
// Make newform 2070.3.c.b in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2070_c();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2070_3_c_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_2070_c();"
function MakeCharacter_2070_c()
    N := 2070;
    order := 2;
    char_gens := [461, 1657, 1891];
    v := [2, 2, 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_2070_c_Hecke(Kf)
    return MakeCharacter_2070_c();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_2070_3_c_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_2070_3_c_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2070_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<7,R![18769275101392048128256, 0, 135832254657198030181120, 0, 159024519166851411837024, 0, 73128112930174585469936, 0, 16145034383308106074977, 0, 2027498661252019008108, 0, 159640181933592944898, 0, 8351755281099154860, 0, 301034080570037423, 0, 7641873673604696, 0, 138101029163644, 0, 1777239005864, 0, 16105686735, 0, 100070460, 0, 404546, 0, 956, 0, 1]>],Snew);
    return Vf;
end function;