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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.2.a.a \(1\) \(0.160\) \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
20.2.e.a \(2\) \(0.160\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
20.3.b.a \(4\) \(0.545\) \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)
20.3.d.a \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)
20.3.f.a \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)
20.4.a.a \(1\) \(1.180\) \(\Q\) None \(0\) \(4\) \(5\) \(-16\) \(+\) \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
20.4.c.a \(2\) \(1.180\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
20.4.e.a \(2\) \(1.180\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(-4\) \(0\) \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b \(12\) \(1.180\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
20.5.b.a \(8\) \(2.067\) 8.0.\(\cdots\).1 None \(6\) \(0\) \(0\) \(0\) \(q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(-2+\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)
20.5.d.a \(1\) \(2.067\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-4\) \(2\) \(25\) \(82\) \(q-4q^{2}+2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.b \(1\) \(2.067\) \(\Q\) \(\Q(\sqrt{-5}) \) \(4\) \(-2\) \(25\) \(-82\) \(q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.c \(8\) \(2.067\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(-40\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-6+\beta _{3})q^{4}+(-5+\cdots)q^{5}+\cdots\)
20.5.f.a \(4\) \(2.067\) \(\Q(i, \sqrt{241})\) None \(0\) \(-10\) \(-6\) \(110\) \(q+(-2+2\beta _{1}+\beta _{2})q^{3}+(-6\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
20.6.a.a \(1\) \(3.208\) \(\Q\) None \(0\) \(22\) \(-25\) \(218\) \(-\) \(q+22q^{3}-5^{2}q^{5}+218q^{7}+241q^{9}+\cdots\)
20.6.c.a \(2\) \(3.208\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(-10\) \(0\) \(q-\beta q^{3}+(-5-5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)
20.6.e.a \(2\) \(3.208\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(8\) \(0\) \(76\) \(0\) \(q+(4+4i)q^{2}+2^{5}iq^{4}+(38+41i)q^{5}+\cdots\)
20.6.e.b \(24\) \(3.208\) None \(-10\) \(0\) \(-80\) \(0\)
20.7.b.a \(12\) \(4.601\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-10\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(13+\cdots)q^{4}+\cdots\)
20.7.d.a \(1\) \(4.601\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-8\) \(-44\) \(-125\) \(524\) \(q-8q^{2}-44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\)
20.7.d.b \(1\) \(4.601\) \(\Q\) \(\Q(\sqrt{-5}) \) \(8\) \(44\) \(-125\) \(-524\) \(q+8q^{2}+44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\)
20.7.d.c \(2\) \(4.601\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-234\) \(0\) \(q+2iq^{2}-2^{6}q^{4}+(-117+11i)q^{5}+\cdots\)
20.7.d.d \(12\) \(4.601\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(460\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(6+\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
20.7.f.a \(6\) \(4.601\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(32\) \(-156\) \(-264\) \(q+(5+5\beta _{1}+\beta _{3})q^{3}+(-5^{2}+20\beta _{1}+\cdots)q^{5}+\cdots\)
20.8.a.a \(1\) \(6.248\) \(\Q\) None \(0\) \(-6\) \(-125\) \(-706\) \(-\) \(q-6q^{3}-5^{3}q^{5}-706q^{7}-2151q^{9}+\cdots\)
20.8.a.b \(2\) \(6.248\) \(\Q(\sqrt{1129}) \) None \(0\) \(-20\) \(250\) \(1660\) \(+\) \(q+(-10-\beta )q^{3}+5^{3}q^{5}+(830+9\beta )q^{7}+\cdots\)
20.8.c.a \(4\) \(6.248\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(-156\) \(0\) \(q+\beta _{1}q^{3}+(-39-\beta _{1}+\beta _{2})q^{5}+(-5\beta _{1}+\cdots)q^{7}+\cdots\)
20.8.e.a \(2\) \(6.248\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-16\) \(0\) \(556\) \(0\) \(q+(-8-8i)q^{2}+2^{7}iq^{4}+(278+29i)q^{5}+\cdots\)
20.8.e.b \(36\) \(6.248\) None \(14\) \(0\) \(-560\) \(0\)
20.9.b.a \(16\) \(8.148\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(6\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{3}+\cdots)q^{4}+\cdots\)
20.9.d.a \(1\) \(8.148\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-16\) \(158\) \(625\) \(-1922\) \(q-2^{4}q^{2}+158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.b \(1\) \(8.148\) \(\Q\) \(\Q(\sqrt{-5}) \) \(16\) \(-158\) \(625\) \(1922\) \(q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.c \(20\) \(8.148\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-1420\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-38+\beta _{3}+\cdots)q^{4}+\cdots\)
20.9.f.a \(8\) \(8.148\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-70\) \(894\) \(-2030\) \(q+(-9-9\beta _{1}+\beta _{2})q^{3}+(112-58\beta _{1}+\cdots)q^{5}+\cdots\)
20.10.a.a \(1\) \(10.301\) \(\Q\) None \(0\) \(-48\) \(625\) \(-532\) \(+\) \(q-48q^{3}+5^{4}q^{5}-532q^{7}-17379q^{9}+\cdots\)
20.10.a.b \(2\) \(10.301\) \(\Q(\sqrt{79}) \) None \(0\) \(-260\) \(-1250\) \(-380\) \(-\) \(q+(-130+\beta )q^{3}-5^{4}q^{5}+(-190+\cdots)q^{7}+\cdots\)
20.10.c.a \(4\) \(10.301\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(660\) \(0\) \(q+\beta _{1}q^{3}+(165+\beta _{1}-\beta _{2})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
20.10.e.a \(2\) \(10.301\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-32\) \(0\) \(1436\) \(0\) \(q+(-2^{4}-2^{4}i)q^{2}+2^{9}iq^{4}+(718+\cdots)q^{5}+\cdots\)
20.10.e.b \(48\) \(10.301\) None \(30\) \(0\) \(-1440\) \(0\)
20.11.b.a \(20\) \(12.707\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(22\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-2^{5}+\cdots)q^{4}+\cdots\)
20.11.d.a \(1\) \(12.707\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-32\) \(-236\) \(-3125\) \(-33364\) \(q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.b \(1\) \(12.707\) \(\Q\) \(\Q(\sqrt{-5}) \) \(32\) \(236\) \(-3125\) \(33364\) \(q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.c \(2\) \(12.707\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-474\) \(0\) \(q+8iq^{2}-2^{10}q^{4}+(-237+779i)q^{5}+\cdots\)
20.11.d.d \(24\) \(12.707\) None \(0\) \(0\) \(8280\) \(0\)
20.11.f.a \(10\) \(12.707\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(62\) \(894\) \(22286\) \(q+(6+6\beta _{1}-\beta _{2})q^{3}+(90-174\beta _{1}+\cdots)q^{5}+\cdots\)
20.12.a.a \(1\) \(15.367\) \(\Q\) None \(0\) \(306\) \(-3125\) \(-32074\) \(-\) \(q+306q^{3}-5^{5}q^{5}-32074q^{7}-83511q^{9}+\cdots\)
20.12.a.b \(2\) \(15.367\) \(\Q(\sqrt{46729}) \) None \(0\) \(220\) \(6250\) \(3340\) \(+\) \(q+(110-\beta )q^{3}+5^{5}q^{5}+(1670-111\beta )q^{7}+\cdots\)
20.12.c.a \(6\) \(15.367\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-4126\) \(0\) \(q+\beta _{1}q^{3}+(-688+2\beta _{1}-\beta _{2})q^{5}+\cdots\)
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