
// Make newform 888.2.bo.c in Magma, downloaded from the LMFDB on 21 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_888_bo();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_888_2_bo_c();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_888_bo();"
function MakeCharacter_888_bo()
    N := 888;
    order := 9;
    char_gens := [223, 445, 593, 409];
    v := [9, 9, 9, 7];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_888_bo_Hecke(Kf)
    return MakeCharacter_888_bo();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_888_2_bo_c();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_888_2_bo_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_888_bo();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![353477601, -42133041, 466814178, 237978945, 102725415, 100713645, 282487734, 146210562, 73512774, 43135410, 4010715, -5728152, -1277222, -148788, 223611, 102754, -8379, -9123, -184, 198, 210, -1, -9, -3, 1]>],Snew);
    return Vf;
end function;