
// Make newform 2100.2.ce.e in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2100_ce();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_ce_e();".
// 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_ce();"
function MakeCharacter_2100_ce()
    N := 2100;
    order := 12;
    char_gens := [1051, 701, 1177, 1501];
    v := [12, 12, 3, 2];
    // 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_ce_Hecke(Kf)
    return MakeCharacter_2100_ce();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2100_2_ce_e();".
// 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_ce_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2100_ce();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![14668900, -33167800, 65259740, -40152600, 29979024, -8329424, 6356356, -1337440, 869734, -86004, 64752, -6448, 2898, -168, 70, -4, 1]>,<17,R![2798410000, -47889312000, 409765939200, -2337447444480, 8882733463856, -20876849739360, 32792417164800, -34796029975200, 19175307686400, 3114991036896, -13416614511840, 14412015896256, -7060596329552, -1772399277840, 4614807235968, -5693333067360, 3678956345612, -360876544128, 9930480768, 10452347424, -6620530616, -23812824, 5171328, 11088768, 10032252, 235632, 0, -3216, -3448, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;