
// Make newform 525.2.bf.f in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_525_bf();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_2_bf_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_525_bf();"
function MakeCharacter_525_bf()
    N := 525;
    order := 12;
    char_gens := [176, 127, 451];
    v := [6, 3, 8];
    // 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_525_bf_Hecke(Kf)
    return MakeCharacter_525_bf();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_2_bf_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_525_2_bf_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_525_bf();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![10000, 0, 0, 0, -1118000, 0, 0, 0, 122918800, 0, 0, 0, -229926880, 0, 0, 0, 323534556, 0, 0, 0, -164139168, 0, 0, 0, 58992592, 0, 0, 0, -11151456, 0, 0, 0, 1495233, 0, 0, 0, -84374, 0, 0, 0, 3423, 0, 0, 0, -70, 0, 0, 0, 1]>,<13,R![30976, -49280, 39200, -15848, 6361, -4826, 3682, -1504, 334, -26, 8, -4, 1]>],Snew);
    return Vf;
end function;