
// Make newform 462.2.y.b in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_462_y();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_462_2_y_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_462_y();"
function MakeCharacter_462_y()
    N := 462;
    order := 15;
    char_gens := [155, 199, 211];
    v := [15, 10, 12];
    // 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_462_y_Hecke(Kf)
    return MakeCharacter_462_y();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_462_2_y_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_462_2_y_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_462_y();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![14641, -61226, -14520, -244002, 2720936, -4893934, 4809293, -4513343, 3679003, -1960996, 1224495, -988802, 457230, -139056, 52124, -3171, -2470, -3105, 1932, -747, 340, -38, 1, -5, 1]>],Snew);
    return Vf;
end function;