# Properties

 Label 125.2.e Level $125$ Weight $2$ Character orbit 125.e Rep. character $\chi_{125}(24,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $16$ Newform subspaces $2$ Sturm bound $25$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$125 = 5^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 125.e (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$25$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(125, [\chi])$$.

Total New Old
Modular forms 72 40 32
Cusp forms 32 16 16
Eisenstein series 40 24 16

## Trace form

 $$16 q + 5 q^{2} + 5 q^{3} + 3 q^{4} - 3 q^{6} - 10 q^{8} - 3 q^{9} + O(q^{10})$$ $$16 q + 5 q^{2} + 5 q^{3} + 3 q^{4} - 3 q^{6} - 10 q^{8} - 3 q^{9} - 8 q^{11} - 15 q^{12} + 5 q^{13} + 11 q^{14} - 9 q^{16} + 10 q^{17} + 5 q^{19} - 8 q^{21} - 5 q^{23} - 20 q^{24} - 18 q^{26} + 5 q^{27} + 15 q^{28} - 15 q^{29} - 3 q^{31} - 10 q^{33} + q^{34} + 11 q^{36} - 30 q^{37} - 15 q^{38} - 21 q^{39} + 12 q^{41} + 15 q^{42} - 14 q^{44} + 7 q^{46} + 30 q^{48} + 58 q^{49} - 28 q^{51} + 10 q^{52} + 10 q^{53} + 25 q^{54} + 10 q^{56} - 20 q^{58} + 17 q^{61} + 30 q^{62} - 10 q^{63} - 2 q^{64} + 24 q^{66} - 20 q^{67} + 19 q^{69} + 22 q^{71} - 5 q^{72} - 15 q^{73} - 24 q^{74} + 20 q^{76} - 10 q^{77} - 25 q^{78} - 15 q^{79} + 26 q^{81} + 45 q^{83} + 26 q^{84} - 3 q^{86} + 20 q^{87} + 20 q^{88} + 15 q^{89} - 18 q^{91} - 30 q^{92} - 29 q^{94} + 12 q^{96} + 60 q^{97} + 10 q^{98} - 56 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(125, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
125.2.e.a $8$ $0.998$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+\cdots$$
125.2.e.b $8$ $0.998$ 8.0.58140625.2 None $$5$$ $$5$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(125, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(125, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 2}$$