Let $f=\sum_{n\ge 1} a(n)q^n\in M_{k+\frac{1}{2}}(\Gamma_0(4N),\chi)$ be a modular form of half-integral wieght wich is not a single variable theta-function.

Can someone prove or disprove that: $$X\ll \dfrac{\left(\sum_{n\le X}a(n)\right)^2}{\underset{n\le X}{\sum} a(n)^2}$$

Thanks !

Let $f=\sum_{n\ge 1} a(n)q^n\in M_{k+\frac{1}{2}}(\Gamma_0(4N),\chi)$ be a modular form of half-integral wieght.

Can someone prove or disprove that: $$X\ll \dfrac{\left(\sum_{n\le X}a(n)\right)^2}{\underset{n\le X}{\sum} a(n)^2}$$

Thanks !

Let $f=\sum_{n\ge 1} a(n)q^n\in M_{k+\frac{1}{2}}(N,\chi)$ be a modular form of half-integral wieght wich is not a single variable theta-function.

Can someone prove or disprove that: $$X\ll \dfrac{\left(\sum_{n\le X}a(n)\right)^2}{\underset{n\le X}{\sum} a(n)^2}$$

Thanks !

Let $f=\sum_{n\ge 1} a(n)q^n\in M_{k+\frac{1}{2}}(\Gamma_0(4N),\chi)$ be a modular form of half-integral wieght wich is not a single variable theta-function.

Can someone prove or disprove that: $$X\ll \dfrac{\left(\sum_{n\le X}a(n)\right)^2}{\underset{n\le X}{\sum} a(n)^2}$$

Thanks !