Given a modular form with CM type vanishing behavior of its coefficients $a_p$ (as described in Ribet) it is often not difficult to find a Hecke character whose L-series agrees with those of your given form. Sturm's bound in terms of the weight $k$ and the level $N$ then tells you how many terms you have to consider in order to ensure that the two forms are the same. (See Sturm 1987, On the congruence of modular forms.)
Laie
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