# Properties

 Label 725.2.e Level $725$ Weight $2$ Character orbit 725.e Rep. character $\chi_{725}(157,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $86$ Newform subspaces $4$ Sturm bound $150$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$725 = 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 725.e (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

 $$86 q + 4 q^{3} - 82 q^{4} + 4 q^{7} + 94 q^{9} + O(q^{10})$$ $$86 q + 4 q^{3} - 82 q^{4} + 4 q^{7} + 94 q^{9} + 4 q^{11} + 8 q^{12} + 14 q^{13} + 16 q^{14} + 66 q^{16} - 44 q^{21} - 8 q^{22} + 4 q^{23} + 6 q^{26} + 4 q^{27} - 8 q^{28} - 28 q^{31} - 16 q^{34} - 154 q^{36} - 16 q^{37} - 8 q^{38} - 68 q^{39} - 30 q^{41} - 4 q^{42} - 12 q^{43} - 36 q^{44} - 8 q^{46} + 36 q^{47} - 4 q^{48} - 26 q^{52} - 14 q^{53} - 56 q^{56} - 12 q^{57} - 58 q^{58} - 18 q^{61} + 28 q^{62} + 60 q^{63} + 54 q^{64} + 20 q^{66} + 32 q^{67} - 12 q^{69} - 100 q^{76} - 56 q^{78} + 8 q^{79} + 190 q^{81} + 58 q^{82} + 60 q^{83} + 56 q^{84} + 12 q^{87} + 68 q^{88} - 62 q^{89} - 28 q^{92} - 8 q^{93} + 8 q^{97} - 34 q^{98} + 36 q^{99} + O(q^{100})$$

## 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.e.a $4$ $5.789$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-3q^{4}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{2}q^{8}+\cdots$$
725.2.e.b $16$ $5.789$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots$$
725.2.e.c $26$ $5.789$ None $$0$$ $$4$$ $$0$$ $$4$$
725.2.e.d $40$ $5.789$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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