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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
22.2.c.a \(4\) \(0.176\) \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(-6\) \(2\) \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
22.3.b.a \(2\) \(0.599\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
22.3.d.a \(8\) \(0.599\) 8.0.64000000.1 None \(0\) \(-2\) \(2\) \(-30\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
22.4.a.a \(1\) \(1.298\) \(\Q\) None \(-2\) \(-7\) \(-19\) \(14\) \(-\) \(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\)
22.4.a.b \(1\) \(1.298\) \(\Q\) None \(-2\) \(4\) \(14\) \(-8\) \(+\) \(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\)
22.4.a.c \(1\) \(1.298\) \(\Q\) None \(2\) \(1\) \(-3\) \(-10\) \(+\) \(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\)
22.4.c.a \(4\) \(1.298\) \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(3\) \(25\) \(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b \(8\) \(1.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(3\) \(5\) \(-1\) \(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.5.b.a \(4\) \(2.274\) \(\Q(\sqrt{-2}, \sqrt{553})\) None \(0\) \(2\) \(-30\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-8q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots\)
22.5.d.a \(16\) \(2.274\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(30\) \(150\) \(q-\beta _{4}q^{2}+(1+\beta _{2}+3\beta _{3}-\beta _{10}-\beta _{13}+\cdots)q^{3}+\cdots\)
22.6.a.a \(1\) \(3.528\) \(\Q\) None \(-4\) \(-21\) \(81\) \(98\) \(-\) \(q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots\)
22.6.a.b \(1\) \(3.528\) \(\Q\) None \(-4\) \(1\) \(-51\) \(-166\) \(+\) \(q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots\)
22.6.a.c \(1\) \(3.528\) \(\Q\) None \(4\) \(-29\) \(-31\) \(-230\) \(+\) \(q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots\)
22.6.a.d \(2\) \(3.528\) \(\Q(\sqrt{793}) \) None \(8\) \(29\) \(-13\) \(-14\) \(-\) \(q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)
22.6.c.a \(8\) \(3.528\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(20\) \(-30\) \(48\) \(q-4\beta _{3}q^{2}+(3+3\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.6.c.b \(12\) \(3.528\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(44\) \(-326\) \(q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
22.7.b.a \(6\) \(5.061\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-52\) \(368\) \(0\) \(q+\beta _{2}q^{2}+(-9+\beta _{1})q^{3}-2^{5}q^{4}+(61+\cdots)q^{5}+\cdots\)
22.7.d.a \(24\) \(5.061\) None \(0\) \(52\) \(-368\) \(720\)
22.8.a.a \(1\) \(6.872\) \(\Q\) None \(-8\) \(-19\) \(317\) \(-1030\) \(-\) \(q-8q^{2}-19q^{3}+2^{6}q^{4}+317q^{5}+\cdots\)
22.8.a.b \(1\) \(6.872\) \(\Q\) None \(-8\) \(91\) \(185\) \(-722\) \(+\) \(q-8q^{2}+91q^{3}+2^{6}q^{4}+185q^{5}+\cdots\)
22.8.a.c \(1\) \(6.872\) \(\Q\) None \(8\) \(-21\) \(-551\) \(62\) \(-\) \(q+8q^{2}-21q^{3}+2^{6}q^{4}-551q^{5}+\cdots\)
22.8.a.d \(2\) \(6.872\) \(\Q(\sqrt{14881}) \) None \(16\) \(-23\) \(331\) \(1794\) \(+\) \(q+8q^{2}+(-11-\beta )q^{3}+2^{6}q^{4}+(165+\cdots)q^{5}+\cdots\)
22.8.c.a \(12\) \(6.872\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-24\) \(44\) \(220\) \(534\) \(q+(-8+8\beta _{1}+8\beta _{2}+8\beta _{3})q^{2}+(5\beta _{1}+\cdots)q^{3}+\cdots\)
22.8.c.b \(16\) \(6.872\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(-96\) \(-82\) \(-700\) \(q-8\beta _{2}q^{2}+(-10-10\beta _{2}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)
22.9.b.a \(8\) \(8.962\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(182\) \(-1410\) \(0\) \(q-\beta _{4}q^{2}+(23+\beta _{1})q^{3}-2^{7}q^{4}+(-176+\cdots)q^{5}+\cdots\)
