
// Make newform 180.7.c.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_180_c();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_180_7_c_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_180_c();"
function MakeCharacter_180_c()
    N := 180;
    order := 2;
    char_gens := [91, 101, 37];
    v := [1, 2, 2];
    // 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_180_c_Hecke(Kf)
    return MakeCharacter_180_c();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_180_7_c_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_180_7_c_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_180_c();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,7,sign)));
    Vf := Kernel([<7,R![30764260265583046012250766932116079312602889442330218070016, 0, 11738682055488174037262681195720522027774938181617582080, 0, 1733250832401789586648914851275690851304781276774400, 0, 128653858853556879616536683646988551308959547392, 0, 5330262931046615359410348684747324417638400, 0, 132001900564439429245789253165981368320, 0, 2039117547678864554722644809744384, 0, 20110188862396868650220912640, 0, 127540842882443848581120, 0, 514466031616974848, 0, 1268405172480, 0, 1733280, 0, 1]>],Snew);
    return Vf;
end function;