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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.5.b.a \(1\) \(0.413\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(-14\) \(0\) \(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
4.6.a.a \(1\) \(0.642\) \(\Q\) None \(0\) \(-12\) \(54\) \(-88\) \(-\) \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
4.7.b.a \(2\) \(0.920\) \(\Q(\sqrt{-15}) \) None \(4\) \(0\) \(20\) \(0\) \(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)
4.9.b.a \(1\) \(1.630\) \(\Q\) \(\Q(\sqrt{-1}) \) \(16\) \(0\) \(-1054\) \(0\) \(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
4.9.b.b \(2\) \(1.630\) \(\Q(\sqrt{-39}) \) None \(-20\) \(0\) \(1220\) \(0\) \(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\)
4.10.a.a \(1\) \(2.060\) \(\Q\) None \(0\) \(228\) \(-666\) \(-6328\) \(-\) \(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)
4.11.b.a \(4\) \(2.541\) 4.0.26777625.2 None \(-12\) \(0\) \(-1560\) \(0\) \(q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.12.a.a \(1\) \(3.073\) \(\Q\) None \(0\) \(-516\) \(-10530\) \(49304\) \(-\) \(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
4.13.b.a \(1\) \(3.656\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-64\) \(0\) \(23506\) \(0\) \(q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots\)
4.13.b.b \(4\) \(3.656\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(108\) \(0\) \(-18360\) \(0\) \(q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots\)
4.14.a.a \(1\) \(4.289\) \(\Q\) None \(0\) \(468\) \(56214\) \(333032\) \(-\) \(q+468q^{3}+56214q^{5}+333032q^{7}+\cdots\)
4.15.b.a \(6\) \(4.973\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-92\) \(0\) \(8060\) \(0\) \(q+(-15+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.16.a.a \(1\) \(5.708\) \(\Q\) None \(0\) \(-276\) \(-132210\) \(-3585736\) \(-\) \(q-276q^{3}-132210q^{5}-3585736q^{7}+\cdots\)
4.17.b.a \(1\) \(6.493\) \(\Q\) \(\Q(\sqrt{-1}) \) \(256\) \(0\) \(329666\) \(0\) \(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
4.17.b.b \(6\) \(6.493\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-164\) \(0\) \(-506740\) \(0\) \(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.18.a.a \(2\) \(7.329\) \(\Q(\sqrt{9361}) \) None \(0\) \(-5880\) \(604044\) \(25350160\) \(-\) \(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)
4.19.b.a \(8\) \(8.215\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(84\) \(0\) \(860880\) \(0\) \(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)
4.20.a.a \(1\) \(9.153\) \(\Q\) None \(0\) \(-36\) \(-196290\) \(-35905576\) \(-\) \(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\)
4.21.b.a \(1\) \(10.141\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-1024\) \(0\) \(-19306574\) \(0\) \(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
4.21.b.b \(8\) \(10.141\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(396\) \(0\) \(18568080\) \(0\) \(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)
4.22.a.a \(2\) \(11.179\) \(\Q(\sqrt{2161}) \) None \(0\) \(65640\) \(13689324\) \(-260508080\) \(-\) \(q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots\)
4.23.b.a \(10\) \(12.268\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1540\) \(0\) \(-17091100\) \(0\) \(q+(154-\beta _{1})q^{2}+(-19\beta _{1}-\beta _{2})q^{3}+\cdots\)
4.24.a.a \(2\) \(13.408\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(170520\) \(-92266020\) \(192083440\) \(-\) \(q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots\)
4.25.b.a \(1\) \(14.599\) \(\Q\) \(\Q(\sqrt{-1}) \) \(4096\) \(0\) \(64250786\) \(0\) \(q+2^{12}q^{2}+2^{24}q^{4}+64250786q^{5}+\cdots\)
4.25.b.b \(10\) \(14.599\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-6212\) \(0\) \(56758100\) \(0\) \(q+(-621+\beta _{1})q^{2}+(-3-15\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.26.a.a \(2\) \(15.840\) \(\Q(\sqrt{358121}) \) None \(0\) \(-899640\) \(-399350196\) \(-40518462320\) \(-\) \(q+(-449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots\)
4.27.b.a \(12\) \(17.132\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(180\) \(0\) \(-298775880\) \(0\) \(q+(15-\beta _{1})q^{2}-\beta _{2}q^{3}+(-1879252+\cdots)q^{4}+\cdots\)
