
// Make newform 425.2.n.c in Magma, downloaded from the LMFDB on 12 March 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_425_n();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_425_2_n_c();".
// 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_425_n();"
function MakeCharacter_425_n()
    N := 425;
    order := 8;
    char_gens := [52, 326];
    v := [4, 3];
    // 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_425_n_Hecke( : Kf := Kf)
    return MakeCharacter_425_n();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_425_2_n_c();".
// 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_425_2_n_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_425_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![289, 136, 32, -1888, 25878, -6608, 192, 8128, 59339, 2864, 32, 704, 20112, 640, 0, -128, 2327, -8, 0, 0, 90, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;