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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
88.1.l.a \(4\) \(0.044\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
88.2.a.a \(1\) \(0.703\) \(\Q\) None None \(0\) \(-3\) \(-3\) \(-2\) \(+\) \(q-3q^{3}-3q^{5}-2q^{7}+6q^{9}-q^{11}+\cdots\)
88.2.a.b \(2\) \(0.703\) \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(3\) \(-2\) \(-\) \(q+\beta q^{3}+(2-\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
88.2.c.a \(10\) \(0.703\) 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\cdots\)
88.2.g.a \(2\) \(0.703\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+\beta q^{2}+2q^{3}-2q^{4}+2\beta q^{6}-2\beta q^{8}+\cdots\)
88.2.g.b \(8\) \(0.703\) 8.0.\(\cdots\).6 None None \(0\) \(-8\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-1-\beta _{4})q^{3}+(-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
88.2.i.a \(4\) \(0.703\) \(\Q(\zeta_{10})\) None None \(0\) \(3\) \(3\) \(-3\) \(q+(1-\zeta_{10})q^{3}+(1-\zeta_{10}^{3})q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots\)
88.2.i.b \(8\) \(0.703\) 8.0.682515625.5 None None \(0\) \(-1\) \(-3\) \(7\) \(q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
88.2.k.a \(8\) \(0.703\) 8.0.64000000.1 \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
88.2.k.b \(32\) \(0.703\) None None \(-5\) \(-2\) \(0\) \(0\)
88.2.o.a \(40\) \(0.703\) None None \(-5\) \(0\) \(0\) \(-10\)
88.3.b.a \(1\) \(2.398\) \(\Q\) \(\Q(\sqrt{-22}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+11q^{11}+\cdots\)
88.3.b.b \(1\) \(2.398\) \(\Q\) \(\Q(\sqrt{-22}) \) None \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-11q^{11}+\cdots\)
88.3.b.c \(20\) \(2.398\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}-\beta _{3}q^{3}-\beta _{6}q^{4}+\beta _{13}q^{5}+\cdots\)
88.3.f.a \(20\) \(2.398\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{10}q^{5}+\cdots\)
88.3.h.a \(6\) \(2.398\) 6.0.1750426112.2 None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
88.3.j.a \(24\) \(2.398\) None None \(0\) \(4\) \(0\) \(0\)
88.3.l.a \(8\) \(2.398\) 8.0.64000000.1 \(\Q(\sqrt{-2}) \) None \(4\) \(4\) \(0\) \(0\) \(q+2\beta _{6}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
88.3.l.b \(80\) \(2.398\) None None \(-5\) \(-10\) \(0\) \(0\)
88.3.p.a \(88\) \(2.398\) None None \(-5\) \(0\) \(0\) \(-10\)
88.4.a.a \(1\) \(5.192\) \(\Q\) None None \(0\) \(-1\) \(-7\) \(-6\) \(-\) \(q-q^{3}-7q^{5}-6q^{7}-26q^{9}-11q^{11}+\cdots\)
88.4.a.b \(1\) \(5.192\) \(\Q\) None None \(0\) \(7\) \(9\) \(2\) \(+\) \(q+7q^{3}+9q^{5}+2q^{7}+22q^{9}-11q^{11}+\cdots\)
88.4.a.c \(2\) \(5.192\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-6\) \(-56\) \(-\) \(q+(-1-\beta )q^{3}+(-3+4\beta )q^{5}+(-28+\cdots)q^{7}+\cdots\)
88.4.a.d \(3\) \(5.192\) 3.3.11109.1 None None \(0\) \(2\) \(8\) \(24\) \(+\) \(q+(1-\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(8-\beta _{1}+\cdots)q^{7}+\cdots\)
88.4.c.a \(30\) \(5.192\) None None \(0\) \(0\) \(0\) \(0\)
