ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 27 Mar 2022 00:21:01 +0100Fix a number field embedding for a newform for $\Gamma_0(N)$https://ask.sagemath.org/question/61683/fix-a-number-field-embedding-for-a-newform-for-gamma_0n/I am trying to do some numerics with newforms for $\Gamma_0(N)$. E.g
sage: g=CuspForms(group=Gamma0(2),weight=26).newforms(names='a')[0].q_expansion(prec=10).truncate()
sage: g(exp(-10.))
gives me (an approximation) of the chosen newform at $10i/2\pi\in \mathbb H$. The chosen newform has coefficients in $\mathbb Q$
If instead I choose another newform
sage: g=CuspForms(group=Gamma0(2),weight=26).newforms(names='a')[1].q_expansion(prec=10).truncate()here
which has coefficients in the number field with defining polynomial $x^2 - 767888x - 9686519804864$ the command
sage:g(exp(-10.))
gives me an error which I interpret as Sage not knowing where to compute or that I have not fixed an embedding of the number field.
How do I fix an embedding and compute `g(exp(-10.))`?mrisagerSun, 27 Mar 2022 00:21:01 +0100https://ask.sagemath.org/question/61683/Real analytic Eisenstein serieshttps://ask.sagemath.org/question/51911/real-analytic-eisenstein-series/I'd to compute values of a certain function in Sage, a kind of a modular form, the so-called [real analytic Eisenstein series](https://en.wikipedia.org/wiki/Real_analytic_Eisenstein_series). Does anybody know how to do it? I could not have found the Sage name for it.
More precisely, I would like to plot the the graph of the real analytic Eisenstein series, their real and imaginary values in a square of the complex plane (variable z) each for a certain value of the parameter s. Thus s is fixed in each of the graphs.
Real analytic Eisenstein series (also this is this their name at wikipedia) are defined for a complex z and a complex s. They are not the [Eisenstein series](https://en.wikipedia.org/wiki/Eisenstein_series) defined for complex z and an integer k. If s is k and an integer, they are connected by the multiple of Im(z)^s. Thus an easy connection, but I'd like to know the value of the series for a complex s. They are modular functions, not holomorphic and connected to theta series.svarotThu, 11 Jun 2020 20:40:09 +0200https://ask.sagemath.org/question/51911/