
// Make newform 950.2.u.f in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_u();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_u_f();".
// 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_950_u();"
function MakeCharacter_950_u()
    N := 950;
    order := 18;
    char_gens := [77, 401];
    v := [9, 2];
    // 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_950_u_Hecke(Kf)
    return MakeCharacter_950_u();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_u_f();".
// 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_950_2_u_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_u();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![331776, 0, -3400704, 0, 8315136, 0, 10185984, 0, 4943520, 0, -364428, 0, -32147, 0, -25425, 0, 981, 0, 368, 0, 126, 0, 9, 0, 1]>,<7,R![533794816, 0, -947079168, 0, 1171593984, 0, -651780608, 0, 246601008, 0, -64685844, 0, 12802965, 0, -1888461, 0, 213723, 0, -17744, 0, 1083, 0, -42, 0, 1]>],Snew);
    return Vf;
end function;