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2012-08-07 14:27:47 -0600 commented question Modular Symbols with Character & Manin Symbols

Oh, I see what you're saying. Thank you!

2012-08-07 11:44:58 -0600 commented question Modular Symbols with Character & Manin Symbols

Hi Daniels, Thanks for the suggestion! Unfortunately, I need to work with these algebraic objects with complete precision, so taking approximations like that won't work for me.

2012-08-07 08:28:47 -0600 asked a question 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 + 2x^3 + 2x^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?