
// Make newform 100.7.b.f in Magma, downloaded from the LMFDB on 16 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_100_b();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_100_b_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_100_7_b_f();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_100_7_b_f();".
// 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 ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [1000000, 0, -160000, 0, -1000, 0, 1775, 0, -10, 0, -16, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 770000, 0, -89000, 0, -8775, 0, 970, 0, 64, 0, -9], [0, -230000, 0, -28375, 0, 2900, 0, 260, 0, -33, 0, -2], [-20000, 0, -87000, 0, -775, 0, 1050, 0, -16, 0, -9, 0], [0, 290000, 0, -24500, 0, -3125, 0, 350, 0, 28, 0, -3], [327500, 0, -34500, 0, -3125, 0, 350, 0, 28, 0, -3, 0], [0, 6070000, 0, -355000, 0, -56575, 0, 4410, 0, 464, 0, -49], [586250, 0, -5000, 0, -5975, 0, 170, 0, 56, 0, -1, 0], [0, 26490000, 0, 957000, 0, -226775, 0, -5590, 0, 2512, 0, 103], [-238125, 0, 225500, 0, 7850, 0, -1900, 0, 28, 0, 22, 0], [0, -17970000, 0, 2027000, 0, 182175, 0, -20890, 0, -1744, 0, 209], [-4712500, 0, 547500, 0, 49675, 0, -6050, 0, -436, 0, 61, 0]];
    Rf_basisdens := [1, 50000, 12500, 1250, 6250, 2500, 25000, 1250, 50000, 625, 50000, 2500];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_100_b();"
function MakeCharacter_100_b()
    N := 100;
    order := 2;
    char_gens := [51, 77];
    v := [1, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_100_b_Hecke();"
function MakeCharacter_100_b_Hecke(Kf)
    N := 100;
    order := 2;
    char_gens := [51, 77];
    char_values := [[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := true, Kf := Kf); // the value of chi on the gens as elements in the Hecke field
    F := Universe(values);// the Hecke field
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),values);
    return chi;
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 7;
    raw_aps := [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, -1, 0, 0, 0, -1, 0, 0, 0], [1, 0, 0, 4, 0, 1, 0, 4, 0, -1, 0, 1], [0, 16, 0, 0, -1, 0, -1, 0, 0, 0, 18, 0], [0, -366, 0, 0, -100, 0, -10, 0, 0, 0, 14, 0], [13, 0, 0, 20, 0, -3, 0, 52, 0, 3, 0, 13], [0, 82, -101, 0, 7, 0, 0, 0, -9, 0, 0, 0], [1218, 0, 0, 0, 0, 34, 0, -220, 0, 0, 0, 110], [8, 0, 0, 192, 0, 40, 0, 128, 0, 8, 0, 56], [0, 1446, 0, 0, 375, 0, 21, 0, 0, 0, -12, 0], [-16059, 0, 0, 0, 0, 392, 0, 166, 0, 0, 0, -83], [0, 6111, 1063, 0, -1806, 0, 0, 0, 50, 0, 0, 0], [0, 5004, 301, 0, -1397, 0, 0, 0, 283, 0, 0, 0], [0, -10880, 0, 0, -2739, 