Hello,Thank you for your prompt and clear answer.I assumed this is so, but was not able to verify it numerically as everything was mismatched, so I suspected I misunderstood the principle. I evaluated the function via q expansion all up to order 100, did not work, that at some point it succeeded with 100,000 terms of infinite product and you really need so many to reach the precision, and finally simply used eta relation as eta(z) is available in some numerical libraries, and it works perfectly.Then, I noticed some are not available via eta quotient. Is there some theorem for specific N, k, chi for which this is not possible, or it was simply not yet found or not documented? Or some other smarter hint how to evaluate them numerically to get "numerical modularity"? E.g.:HrvojeOn Mon, Apr 18, 2022 at 9:36 PM John Jones <j...@asu.edu> wrote:Hi,On the LMFDB feedback page, you wrote:Hello, Thank you for creating this impressive site of the ultimate math beauty. I'm a layman compared to pro maths, do some research & numerical experiments for hobby, and I wonder for some modular form, e.g. link provided, where can I get or identify underlying SL linear transformation matrix, so (a b; c d)? Thank you in advance, HrvojeI am not sure what you mean. The form satisfies an equation for every matrix M in a certain subgroup of SL(2,Z) (see https://www.lmfdb.org/knowledge/show/cmf?timestamp=1545201145469776). In this case, the subgroup is Gamma_0(12) because it is level 12 (see https://www.lmfdb.org/knowledge/show/group.sl2z.subgroup.gamma0n?timestamp=1555023477327750 ). This is an infinite group, so there are infinitely many matrices involved.I hope that answers your question.John Jones