0.998$ $$\Q(\sqrt{5})$$ None $$1$$ $$3$$ $$0$$ $$6$$ $-$ $$q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$$
125.2.a.c $4$ $0.998$ 4.4.4400.1 None $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-2\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$