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Can you give an a non-trivial example of an integer weight cusp form which does not lie in the old subspace and it has $a_p=0$ for all primes $p$?

If such a form cannot exist then why?

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# Modular forms with prime Fourier coefficients zero

Can you give an example of an integer weight cusp form which does not lie in the old subspace and it has $a_p=0$ for all primes $p$?

If such a form cannot exist then why?