︠a619a237-2826-4f93-aa0c-d406467478d9o︠
for N in [24..100]:
    S = CuspForms(N,2)
    print N
    print S.newforms('a')
︡991fde04-684b-48fa-9a75-883c04415f6f︡{"stdout":"24\n[q - q^3 - 2*q^5 + O(q^6)]\n25\n[]\n26\n[q - q^2 + q^3 + q^4 - 3*q^5 + O(q^6), q + q^2 - 3*q^3 + q^4 - q^5 + O(q^6)]\n27\n[q - 2*q^4 + O(q^6)]\n28\n[]\n29\n[q + a0*q^2 - a0*q^3 + (-2*a0 - 1)*q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n30\n[q - q^2 + q^3 + q^4 - q^5 + O(q^6)]\n31\n[q + a0*q^2 - 2*a0*q^3 + (a0 - 1)*q^4 + q^5 + O(q^6)]\n32\n[q - 2*q^5 + O(q^6)]"}︡{"stdout":"\n33\n[q + q^2 - q^3 - q^4 - 2*q^5 + O(q^6)]\n34\n[q + q^2 - 2*q^3 + q^4 + O(q^6)]\n35\n[q + q^3 - 2*q^4 - q^5 + O(q^6), q + a1*q^2 + (-a1 - 1)*q^3 + (-a1 + 2)*q^4 + q^5 + O(q^6)]"}︡{"stdout":"\n36\n[q + O(q^6)]\n37\n[q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + O(q^6), q + q^3 - 2*q^4 + O(q^6)]\n38\n[q - q^2 + q^3 + q^4 + O(q^6), q + q^2 - q^3 + q^4 - 4*q^5 + O(q^6)]"}︡{"stdout":"\n39\n[q + q^2 - q^3 - q^4 + 2*q^5 + O(q^6), q + a1*q^2 + q^3 + (-2*a1 - 1)*q^4 + (-2*a1 - 2)*q^5 + O(q^6)]\n40\n[q + q^5 + O(q^6)]"}︡{"stdout":"\n41\n[q + a0*q^2 + (-1/2*a0^2 - a0 + 3/2)*q^3 + (a0^2 - 2)*q^4 + (-a0 - 1)*q^5 + O(q^6)]\n42\n[q + q^2 - q^3 + q^4 - 2*q^5 + O(q^6)]\n43\n[q - 2*q^2 - 2*q^3 + 2*q^4 - 4*q^5 + O(q^6), q + a1*q^2 - a1*q^3 + (-a1 + 2)*q^5 + O(q^6)]"}︡{"stdout":"\n44\n[q + q^3 - 3*q^5 + O(q^6)]\n45\n[q + q^2 - q^4 - q^5 + O(q^6)]\n46\n[q - q^2 + q^4 + 4*q^5 + O(q^6)]"}︡{"stdout":"\n47\n[q + a0*q^2 + (a0^3 - a0^2 - 6*a0 + 4)*q^3 + (a0^2 - 2)*q^4 + (-4*a0^3 + 2*a0^2 + 20*a0 - 10)*q^5 + O(q^6)]\n48\n[q + q^3 - 2*q^5 + O(q^6)]\n49\n[q + q^2 - q^4 + O(q^6)]"}︡{"stdout":"\n50\n[q - q^2 + q^3 + q^4 + O(q^6), q + q^2 - q^3 + q^4 + O(q^6)]\n51\n[q + q^3 - 2*q^4 + 3*q^5 + O(q^6), q + a1*q^2 - q^3 + (-a1 + 2)*q^4 + (-a1 + 1)*q^5 + O(q^6)]"}︡{"stdout":"\n52\n[q + 2*q^5 + O(q^6)]\n53\n[q - q^2 - 3*q^3 - q^4 + O(q^6), q + a1*q^2 + (-a1^2 - a1 + 3)*q^3 + (a1^2 - 2)*q^4 + (a1^2 - 3)*q^5 + O(q^6)]"}︡{"stdout":"\n54\n[q - q^2 + q^4 + 3*q^5 + O(q^6), q + q^2 + q^4 - 3*q^5 + O(q^6)]\n55\n[q + q^2 - q^4 + q^5 + O(q^6), q + a1*q^2 + (-2*a1 + 2)*q^3 + (2*a1 - 1)*q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n56\n[q + 2*q^5 + O(q^6), q + 2*q^3 - 4*q^5 + O(q^6)]\n57\n[q - 2*q^2 - q^3 + 2*q^4 - 3*q^5 + O(q^6), q - 2*q^2 + q^3 + 2*q^4 + q^5 + O(q^6), q + q^2 + q^3 - q^4 - 2*q^5 + O(q^6)]"}︡{"stdout":"\n58\n[q - q^2 - 3*q^3 + q^4 - 3*q^5 + O(q^6), q + q^2 - q^3 + q^4 + q^5 + O(q^6)]\n59\n[q + a0*q^2 + (-1/4*a0^4 + 5/4*a0^2 - 1/2*a0)*q^3 + (a0^2 - 2)*q^4 + (3/4*a0^4 + 1/2*a0^3 - 23/4*a0^2 - 3*a0 + 7)*q^5 + O(q^6)]"}︡{"stdout":"\n60\n[]\n61\n[q - q^2 - 2*q^3 - q^4 - 3*q^5 + O(q^6), q + a1*q^2 + (-a1^2 + 3)*q^3 + (a1^2 - 2)*q^4 + (a1^2 - 2*a1 - 2)*q^5 + O(q^6)]\n62\n[q + q^2 + q^4 - 2*q^5 + O(q^6), q - q^2 + (1/2*a1 + 1/2)*q^3 + q^4 + (-a1 + 1)*q^5 + O(q^6)]"}︡{"stdout":"\n63\n[q + q^2 - q^4 + 2*q^5 + O(q^6), q + a1*q^2 + q^4 - 2*a1*q^5 + O(q^6)]\n64\n[q + 2*q^5 + O(q^6)]"}︡{"stdout":"\n65\n[q - q^2 - 2*q^3 - q^4 - q^5 + O(q^6), q + a1*q^2 + (a1 + 1)*q^3 + (-2*a1 - 1)*q^4 + q^5 + O(q^6), q + a2*q^2 + (-a2 + 1)*q^3 + q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n66\n[q - q^2 + q^3 + q^4 + O(q^6), q + q^2 - q^3 + q^4 + 2*q^5 + O(q^6), q + q^2 + q^3 + q^4 - 4*q^5 + O(q^6)]"}︡{"stdout":"\n67\n[q + 2*q^2 - 2*q^3 + 2*q^4 + 2*q^5 + O(q^6), q + a1*q^2 + (-a1 - 3)*q^3 + (-3*a1 - 3)*q^4 - 3*q^5 + O(q^6), q + a2*q^2 + (a2 + 1)*q^3 + (-a2 - 1)*q^4 + (-2*a2 + 1)*q^5 + O(q^6)]\n68\n[q + a0*q^3 + (-2*a0 + 2)*q^5 + O(q^6)]"}︡{"stdout":"\n69\n[q + q^2 + q^3 - q^4 + O(q^6), q + a1*q^2 - q^3 + 3*q^4 + (-a1 - 1)*q^5 + O(q^6)]\n70\n[q + q^2 + q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n71\n[q + a0*q^2 - a0*q^3 + (a0^2 - 2)*q^4 + (-a0^2 + a0 + 5)*q^5 + O(q^6), q + a1*q^2 + (-a1^2 + 3)*q^3 + (a1^2 - 2)*q^4 + (-a1 - 1)*q^5 + O(q^6)]"}︡{"stdout":"\n72\n[q + 2*q^5 + O(q^6)]\n73\n[q + q^2 - q^4 + 2*q^5 + O(q^6), q + a1*q^2 + (-a1 - 3)*q^3 + (-3*a1 - 3)*q^4 + a1*q^5 + O(q^6), q + a2*q^2 + (-a2 + 1)*q^3 + (a2 + 1)*q^4 - a2*q^5 + O(q^6)]"}︡{"stdout":"\n74\n[q - q^2 + (-a0 - 1)*q^3 + q^4 + (a0 + 2)*q^5 + O(q^6), q + q^2 + (a1 - 1)*q^3 + q^4 + (-3*a1 + 2)*q^5 + O(q^6)]"}︡{"stdout":"\n75\n[q - 2*q^2 + q^3 + 2*q^4 + O(q^6), q + q^2 + q^3 - q^4 + O(q^6), q + 2*q^2 - q^3 + 2*q^4 + O(q^6)]\n76\n[q + 2*q^3 - q^5 + O(q^6)]"}︡{"stdout":"\n77\n[q - 3*q^3 - 2*q^4 - q^5 + O(q^6), q + q^3 - 2*q^4 + 3*q^5 + O(q^6), q + q^2 + 2*q^3 - q^4 - 2*q^5 + O(q^6), q + a3*q^2 + (-a3 + 1)*q^3 + 3*q^4 - 2*q^5 + O(q^6)]"}︡{"stdout":"\n78\n[q - q^2 - q^3 + q^4 + 2*q^5 + O(q^6)]\n79\n[q - q^2 - q^3 - q^4 - 3*q^5 + O(q^6), q + a1*q^2 + (-a1^4 + a1^3 + 3*a1^2 - 3*a1 + 1)*q^3 + (a1^2 - 2)*q^4 + (a1^4 - 4*a1^2 - a1 + 3)*q^5 + O(q^6)]"}︡{"stdout":"\n80\n[q + q^5 + O(q^6), q + 2*q^3 - q^5 + O(q^6)]\n81\n[q + a0*q^2 + q^4 - a0*q^5 + O(q^6)]"}︡{"stdout":"\n82\n[q - q^2 - 2*q^3 + q^4 - 2*q^5 + O(q^6), q + q^2 + (-1/2*a1 + 1/2)*q^3 + q^4 + (a1 - 1)*q^5 + O(q^6)]"}︡{"stdout":"\n83\n[q - q^2 - q^3 - q^4 - 2*q^5 + O(q^6), q + a1*q^2 + (1/2*a1^4 - 1/2*a1^3 - 7/2*a1^2 + 3/2*a1 + 4)*q^3 + (a1^2 - 2)*q^4 + (-1/2*a1^5 - 1/2*a1^4 + 9/2*a1^3 + 7/2*a1^2 - 8*a1 - 2)*q^5 + O(q^6)]\n84\n[q - q^3 + 4*q^5 + O(q^6), q + q^3 + O(q^6)]"}︡{"stdout":"\n85\n[q + q^2 + 2*q^3 - q^4 - q^5 + O(q^6), q + a1*q^2 + (-a1 - 3)*q^3 + (-2*a1 - 1)*q^4 - q^5 + O(q^6), q + a2*q^2 + (-a2 + 1)*q^3 + q^4 + q^5 + O(q^6)]"}︡{"stdout":"\n86\n[q - q^2 + (1/2*a0 + 1/2)*q^3 + q^4 + (-1/2*a0 + 1/2)*q^5 + O(q^6), q + q^2 + (-a1 + 1)*q^3 + q^4 + (a1 - 2)*q^5 + O(q^6)]"}︡{"stdout":"\n87\n[q + a0*q^2 + q^3 + (a0 - 1)*q^4 + (-2*a0 + 2)*q^5 + O(q^6), q + a1*q^2 - q^3 + (a1^2 - 2)*q^4 + (-2*a1^2 + 8)*q^5 + O(q^6)]"}︡{"stdout":"\n88\n[q - 3*q^3 - 3*q^5 + O(q^6), q + a1*q^3 + (-a1 + 2)*q^5 + O(q^6)]"}︡{"stdout":"\n89\n[q - q^2 - q^3 - q^4 - q^5 + O(q^6), q + q^2 + 2*q^3 - q^4 - 2*q^5 + O(q^6), q + a2*q^2 + (-1/2*a2^4 + 1/2*a2^3 + 7/2*a2^2 - 5/2*a2 - 4)*q^3 + (a2^2 - 2)*q^4 + (-a2^2 + 4)*q^5 + O(q^6)]\n90\n[q - q^2 + q^4 + q^5 + O(q^6), q + q^2 + q^4 - q^5 + O(q^6), q + q^2 + q^4 + q^5 + O(q^6)]"}︡{"stdout":"\n91\n[q - 2*q^2 + 2*q^4 - 3*q^5 + O(q^6), q - 2*q^3 - 2*q^4 - 3*q^5 + O(q^6), q + a2*q^2 - a2*q^3 + (a2 + 3)*q^5 + O(q^6), q + a3*q^2 + (-a3^2 + a3 + 2)*q^3 + (a3^2 - 2)*q^4 + (-a3 + 1)*q^5 + O(q^6)]"}︡{"stdout":"\n92\n[q - 3*q^3 - 2*q^5 + O(q^6), q + q^3 + O(q^6)]\n93\n[q + a0*q^2 - q^3 + (-3*a0 - 3)*q^4 + (-2*a0 - 5)*q^5 + O(q^6), q + a1*q^2 + q^3 + (a1^2 - 2)*q^4 + (-a1^2 - a1 + 2)*q^5 + O(q^6)]"}︡{"stdout":"\n94\n[q + q^2 + q^4 + O(q^6), q - q^2 + (1/2*a1 + 1/2)*q^3 + q^4 + (-1/4*a1 + 7/4)*q^5 + O(q^6)]"}︡{"stdout":"\n95\n[q + a0*q^2 + (-a0^2 + 3)*q^3 + (a0^2 - 2)*q^4 + q^5 + O(q^6), q + a1*q^2 + (-a1^3 + 5*a1 - 2)*q^3 + (a1^2 - 2)*q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n96\n[q - q^3 + 2*q^5 + O(q^6), q + q^3 + 2*q^5 + O(q^6)]\n97\n[q + a0*q^2 + (-a0^2 - 3*a0 - 2)*q^3 + (a0^2 - 2)*q^4 + (2*a0^2 + 5*a0 - 1)*q^5 + O(q^6), q + a1*q^2 + (-a1^2 + a1 + 2)*q^3 + (a1^2 - 2)*q^4 + (-a1 + 1)*q^5 + O(q^6)]"}︡{"stdout":"\n98\n[q - q^2 + 2*q^3 + q^4 + O(q^6), q + q^2 + (a1 - 1)*q^3 + q^4 + (-2*a1 + 2)*q^5 + O(q^6)]\n99\n[q - q^2 - q^4 - 4*q^5 + O(q^6), q - q^2 - q^4 + 2*q^5 + O(q^6), q + q^2 - q^4 + 4*q^5 + O(q^6), q + 2*q^2 + 2*q^4 - q^5 + O(q^6)]"}︡{"stdout":"\n100\n[q + 2*q^3 + O(q^6)]\n"}︡
︠a33f1635-b084-40ca-92d3-fd47bb53cbf1︠
S = CuspForms(41,2)
D = S.newforms('a')
D
︡e56707c3-2c14-4aa3-a27b-62e7eab0ccc5︡{"stdout":"[q + a0*q^2 + (-1/2*a0^2 - a0 + 3/2)*q^3 + (a0^2 - 2)*q^4 + (-a0 - 1)*q^5 + O(q^6)]\n"}︡
︠050a2cc7-405b-4926-9742-40e640b3da4d︠
f = D[0]
︡9b41061e-0ddf-4363-855d-26975af4beb3︡
︠9d5a170d-3697-4c77-bd2c-65bb6874fa0b︠
K = f.hecke_eigenvalue_field(); K
︡9132dcc6-da0c-46cc-87e7-22f6b14082cd︡{"stdout":"Number Field in a0 with defining polynomial x^3 + x^2 - 5*x - 1\n"}︡
︠476b7ad0-3d31-442a-a375-5bc00dce6639︠
K.signature()
︡8e1710e9-111e-4de5-b250-44bbc64f1571︡{"stdout":"(3, 0)\n"}︡
︠0d58f6cd-d4ac-4aa7-ad49-2b5402000c69︠
proof.number_field(False)
%time U = CyclotomicField(29).unit_group()
︡d2e4265c-b435-4261-aae4-c334087af738︡{"stdout":"CPU time: 0.62 s, Wall time: 0.63 s"}︡{"stdout":"\n"}︡
︠35aef9ec-90f2-4e32-a5c7-b9ca452d7fce︠











Collaborative Calculation and Data Science

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