4.28.a.a \(2\) \(18.474\) \(\Q(\sqrt{1059289}) \) None \(0\) \(-483720\) \(145079100\) \(60475251760\) \(-\) \(q+(-241860-\beta )q^{3}+(72539550+\cdots)q^{5}+\cdots\)
4.29.b.a \(1\) \(19.867\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-16384\) \(0\) \(11167097746\) \(0\) \(q-2^{14}q^{2}+2^{28}q^{4}+11167097746q^{5}+\cdots\)
4.29.b.b \(12\) \(19.867\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(24300\) \(0\) \(-12399664680\) \(0\) \(q+(45^{2}+\beta _{1})q^{2}+(-6\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.30.a.a \(3\) \(21.311\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(6139068\) \(13945023234\) \(360544308792\) \(-\) \(q+(2046356-\beta _{1})q^{3}+(4648341078+\cdots)q^{5}+\cdots\)
4.31.b.a \(14\) \(22.806\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-24476\) \(0\) \(14864798540\) \(0\) \(q+(-1748+\beta _{1})q^{2}+(9+30\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.32.a.a \(2\) \(24.351\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-31205160\) \(1872305820\) \(60\!\cdots\!80\) \(-\) \(q+(-15602580-\beta )q^{3}+(936152910+\cdots)q^{5}+\cdots\)
4.33.b.a \(1\) \(25.947\) \(\Q\) \(\Q(\sqrt{-1}) \) \(65536\) \(0\) \(-196496109694\) \(0\) \(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.33.b.b \(14\) \(25.947\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-23780\) \(0\) \(138121491740\) \(0\) \(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.34.a.a \(3\) \(27.593\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(92491788\) \(-53880683886\) \(45\!\cdots\!92\) \(-\) \(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)
4.35.b.a \(16\) \(29.290\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-27372\) \(0\) \(-21372255840\) \(0\) \(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.36.a.a \(3\) \(31.038\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(50908884\) \(280720890\) \(-5\!\cdots\!16\) \(-\) \(q+(16969628+\beta _{1})q^{3}+(93573630+\cdots)q^{5}+\cdots\)
4.37.b.a \(1\) \(32.837\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-262144\) \(0\) \(-4\!\cdots\!34\) \(0\) \(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
4.37.b.b \(16\) \(32.837\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(177228\) \(0\) \(58\!\cdots\!60\) \(0\) \(q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.38.a.a \(3\) \(34.686\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-272163492\) \(36\!\cdots\!94\) \(15\!\cdots\!92\) \(-\) \(q+(-90721164-\beta _{1})q^{3}+(1213681705398+\cdots)q^{5}+\cdots\)
4.39.b.a \(18\) \(36.585\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(364228\) \(0\) \(-8\!\cdots\!20\) \(0\) \(q+(20235-\beta _{1})q^{2}+(-18+165\beta _{1}+\cdots)q^{3}+\cdots\)
4.40.a.a \(3\) \(38.536\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-1269987036\) \(-8\!\cdots\!90\) \(26\!\cdots\!24\) \(-\) \(q+(-423329012+\beta _{1})q^{3}+(-27008612411730+\cdots)q^{5}+\cdots\)
4.41.b.a \(1\) \(40.537\) \(\Q\) \(\Q(\sqrt{-1}) \) \(1048576\) \(0\) \(18\!\cdots\!26\) \(0\) \(q+2^{20}q^{2}+2^{40}q^{4}+182008936336226q^{5}+\cdots\)
4.41.b.b \(18\) \(40.537\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-1801604\) \(0\) \(-1\!\cdots\!20\) \(0\) \(q+(-100089-\beta _{1})q^{2}+(4-6^{2}\beta _{1}+\cdots)q^{3}+\cdots\)
4.42.a.a \(4\) \(42.589\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(1162346640\) \(22\!\cdots\!24\) \(-4\!\cdots\!80\) \(-\) \(q+(290586660-\beta _{1})q^{3}+(55732604152806+\cdots)q^{5}+\cdots\)
4.43.b.a \(20\) \(44.691\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(802164\) \(0\) \(13\!\cdots\!00\) \(0\) \(q+(40108+\beta _{1})q^{2}+(2^{4}-78\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.44.a.a \(3\) \(46.844\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(7902569844\) \(29\!\cdots\!30\) \(-2\!\cdots\!36\) \(-\) \(q+(2634189948-\beta _{1})q^{3}+(9956588758110+\cdots)q^{5}+\cdots\)
4.45.b.a \(1\) \(49.048\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-4194304\) \(0\) \(94\!\cdots\!86\) \(0\) \(q-2^{22}q^{2}+2^{44}q^{4}+94681488501586q^{5}+\cdots\)
4.45.b.b \(20\) \(49.048\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(4799916\) \(0\) \(-1\!\cdots\!00\) \(0\) \(q+(239996+\beta _{1})q^{2}+(86+431\beta _{1}+\cdots)q^{3}+\cdots\)
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