0, 253, 0, 0, 0, 582, 0], [99, 0, 0, -340, 0, -205, 0, 268, 0, 141, 0, 35], [15151, 0, 0, 0, 0, 6347, 0, -1364, 0, 0, 0, 682], [0, 8541, 3089, 0, -2710, 0, 0, 0, -790, 0, 0, 0], [-38, 0, 0, -952, 0, -166, 0, -696, 0, -106, 0, -310], [0, -33742, 0, 0, -8794, 0, -1088, 0, 0, 0, -742, 0], [-1748, 0, 0, 400, 0, 1068, 0, -5232, 0, -188, 0, -868], [0, 43331, 6687, 0, -12282, 0, 0, 0, -890, 0, 0, 0], [365994, 0, 0, 0, 0, -5858, 0, 3724, 0, 0, 0, -1862], [0, -11622, 0, 0, -1376, 0, 3906, 0, 0, 0, 1694, 0], [680790, 0, 0, 0, 0, -16846, 0, -1308, 0, 0, 0, 654], [0, 103578, -6005, 0, -24945, 0, 0, 0, 2207, 0, 0, 0], [0, 42603, 33289, 0, -18916, 0, 0, 0, -228, 0, 0, 0], [-198035, 0, 0, 0, 0, -49245, 0, -1472, 0, 0, 0, 736], [0, 24072, 0, 0, 1908, 0, -4964, 0, 0, 0, 6512, 0], [0, 30642, -10867, 0, -5939, 0, 0, 0, 3981, 0, 0, 0], [3103, 0, 0, -5028, 0, -2001, 0, 5180, 0, -1615, 0, -513], [0, -142428, 0, 0, -31326, 0, 7798, 0, 0, 0, -1528, 0], [10911, 0, 0, 1660, 0, -4673, 0, 32828, 0, -735, 0, 5503], [-1560543, 0, 0, 0, 0, 6481, 0, 3836, 0, 0, 0, -1918], [7630, 0, 0, -10440, 0, -7314, 0, 19448, 0, 1778, 0, 2094], [0, 228754, 0, 0, 44829, 0, -14281, 0, 0, 0, 20876, 0], [0, -313539, 200575, 0, 26836, 0, 0, 0, 5620, 0, 0, 0], [0, -72926, -40107, 0, 30405, 0, 0, 0, -8587, 0, 0, 0], [0, 201134, 0, 0, 46495, 0, 7589, 0, 0, 0, 30332, 0], [-9563, 0, 0, 20180, 0, 9221, 0, -17388, 0, 1211, 0, 869], [-497762, 0, 0, 0, 0, 22598, 0, 17004, 0, 0, 0, -8502], [-24656, 0, 0, 29056, 0, 21424, 0, -63104, 0, -3664, 0, -6896], [0, 745770, 0, 0, 201592, 0, 13674, 0, 0, 0, -33250, 0], [0, 4084, 0, 0, 13223, 0, 7803, 0, 0, 0, -33202, 0], [-22650, 0, 0, 33720, 0, 19398, 0, -50376, 0, 714, 0, -2538], [-1309, 0, 0, 34284, 0, 10739, 0, 10188, 0, -3027, 0, 6403], [0, 103314, -295565, 0, 44287, 0, 0, 0, 15103, 0, 0, 0], [0, -93061, 133889, 0, -13484, 0, 0, 0, 13108, 0, 0, 0], [2030954, 0, 0, 0, 0, -144098, 0, 60284, 0, 0, 0, -30142], [0, -176974, 0, 0, -44258, 0, 2232, 0, 0, 0, 4522, 0], [-54524, 0, 0, 46960, 0, 41572, 0, -145232, 0, -5140, 0, -18092], [2805437, 0, 0, 0, 0, 308160, 0, 71430, 0, 0, 0, -35715], [-84755, 0, 0, -12940, 0, 34253, 0, -250956, 0, 9779, 0, -40723], [0, -102360, 0, 0, -98752, 0, -89624, 0, 0, 0, 113400, 0], [0, 1447548, -109669, 0, -328779, 0, 0, 0, -22763, 0, 0, 0], [14049, 0, 0, 0, 0, -88283, 0, -156716, 0, 0, 0, 78358], [66052, 0, 0, -20752, 0, -37308, 0, 185968, 0, -1812, 0, 26932], [0, -501682, 0, 0, -73773, 0, 92089, 0, 0, 0, -22412, 0], [337857, 0, 0, 0, 0, 381230, 0, 160930, 0, 0, 0, -80465], [0, 782565, 148999, 0, -240092, 0, 0, 0, 28804, 