
// Make newform 2100.2.bo.i in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2100_bo();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_bo_i();".
// 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_2100_bo();"
function MakeCharacter_2100_bo()
    N := 2100;
    order := 6;
    char_gens := [1051, 701, 1177, 1501];
    v := [6, 3, 3, 5];
    // 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_2100_bo_Hecke(Kf)
    return MakeCharacter_2100_bo();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_bo_i();".
// 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_2100_2_bo_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2100_bo();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![1475789056, 0, -559605872, 0, 144546913, 0, -19966919, 0, 1984747, 0, -101180, 0, 3715, 0, -74, 0, 1]>,<13,R![25, 0, -78, 0, 71, 0, -21, 0, 1]>,<19,R![6889, -27888, 40869, -13104, 596, 351, -12, -9, 1]>],Snew);
    return Vf;
end function;