
// Make newform 1120.3.c.g in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1120_c();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1120_3_c_g();".
// 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_1120_c();"
function MakeCharacter_1120_c()
    N := 1120;
    order := 2;
    char_gens := [351, 421, 897, 801];
    v := [2, 1, 1, 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_1120_c_Hecke(Kf)
    return MakeCharacter_1120_c();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1120_3_c_g();".
// 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_1120_3_c_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1120_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<3,R![198778880, 0, 707371008, 0, 877811712, 0, 504345792, 0, 148763328, 0, 24998482, 0, 2533457, 0, 157280, 0, 5830, 0, 118, 0, 1]>,<17,R![1122164161606005555200, 0, -36798329032574359306240, 0, 1227740276398867677184, 0, -17208148416471121920, 0, 134232068668425728, 0, -645646585281840, 0, 1992034464329, 0, -3949525828, 0, 4857182, 0, -3364, 0, 1]>,<19,R![10547319320141744046080, 0, -1600214258594107686912, 0, 85443824980975403008, 0, -2240535924709965824, 0, 32100042753822720, 0, -258328823935104, 0, 1165275765952, 0, -2993454464, 0, 4331920, 0, -3274, 0, 1]>],Snew);
    return Vf;
end function;