# Properties

 Label 625.2.e Level $625$ Weight $2$ Character orbit 625.e Rep. character $\chi_{625}(124,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $136$ Newform subspaces $11$ Sturm bound $125$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$625 = 5^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 625.e (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$11$$ Sturm bound: $$125$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(625, [\chi])$$.

Total New Old
Modular forms 312 184 128
Cusp forms 192 136 56
Eisenstein series 120 48 72

## Trace form

 $$136 q + 28 q^{4} + 12 q^{6} + 22 q^{9} + O(q^{10})$$ $$136 q + 28 q^{4} + 12 q^{6} + 22 q^{9} + 12 q^{11} - 24 q^{14} - 4 q^{16} + 12 q^{21} + 40 q^{24} - 68 q^{26} + 20 q^{29} + 12 q^{31} - 14 q^{34} - 24 q^{36} + 24 q^{39} - 8 q^{41} + 16 q^{44} + 12 q^{46} + 8 q^{49} - 48 q^{51} - 60 q^{54} - 20 q^{56} - 8 q^{61} - 32 q^{64} - 36 q^{66} - 36 q^{69} - 28 q^{71} + 36 q^{74} - 80 q^{76} - 14 q^{81} - 104 q^{84} + 12 q^{86} + 10 q^{89} + 12 q^{91} + 106 q^{94} - 78 q^{96} + 64 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(625, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.e.a $8$ $4.991$ 8.0.58140625.2 None $$0$$ $$-5$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{5}+\beta _{7})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$
625.2.e.b $8$ $4.991$ 8.0.484000000.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1+\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots$$
625.2.e.c $8$ $4.991$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+(-1+\cdots)q^{4}+\cdots$$
625.2.e.d $8$ $4.991$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(\zeta_{20}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}+\cdots$$
625.2.e.e $8$ $4.991$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$$
625.2.e.f $8$ $4.991$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(\zeta_{20}+\cdots)q^{3}+\cdots$$
625.2.e.g $8$ $4.991$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\cdots)q^{3}+\cdots$$
625.2.e.h $8$ $4.991$ 8.0.484000000.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{6})q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\cdots$$
625.2.e.i $8$ $4.991$ 8.0.58140625.2 None $$0$$ $$5$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots$$
625.2.e.j $32$ $4.991$ None $$0$$ $$0$$ $$0$$ $$0$$
625.2.e.k $32$ $4.991$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(625, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(625, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(125, [\chi])$$$$^{\oplus 2}$$