
// Make newform 722.2.e.r in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_722_e();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_722_2_e_r();".
// 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_722_e();"
function MakeCharacter_722_e()
    N := 722;
    order := 9;
    char_gens := [363];
    v := [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_722_e_Hecke(Kf)
    return MakeCharacter_722_e();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_722_2_e_r();".
// 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_722_2_e_r( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_722_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![4096, 0, 0, 49152, 0, 0, 568320, 0, 0, 259072, 0, 0, 119104, 0, 0, -1152, 0, 0, 400, 0, 0, 8, 0, 0, 1]>,<5,R![47045881, 0, 0, -72280142, 0, 0, 102640310, 0, 0, -12617792, 0, 0, 1278099, 0, 0, -48048, 0, 0, 1710, 0, 0, 22, 0, 0, 1]>,<7,R![16, -48, 120, -88, 64, -12, 10, -2, 1]>,<13,R![51520374361, 0, 0, 1829557198438, 0, 0, 64940441655990, 0, 0, 1049930053408, 0, 0, 11801523939, 0, 0, 67527952, 0, 0, 281870, 0, 0, 642, 0, 0, 1]>],Snew);
    return Vf;
end function;