
// Make newform 950.2.bb.d in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_bb();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_bb_d();".
// 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_bb();"
function MakeCharacter_950_bb()
    N := 950;
    order := 36;
    char_gens := [77, 401];
    v := [27, 34];
    // 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_bb_Hecke(Kf)
    return MakeCharacter_950_bb();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_bb_d();".
// 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_bb_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_bb();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![16777216, 0, 0, 0, 4516601659392, 0, 0, 0, 10081241615791620096, 0, 0, 0, -35883365901902970880, 0, 0, 0, -1089237717512610906624, 0, 0, 0, -5076596244740925289008, 0, 0, 0, 143619912702618049642321, 0, 0, 0, 117268219596640988320749, 0, 0, 0, 468213110516653279442874, 0, 0, 0, 115636155448518570480401, 0, 0, 0, -6605721582061392700212, 0, 0, 0, -11753967646623987814920, 0, 0, 0, 1224150661756588118320, 0, 0, 0, 84736343032981605987, 0, 0, 0, 2486866365991333281, 0, 0, 0, -118116735099471583, 0, 0, 0, 1706507845776738, 0, 0, 0, -78123724274133, 0, 0, 0, 1627100205760, 0, 0, 0, -328308009, 0, 0, 0, 64009581, 0, 0, 0, -1348375, 0, 0, 0, 1605, 0, 0, 0, -57, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;