
// Make newform 966.2.q.j in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_966_q();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_966_2_q_j();".
// 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_966_q();"
function MakeCharacter_966_q()
    N := 966;
    order := 11;
    char_gens := [323, 829, 925];
    v := [11, 11, 4];
    // 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_966_q_Hecke(Kf)
    return MakeCharacter_966_q();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_966_2_q_j();".
// 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_966_2_q_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_966_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![2431673344, -35888090112, 376549054208, 7260291966848, 38949044351040, 110550184467904, 206090041104032, 286574263002032, 325412984814736, 318078138640392, 267095870183745, 190117219221034, 121635549147969, 56072989680956, 29706409725983, 8035173693367, 6660477748551, 2107112132084, 1819873767818, 568929838888, 221002064871, 39482607510, 12484381626, -2114155368, 812909394, 239907125, 149574594, 35740933, 13135036, 3926303, 1150213, 216659, 118594, 28920, 7284, 1798, 634, 84, 17, 4, 1]>],Snew);
    return Vf;
end function;