Modular Symbols

ModularSymbols(M): ModFrm -> SeqEnum

The sequence of characteristic \(0\) spaces of modular symbols with given sign associated to the space of modular forms \(M\), when this makes sense.

ModularSymbols(M, sign): ModFrm, RngIntElt -> ModSym

The sequence of characteristic \(0\) spaces of modular symbols with given sign associated to the space of modular forms \(M\), when this makes sense.

Example: Modular Symbols (ex-33a446)

> M := ModularForms(Gamma0(389),2);
> ModularSymbols(M,+1);
[
    Full Modular symbols space of level 389, weight 2, and dimension
    33
]
> ModularSymbols(M,-1);
[
    Full Modular symbols space of level 389, weight 2, and dimension
    32
]
> M := ModularForms(Gamma1(13),2);
> ModularSymbols(M);
[
    Full Modular symbols space of level 13, weight 2, and dimension 1,
    Full Modular symbols space of level 13, weight 2, character $.1,
    and dimension 0,
    Full Modular symbols space of level 13, weight 2, character $.1,
    and dimension 4,
    Full Modular symbols space of level 13, weight 2, character $.1,
    and dimension 0,
    Full Modular symbols space of level 13, weight 2, character $.1^2,
    and dimension 2,
    Full Modular symbols space of level 13, weight 2, character $.1,
    and dimension 2
]
> Basis($1)[1];
-1/6*{-7/15, -6/13} + -1/6*{-7/18, -5/13} + -1/6*{-5/16, -4/13} +
-1/6*{-4/17, -3/13} + -1/6*{-3/19, -2/13} + -1/6*{0, oo}

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