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Ask Sage question 69710:
Checking eigenforms in Sage
https://ask.sagemath.org/question/69710> How to check if a half-integer weight form is an eigenform
> in Sage and determine its eigenvalues and eigenvectors?
> For example, If $f(z) - \eta(24z)^11$, how does one find
> the q-series expansion of $f|T_{p^2}$? There seems to be
> a documentation in integer weight cases only.
Any hints from sage-nt subscribers?