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.
Laie
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