0, 0, 0], [0, -867154, 0, 0, -244519, 0, -111649, 0, 0, 0, -112376, 0], [0, -186111, 738977, 0, -131066, 0, 0, 0, -28602, 0, 0, 0], [-108234, 0, 0, -2216, 0, 50230, 0, -319144, 0, 6666, 0, -51338], [0, -175316, 0, 0, -23934, 0, 30590, 0, 0, 0, -18400, 0], [0, -47908, 0, 0, 65277, 0, 59001, 0, 0, 0, -191014, 0], [126513, 0, 0, 47332, 0, -45695, 0, 391748, 0, -11457, 0, 69361], [0, 1404684, 0, 0, 313172, 0, -118608, 0, 0, 0, -85220, 0], [0, 867777, -682295, 0, -32802, 0, 0, 0, -54274, 0, 0, 0], [-21925334, 0, 0, 0, 0, -627162, 0, -250548, 0, 0, 0, 125274], [0, -3426812, 0, 0, -764072, 0, 137644, 0, 0, 0, -95236, 0], [-86946, 0, 0, -109320, 0, 24414, 0, -332040, 0, -16542, 0, -79074], [0, -2946270, -215299, 0, 777165, 0, 0, 0, 52909, 0, 0, 0], [0, -1121734, 0, 0, -498507, 0, -221897, 0, 0, 0, 428500, 0], [-142413, 0, 0, 92940, 0, 99059, 0, -390004, 0, -9235, 0, -52589], [0, -702266, 1233331, 0, -165637, 0, 0, 0, 131483, 0, 0, 0], [-13934175, 0, 0, 0, 0, -656855, 0, 245708, 0, 0, 0, -122854], [0, 2018676, 0, 0, 254481, 0, -378363, 0, 0, 0, 244026, 0], [29720334, 0, 0, 0, 0, -332314, 0, 343068, 0, 0, 0, -171534], [59111059, 0, 0, 0, 0, 2036892, 0, 308834, 0, 0, 0, -154417], [-100967, 0, 0, -335900, 0, -40679, 0, -456476, 0, 14375, 0, -127271], [-28635817, 0, 0, 0, 0, 613923, 0, -136916, 0, 0, 0, 68458], [-28372, 0, 0, -493808, 0, -91508, 0, -367536, 0, -35516, 0, -155396], [0, 6826826, 0, 0, 1689932, 0, -9218, 0, 0, 0, 48662, 0], [-66774, 0, 0, 169640, 0, 68970, 0, -101848, 0, 13654, 0, 15850], [0, -2080591, -3335673, 0, 1299624, 0, 0, 0, 217768, 0, 0, 0], [40091331, 0, 0, 0, 0, 439768, 0, 306122, 0, 0, 0, -153061], [0, 3132352, 0, 0, 1013666, 0, 585410, 0, 0, 0, 248508, 0], [-4886778, 0, 0, 0, 0, 3404930, 0, 265540, 0, 0, 0, -132770], [0, -7187388, 2837683, 0, 1034661, 0, 0, 0, 211061, 0, 0, 0], [0, 3735623, 1677905, 0, -1435000, 0, 0, 0, 326472, 0, 0, 0], [-135928, 0, 0, 254240, 0, 140072, 0, -297760, 0, -17096, 0, -12952], [0, -6845388, -346171, 0, 1837307, 0, 0, 0, -157669, 0, 0, 0], [-272071, 0, 0, 279236, 0, 202121, 0, -669148, 0, 7447, 0, -62503], [514645, 0, 0, -363180, 0, -333227, 0, 1332564, 0, -29781, 0, 151637], [0, -2603750, 3029371, 0, -30945, 0, 0, 0, -301841, 0, 0, 0], [-173333886, 0, 0, 0, 0, 53842, 0, 36164, 0, 0, 0, -18082], [34364322, 0, 0, 0, 0, -6275320, 0, 62480, 0, 0, 0, -31240], [0, -802815, -3772937, 0, 1164872, 0, 0, 0, -83736, 0, 0, 0], [42001102, 0, 0, 0, 0, 2532470, 0, -152820, 0, 0, 0, 76410], [0, -15681657, -594847, 0, 4142168, 0, 0, 0, -292168, 0, 0, 0], [0, -14972406, 0, 0, -4031551, 0, -734221, 0, 