
// Make newform 731.2.f.c in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_731_f();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_731_2_f_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_731_f();"
function MakeCharacter_731_f()
    N := 731;
    order := 4;
    char_gens := [173, 562];
    v := [3, 4];
    // 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_731_f_Hecke(Kf)
    return MakeCharacter_731_f();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_731_2_f_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_731_2_f_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_731_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![8573184, 0, 386427904, 0, 7339011456, 0, 79039562240, 0, 545950107120, 0, 2591646977840, 0, 8851999140204, 0, 22505873047900, 0, 43749238761509, 0, 66449042720498, 0, 80263518542247, 0, 78208530275262, 0, 62177198100867, 0, 40690257772226, 0, 22065244461994, 0, 9960726938604, 0, 3753422014761, 0, 1181715773098, 0, 310547245884, 0, 67915055892, 0, 12294280942, 0, 1827107802, 0, 220263882, 0, 21171884, 0, 1582396, 0, 88532, 0, 3485, 0, 86, 0, 1]>,<3,R![39564100, 104715920, 138577952, -2737248464, 10704622789, -14532342836, 18730925864, -66183751940, 228857314431, -381226030050, 369359071216, -281086663058, 646880626357, -1169886882982, 1186626742114, -506055515544, 678423888274, -1417324462720, 1627462084304, -441040600352, 259823689206, -790673682402, 1162910279136, -157936533396, -9330533752, -188248127046, 463173013608, 13036634010, -19265542125, -10745018706, 103252638772, 22022874764, 587294792, 1061595830, 12174854936, 4143818110, 657984404, 138423946, 723417336, 294874668, 59748442, 5815212, 22303344, 9922448, 2213376, 115248, 356722, 166940, 39192, 1094, 2760, 1338, 325, 4, 8, 4, 1]>],Snew);
    return Vf;
end function;