88.4.g.a \(2\) \(5.192\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-20\) \(0\) \(0\) \(q+2\beta q^{2}-10q^{3}-8q^{4}-20\beta q^{6}+\cdots\)
88.4.g.b \(32\) \(5.192\) None None \(0\) \(16\) \(0\) \(0\)
88.4.i.a \(16\) \(5.192\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-1\) \(-1\) \(-13\) \(q+(-\beta _{3}-\beta _{6})q^{3}+(-1-\beta _{3}+2\beta _{5}+\cdots)q^{5}+\cdots\)
88.4.i.b \(20\) \(5.192\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(3\) \(1\) \(1\) \(q+(1-\beta _{6}+\beta _{7}+\beta _{9})q^{3}+(1+\beta _{3}+\beta _{7}+\cdots)q^{5}+\cdots\)
88.4.k.a \(8\) \(5.192\) 8.0.64000000.1 \(\Q(\sqrt{-2}) \) None \(0\) \(20\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+(\beta _{1}+5\beta _{2}-\beta _{3}-5\beta _{4}+\cdots)q^{3}+\cdots\)
88.4.k.b \(128\) \(5.192\) None None \(-5\) \(-26\) \(0\) \(0\)
88.4.o.a \(136\) \(5.192\) None None \(-1\) \(0\) \(0\) \(22\)
88.5.b.a \(1\) \(9.097\) \(\Q\) \(\Q(\sqrt{-22}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+3^{4}q^{9}-11^{2}q^{11}+\cdots\)
88.5.b.b \(1\) \(9.097\) \(\Q\) \(\Q(\sqrt{-22}) \) None \(4\) \(0\) \(0\) \(0\) \(q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+11^{2}q^{11}+\cdots\)
88.5.b.c \(44\) \(9.097\) None None \(0\) \(0\) \(0\) \(0\)
88.5.f.a \(40\) \(9.097\) None None \(0\) \(0\) \(0\) \(0\)
88.5.h.a \(12\) \(9.097\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(8\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{5}q^{7}+(42+\cdots)q^{9}+\cdots\)
88.5.j.a \(48\) \(9.097\) None None \(0\) \(-8\) \(0\) \(0\)
88.5.l.a \(8\) \(9.097\) 8.0.64000000.1 \(\Q(\sqrt{-2}) \) None \(-8\) \(28\) \(0\) \(0\) \(q+4\beta _{4}q^{2}+(7-\beta _{1}-7\beta _{2}-\beta _{3}+7\beta _{4}+\cdots)q^{3}+\cdots\)
88.5.l.b \(176\) \(9.097\) None None \(-1\) \(-34\) \(0\) \(0\)
88.5.p.a \(184\) \(9.097\) None None \(-5\) \(0\) \(0\) \(-10\)
88.6.a.a \(2\) \(14.114\) \(\Q(\sqrt{37}) \) None None \(0\) \(-14\) \(18\) \(48\) \(+\) \(q+(-7-\beta )q^{3}+9q^{5}+(24+11\beta )q^{7}+\cdots\)
88.6.a.b \(3\) \(14.114\) 3.3.1784453.1 None None \(0\) \(14\) \(56\) \(112\) \(-\) \(q+(5-\beta _{2})q^{3}+(19+\beta _{1}-\beta _{2})q^{5}+(38+\cdots)q^{7}+\cdots\)
88.6.a.c \(4\) \(14.114\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(-13\) \(-19\) \(58\) \(+\) \(q+(-3-\beta _{1})q^{3}+(-5+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
88.6.a.d \(4\) \(14.114\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(-5\) \(93\) \(-94\) \(-\) \(q+(-1-\beta _{1})q^{3}+(24-2\beta _{1}-\beta _{3})q^{5}+\cdots\)
88.6.c.a \(50\) \(14.114\) None None \(0\) \(0\) \(0\) \(0\)
88.6.g.a \(2\) \(14.114\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+4\beta q^{2}+2q^{3}-2^{5}q^{4}+8\beta q^{6}-2^{7}\beta q^{8}+\cdots\)
88.6.g.b \(56\) \(14.114\) None None \(0\) \(-8\) \(0\) \(0\)
88.6.i.a \(28\) \(14.114\) None None \(0\) \(-1\) \(-37\) \(105\)
88.6.i.b \(32\) \(14.114\) None None \(0\) \(-21\) \(37\) \(-181\)
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