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The trace bound for a space of newforms $$S_k^{new}(N, \chi)$$ is the least positive integer $$m$$ such that taking traces down to $$\Q$$ of the coefficients $$a_n$$ for $$n \le m$$ suffices to distinguish all the Galois orbits of newforms in the space; here $a_n$ denotes the $n$th coefficient of the $q$-expansion $\sum a_n q^n$ of a newform.

If the newforms in the space all have distinct dimensions then the trace bound is 1, because the trace of $a_1=1$ from the coefficient field of the newform down to $\Q$ is equal to the dimension of its Galois orbit.

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• Review status: reviewed
• Last edited by David Farmer on 2019-04-28 21:11:21
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