
// Make newform 280.2.bl.b in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_280_bl();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_280_2_bl_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_280_bl();"
function MakeCharacter_280_bl()
    N := 280;
    order := 6;
    char_gens := [71, 141, 57, 241];
    v := [6, 3, 6, 4];
    // 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_280_bl_Hecke(Kf)
    return MakeCharacter_280_bl();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_280_2_bl_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_280_2_bl_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_280_bl();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![25600000000, 0, -692636160000, 0, 13123217848576, 0, -110231366701696, 0, 625852223323568, 0, -2363119848048776, 0, 6526751012899889, 0, -12939415275856936, 0, 19442327618182642, 0, -22763723995031496, 0, 21375029559786701, 0, -16371240195796736, 0, 10384667633494582, 0, -5511662643023816, 0, 2471038204553370, 0, -942472030460184, 0, 307731015041786, 0, -86401903094712, 0, 20931705898869, 0, -4382806514272, 0, 793528737434, 0, -124052279352, 0, 16693146170, 0, -1922571400, 0, 187937782, 0, -15390648, 0, 1036397, 0, -55664, 0, 2274, 0, -64, 0, 1]>],Snew);
    return Vf;
end function;