0, 0, -314644, 0], [0, 10021389, -2755921, 0, -1883884, 0, 0, 0, 270068, 0, 0, 0], [57295203, 0, 0, 0, 0, 10058644, 0, 1313490, 0, 0, 0, -656745], [523837, 0, 0, 559348, 0, -54211, 0, 1715444, 0, -135741, 0, 333885], [0, 15906916, 0, 0, 4173664, 0, 15380, 0, 0, 0, -756980, 0], [0, 16695937, -2605191, 0, -3549138, 0, 0, 0, 105806, 0, 0, 0], [0, -6579224, 0, 0, -1403524, 0, 761316, 0, 0, 0, 557504, 0], [-303550, 0, 0, -351960, 0, -17886, 0, -923288, 0, 163342, 0, -158094], [-31511, 0, 0, 0, 0, -1672654, 0, 1949258, 0, 0, 0, -974629], [0, -13159236, 5258717, 0, 1905899, 0, 0, 0, 276923, 0, 0, 0], [0, 3461572, 0, 0, 924913, 0, 32021, 0, 0, 0, -174038, 0], [0, -9340790, 0, 0, -1805486, 0, 543172, 0, 0, 0, -1032502, 0], [396903, 0, 0, -783940, 0, -322633, 0, 655132, 0, -143607, 0, -69337], [417478, 0, 0, -1505128, 0, -631706, 0, 593240, 0, 93370, 0, -120858], [154332069, 0, 0, 0, 0, 5698796, 0, -487202, 0, 0, 0, 243601], [0, 5059935, 8176975, 0, -3391286, 0, 0, 0, 328234, 0, 0, 0], [0, 14880856, -9946683, 0, -1204697, 0, 0, 0, -115385, 0, 0, 0], [0, -23240284, 0, 0, -6348945, 0, -591405, 0, 0, 0, 972686, 0], [-393011, 0, 0, -1639500, 0, -177555, 0, -2070412, 0, -71629, 0, -642195], [-217882541, 0, 0, 0, 0, 1362881, 0, 2609528, 0, 0, 0, -1304764], [0, -4770786, 0, 0, -242320, 0, 769254, 0, 0, 0, -2262998, 0], [0, -11472384, 0, 0, -1814801, 0, 1600415, 0, 0, 0, -1012350, 0], [0, -3023653, -2648505, 0, 1528998, 0, 0, 0, -443834, 0, 0, 0], [-1333061, 0, 0, 1185036, 0, 980747, 0, -3442580, 0, -35915, 0, -388229], [-85124061, 0, 0, 0, 0, -7492099, 0, 1342688, 0, 0, 0, -671344], [-296041630, 0, 0, 0, 0, 8210170, 0, 1748, 0, 0, 0, -874], [1822348, 0, 0, 383120, 0, -828916, 0, 5685648, 0, 27044, 0, 1020476], [0, -24638484, -14808715, 0, 9729971, 0, 0, 0, 527315, 0, 0, 0], [0, 46850714, 0, 0, 12398019, 0, 1071493, 0, 0, 0, -598376, 0], [29001, 0, 0, 2647140, 0, 474857, 0, 1755428, 0, 344855, 0, 848713], [0, 1773168, -9954661, 0, 2043089, 0, 0, 0, 9137, 0, 0, 0], [-1924740, 0, 0, 745520, 0, 1221724, 0, -5547408, 0, -145948, 0, -848964], [0, 31951570, 0, 0, 8666683, 0, 110741, 0, 0, 0, -2493680, 0], [206465406, 0, 0, 0, 0, 13992782, 0, -1483124, 0, 0, 0, 741562], [139220206, 0, 0, 0, 0, 11569008, 0, -2026368, 0, 0, 0, 1013184], [0, 2453808, 0, 0, -133159, 0, -1785223, 0, 0, 0, -584002, 0], [0, -45585675, 15400673, 0, 7469922, 0, 0, 0, 305314, 0, 0, 0], [0, 12775504, 0, 0, 3376773, 0, 1375173, 0, 0, 0, 2018758, 0], [194349054, 0, 0, 0, 0, 4189672, 0, 770384, 0, 0, 0, -385192], [210281, 0, 0, -2666396, 0, -837239, 0, -571356, 0, 130999, 