
// Make newform 1150.3.c.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1150_c();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1150_3_c_c();".
// 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_1150_c();"
function MakeCharacter_1150_c()
    N := 1150;
    order := 2;
    char_gens := [277, 51];
    v := [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_1150_c_Hecke(Kf)
    return MakeCharacter_1150_c();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1150_3_c_c();".
// 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_1150_3_c_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1150_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<3,R![1784896, 0, 24712224, 0, 22518132, 0, 7286420, 0, 1132361, 0, 94700, 0, 4362, 0, 104, 0, 1]>],Snew);
    return Vf;
end function;