
// Make newform 725.2.p.b in Magma, downloaded from the LMFDB on 12 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_725_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_725_2_p_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_725_p();"
function MakeCharacter_725_p()
    N := 725;
    order := 14;
    char_gens := [552, 176];
    v := [7, 1];
    // 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_725_p_Hecke(Kf)
    return MakeCharacter_725_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_725_2_p_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_725_2_p_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_725_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, 0, 239, 0, 26695, 0, 1813736, 0, 84532685, 0, 21578730, 0, 12560085, 0, 100021975, 0, 100103038, 0, 22343222, 0, 62900926, 0, 12947512, 0, 24454018, 0, 9855696, 0, 3770001, 0, 2274285, 0, 1125495, 0, 373363, 0, 98916, 0, 18044, 0, 2715, 0, 449, 0, 74, 0, 8, 0, 1]>],Snew);
    return Vf;
end function;