
// Make newform 72.7.p.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_72_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_72_7_p_b();".
// 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_72_p();"
function MakeCharacter_72_p()
    N := 72;
    order := 6;
    char_gens := [55, 37, 65];
    v := [3, 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_72_p_Hecke(Kf)
    return MakeCharacter_72_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_72_7_p_b();".
// 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_72_7_p_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_72_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,7,sign)));
    Vf := Kernel([<5,R![7463077949532155049255289672980744711277645162441497677817229671811613172128365637602669426371531706221163273282613140420390665892253573343333638509461806177353613778013283942400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 0, -226348911677288514617323238181398012240534955215782345849407360813131865693376299280387511858004606427843336424537419582732834326309331496547863676754839327575770988438757580800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 0, 4956837765809440946652528407464154330534236223768578993607693154556689681062407172991693425067498091032623784567639773052539561518514040611607509885489476060365367731332086894560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, 0, 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    return Vf;
end function;