0, -495959], [-399700245, 0, 0, 0, 0, 11387069, 0, 44752, 0, 0, 0, -22376], [0, -28958922, -24806693, 0, 13278547, 0, 0, 0, 651427, 0, 0, 0], [0, -7374035, -17587383, 0, 6034786, 0, 0, 0, 822274, 0, 0, 0], [-85139711, 0, 0, 0, 0, -24111603, 0, 260164, 0, 0, 0, -130082], [2331046, 0, 0, 339480, 0, -824826, 0, 6651224, 0, -511654, 0, 994566], [0, 8318720, 0, 0, 3628261, 0, 2161333, 0, 0, 0, -1871658, 0], [0, 38811432, 0, 0, 9472246, 0, -1002850, 0, 0, 0, -1083252, 0], [-3397381, 0, 0, 593420, 0, 1760875, 0, -9723092, 0, 172341, 0, -1464165], [0, -379208, 4407043, 0, -410319, 0, 0, 0, -2386559, 0, 0, 0], [0, 39265054, 0, 0, 8485761, 0, -2295049, 0, 0, 0, 731912, 0], [-381835935, 0, 0, 0, 0, 20106194, 0, 682202, 0, 0, 0, -341101], [0, -59559591, 7467151, 0, 12922808, 0, 0, 0, 401208, 0, 0, 0], [0, 51334576, -12635019, 0, -9567553, 0, 0, 0, -429345, 0, 0, 0], [0, -41727189, -3804247, 0, 11745884, 0, 0, 0, -1452100, 0, 0, 0], [1796836, 0, 0, -49616, 0, -872636, 0, 5289328, 0, -76372, 0, 847828], [196978, 0, 0, -2688280, 0, -1126126, 0, -42072, 0, 711134, 0, -218014], [346013763, 0, 0, 0, 0, -25167896, 0, 7628970, 0, 0, 0, -3814485], [0, -31329674, 0, 0, -7035950, 0, 2910176, 0, 0, 0, 2634478, 0], [388484862, 0, 0, 0, 0, -29507890, 0, -1460420, 0, 0, 0, 730210], [0, 18579413, 21286913, 0, -10584382, 0, 0, 0, 2471202, 0, 0, 0], [0, -32561104, 0, 0, -6439950, 0, 2841410, 0, 0, 0, -1118484, 0], [0, 28293234, -22167307, 0, -1283275, 0, 0, 0, -992827, 0, 0, 0], [2413137, 0, 0, 3860388, 0, -199647, 0, 9085956, 0, -83649, 0, 2129841], [0, -43417306, 0, 0, -9679204, 0, 2062746, 0, 0, 0, -574998, 0], [0, 21141700, 1426699, 0, -5380547, 0, 0, 0, -1046211, 0, 0, 0], [-720456, 0, 0, 2127456, 0, 1143992, 0, -1601440, 0, -503800, 0, -80264], [0, 97540416, 0, 0, 21353311, 0, -5287953, 0, 0, 0, 1551266, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_100_b_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_100_7_b_f();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_100_7_b_f(:prec:=12)
    chi := MakeCharacter_100_b();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 7));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(997) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_100_7_b_f();".
// 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_100_7_b_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_100_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,7,sign)));
    Vf := Kernel([<3,R![60963840, 0, 1742400, 0, 2676, 0, 1]>,<13,R![-93610387146807705600, 0, 133299351330816, 0, -22348032, 0, 1]>],Snew);
    return Vf;
end function;