# Properties

 Label 160.2.a Level $160$ Weight $2$ Character orbit 160.a Rep. character $\chi_{160}(1,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 160.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(160))$$.

Total New Old
Modular forms 32 4 28
Cusp forms 17 4 13
Eisenstein series 15 0 15

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

$$2$$$$5$$FrickeDim
$$+$$$$+$$$+$$$1$$
$$+$$$$-$$$-$$$2$$
$$-$$$$+$$$-$$$1$$
Plus space$$+$$$$1$$
Minus space$$-$$$$3$$

## Trace form

 $$4 q + 12 q^{9} + O(q^{10})$$ $$4 q + 12 q^{9} - 16 q^{13} + 8 q^{17} - 8 q^{21} + 4 q^{25} + 8 q^{29} - 16 q^{33} - 16 q^{37} - 16 q^{41} + 8 q^{45} - 4 q^{49} + 16 q^{53} - 32 q^{57} + 8 q^{65} + 40 q^{69} + 8 q^{73} + 48 q^{77} - 20 q^{81} + 8 q^{89} + 16 q^{93} + 24 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(160))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
160.2.a.a $1$ $1.278$ $$\Q$$ None $$0$$ $$-2$$ $$-1$$ $$-2$$ $+$ $+$ $$q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$$
160.2.a.b $1$ $1.278$ $$\Q$$ None $$0$$ $$2$$ $$-1$$ $$2$$ $-$ $+$ $$q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$$
160.2.a.c $2$ $1.278$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $+$ $-$ $$q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(160))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(160)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(80))$$$$^{\oplus 2}$$