Modular Symbols

ModularSymbols(M) : ModFrm -> SeqEnum

The sequence of characteristic 0 spaces of modular symbols with given sign associated to 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 M, when this makes sense.

Example ModFrm_ModularSymbols (H97E21)

> 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)