
// Make newform 2100.2.bi.n in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2100_bi();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_bi_n();".
// 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_bi();"
function MakeCharacter_2100_bi()
    N := 2100;
    order := 6;
    char_gens := [1051, 701, 1177, 1501];
    v := [6, 3, 6, 1];
    // 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_bi_Hecke(Kf)
    return MakeCharacter_2100_bi();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_bi_n();".
// 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_bi_n( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2100_bi();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![409600, 0, -715520, 0, 954244, 0, -456356, 0, 160258, 0, -19478, 0, 1747, 0, -47, 0, 1]>,<13,R![21904, 0, 8256, 0, 1039, 0, 54, 0, 1]>,<19,R![34596, -29574, 429, 6837, 1504, -129, -40, 3, 1]>,<37,R![84934656, 0, 43103232, 0, 14787225, 0, 2693445, 0, 352972, 0, 28327, 0, 1632, 0, 49, 0, 1]>],Snew);
    return Vf;
end function;