ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 29 Jul 2015 18:28:14 -0500Modular Symbols with Character & Manin Symbolshttp://ask.sagemath.org/question/9215/modular-symbols-with-character-manin-symbols/1) Let $f= q + aq^2 + (a^3 + \frac{1}{2}a^2 +2)q^3 + a^2q^4 + O(5)$ be the level 28, weight 2 newform where $a$ satisfies $x^4 + 2x^3 + 2x^2 + 4x +4$. This modular form has an associated Dirichlet character (which we'll call eps) of conductor 28 mapping $15 \mapsto -1$ and $17 \mapsto (-\frac{1}{2}a^3 - \frac{1}{2}a^2 - a -1)$.
I want to create the space of Modular Symbols
> ModularSymbols(eps,2,1)
When I attempt to do so, I receive this error:
> TypeError: No compatible natural embeddings found for Complex Lazy Field and Number Field in a2 with defining polynomial x^4 + 2*x^3 + 2*x^2 + 4*x + 4
What's going on here? For many Dirichlet characters, the Modular Symbol space is created just fine. What's breaking in this case?
2) As a secondary question, is there any way to create the space of modular symbols
> MS=f.modular_symbols()
in such a way that MS has a manin symbol list?JeffHTue, 07 Aug 2012 08:28:47 -0500http://ask.sagemath.org/question/9215/Approximating Periods of Modular Symbols on Weight Two Modular Formshttp://ask.sagemath.org/question/28721/approximating-periods-of-modular-symbols-on-weight-two-modular-forms/A modular symbol corresponds to an element of homology on a modular curve (relative to the cusps) and a weight two modular form corresponds to a holomorphic one-form. Given a modular symbol and a weight two modular form, how can I approximate the integral of the modular form over the relative cycle corresponding to the modular symbol?
An example (which fails to work) is the following:
f = Newforms(Gamma0(23), 2, names='a')[0];
M = ModularSymbols(23,2);
H = M.basis();
gamma = H[0];
f.period(gamma)Paul ApisaWed, 29 Jul 2015 18:28:14 -0500http://ask.sagemath.org/question/28721/Insufficient RAM for computing newformshttp://ask.sagemath.org/question/7711/insufficient-ram-for-computing-newforms/In a Mac OS X, with a 2.5Ghz processor and 4Gb RAM I ran the following lines in Sage:
D = DirichletGroup(20)
g = D[7].extend(1600) # order 4 character
N = Newforms(g,2,names='a')
In two hours the 4Gb were full and it started writing to swap. Is it normal that 4Gb RAM is not enough to perform the above computation? I'm new to Sage (and to the forum) but since Sage tells me that the space
S = ModularSymbols(g,2,sign=1).cuspidal_subspace().new_submodule()
has dim 34 I was expecting it to be within the powers of my computer. Thanks, NunonbfrSat, 25 Sep 2010 08:36:20 -0500http://ask.sagemath.org/question/7711/