# Properties

 Label 725.2.j Level $725$ Weight $2$ Character orbit 725.j Rep. character $\chi_{725}(307,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $86$ Newform subspaces $4$ Sturm bound $150$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$725 = 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 725.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$145$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$150$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(725, [\chi])$$.

Total New Old
Modular forms 162 94 68
Cusp forms 138 86 52
Eisenstein series 24 8 16

## Trace form

 $$86 q + 6 q^{2} + 82 q^{4} + 4 q^{7} + 18 q^{8} - 94 q^{9} + O(q^{10})$$ $$86 q + 6 q^{2} + 82 q^{4} + 4 q^{7} + 18 q^{8} - 94 q^{9} + 4 q^{11} - 14 q^{13} - 16 q^{14} + 66 q^{16} - 20 q^{17} + 18 q^{18} - 44 q^{21} + 8 q^{22} + 4 q^{23} + 6 q^{26} + 8 q^{28} - 28 q^{31} + 42 q^{32} + 16 q^{34} - 154 q^{36} + 8 q^{38} + 68 q^{39} - 30 q^{41} + 4 q^{42} + 36 q^{44} - 8 q^{46} - 26 q^{52} - 14 q^{53} - 56 q^{56} + 12 q^{57} - 28 q^{58} - 18 q^{61} - 28 q^{62} - 60 q^{63} - 54 q^{64} + 20 q^{66} - 32 q^{67} - 72 q^{68} + 12 q^{69} - 10 q^{72} + 4 q^{73} - 100 q^{76} + 12 q^{77} - 56 q^{78} - 8 q^{79} + 190 q^{81} + 58 q^{82} + 60 q^{83} - 56 q^{84} - 60 q^{87} + 68 q^{88} + 62 q^{89} + 28 q^{92} + 8 q^{93} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(725, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
725.2.j.a $4$ $5.789$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+3q^{4}+(\beta _{2}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots$$
725.2.j.b $16$ $5.789$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots$$
725.2.j.c $26$ $5.789$ None $$6$$ $$0$$ $$0$$ $$4$$
725.2.j.d $40$ $5.789$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(725, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(725, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 2}$$