Remember the Fourier expansion of the full modular form: $$ \Delta(z) = \sum_{n=1} \tau(n)q^n $$ where $\tau(n)$ are the coefficients (Ramanujan Tau function). Ramanujan found that the coefficients satisfy $$ \tau(n) \equiv \sigma_{11}(n) \mod 691 $$ where $\sigma_{11}(n) = \sum_{d|n}d^{11}$. My question:
Do you know other modular forms which Fourier expansion coefficients satisfy such a congruence?
With such I mean this: Let $f(z)$ be a modular form so that $f(z)=\sum a_nq^n$. Now I want to find a congruence such as $$ a_n \equiv g(n) \mod m $$ where $g(n)$ is a (simple) arithmetic function such as the divisor sum function $\sigma(n)$ and $m$ favorable a prime.