
// Make newform 525.2.n.d in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_525_n();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_2_n_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_525_n();"
function MakeCharacter_525_n()
    N := 525;
    order := 5;
    char_gens := [176, 127, 451];
    v := [5, 2, 5];
    // 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_n_Hecke(Kf)
    return MakeCharacter_525_n();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_2_n_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_525_2_n_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_525_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![25, -1600, 40800, -167100, 540565, -1121650, 2012905, -2765860, 3718876, -3014076, 2730206, -1328421, 2547541, -727916, 2765841, 800809, 1873531, 423684, 648146, 61529, 184941, -2481, 44506, -1681, 8656, -346, 1186, -101, 156, -16, 16, -1, 1]>],Snew);
    return Vf;
end function;