22.9.d.a \(32\) \(8.962\) None \(0\) \(-182\) \(1410\) \(-10950\)
22.10.a.a \(1\) \(11.331\) \(\Q\) None \(16\) \(-41\) \(-1039\) \(-3482\) \(+\) \(q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots\)
22.10.a.b \(1\) \(11.331\) \(\Q\) None \(16\) \(137\) \(-595\) \(11354\) \(-\) \(q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots\)
22.10.a.c \(1\) \(11.331\) \(\Q\) None \(16\) \(201\) \(2349\) \(-8806\) \(-\) \(q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots\)
22.10.a.d \(2\) \(11.331\) \(\Q(\sqrt{889}) \) None \(-32\) \(-21\) \(-521\) \(-7490\) \(-\) \(q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots\)
22.10.a.e \(2\) \(11.331\) \(\Q(\sqrt{463}) \) None \(-32\) \(34\) \(-1478\) \(8196\) \(+\) \(q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots\)
22.10.c.a \(16\) \(11.331\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(64\) \(-13\) \(1999\) \(3779\) \(q+(2^{4}+2^{4}\beta _{1}+2^{4}\beta _{2}-2^{4}\beta _{3})q^{2}+\cdots\)
22.10.c.b \(20\) \(11.331\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-80\) \(15\) \(-2455\) \(17413\) \(q+(-2^{4}+2^{4}\beta _{3}-2^{4}\beta _{4}-2^{4}\beta _{5})q^{2}+\cdots\)
22.11.b.a \(10\) \(13.978\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-106\) \(1138\) \(0\) \(q-\beta _{1}q^{2}+(-11-\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
22.11.d.a \(40\) \(13.978\) None \(0\) \(106\) \(-1138\) \(19470\)
22.12.a.a \(2\) \(16.904\) \(\Q(\sqrt{331}) \) None \(64\) \(-426\) \(2290\) \(-86324\) \(-\) \(q+2^{5}q^{2}+(-213+3\beta )q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.b \(3\) \(16.904\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(-70\) \(-5624\) \(-30576\) \(-\) \(q-2^{5}q^{2}+(-23+\beta _{2})q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.c \(3\) \(16.904\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(106\) \(17344\) \(13204\) \(+\) \(q-2^{5}q^{2}+(35+\beta _{1})q^{3}+2^{10}q^{4}+(5771+\cdots)q^{5}+\cdots\)
22.12.a.d \(3\) \(16.904\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(96\) \(370\) \(-1928\) \(58472\) \(+\) \(q+2^{5}q^{2}+(123-\beta _{1})q^{3}+2^{10}q^{4}+\cdots\)
22.12.c.a \(20\) \(16.904\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-160\) \(56\) \(-362\) \(-167178\) \(q+2^{5}\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2}+9\beta _{4}+\cdots)q^{3}+\cdots\)
22.12.c.b \(24\) \(16.904\) None \(192\) \(-36\) \(-11720\) \(20572\)
22.13.b.a \(12\) \(20.108\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-1240\) \(-1440\) \(0\) \(q-\beta _{2}q^{2}+(-103-\beta _{1})q^{3}-2^{11}q^{4}+\cdots\)
22.13.d.a \(48\) \(20.108\) None \(0\) \(1240\) \(1440\) \(439200\)
22.14.a.a \(2\) \(23.591\) \(\Q(\sqrt{100039}) \) None \(-128\) \(-662\) \(-48566\) \(404508\) \(+\) \(q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.b \(2\) \(23.591\) \(\Q(\sqrt{55441}) \) None \(-128\) \(1626\) \(7666\) \(637048\) \(-\) \(q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.c \(2\) \(23.591\) \(\Q(\sqrt{45769}) \) None \(128\) \(-926\) \(2914\) \(-170560\) \(+\) \(q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.d \(3\) \(23.591\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(192\) \(-298\) \(40432\) \(40452\) \(-\) \(q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots\)
22.14.c.a \(24\) \(23.591\) None \(384\) \(2708\) \(32920\) \(-509572\)
22.14.c.b \(28\) \(23.591\) None \(-448\) \(-1248\) \(71554\) \(361734\)
22.15.b.a \(14\) \(27.352\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(4394\) \(69758\) \(0\) \(q+\beta _{2}q^{2}+(314+\beta _{1})q^{3}-2^{13}q^{4}+\cdots\)
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