
// Make newform 1500.2.o.c in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1500_o();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1500_2_o_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_1500_o();"
function MakeCharacter_1500_o()
    N := 1500;
    order := 10;
    char_gens := [751, 1001, 877];
    v := [10, 10, 7];
    // 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_1500_o_Hecke(Kf)
    return MakeCharacter_1500_o();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1500_2_o_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_1500_2_o_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1500_o();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![172554496, 0, 1093572352, 0, 2559664096, 0, 2998987920, 0, 1964246465, 0, 757283742, 0, 177495989, 0, 26062572, 0, 2444070, 0, 146190, 0, 5396, 0, 112, 0, 1]>],Snew);
    return Vf;
end function;