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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**History:**(expand/hide all)

- 2019-04-28 21:11:21 by David Farmer (Reviewed)
- 2019-04-28 21:06:35 by David Farmer (Reviewed)
- 2018-12-25 19:53:42 by Andrew Sutherland

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