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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
196.1.c.a \(1\) \(0.098\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
196.1.g.a \(2\) \(0.098\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
196.2.a.a \(1\) \(1.565\) \(\Q\) None None \(0\) \(-1\) \(-3\) \(0\) \(+\) \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
196.2.a.b \(1\) \(1.565\) \(\Q\) None None \(0\) \(1\) \(3\) \(0\) \(-\) \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
196.2.a.c \(2\) \(1.565\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\)
196.2.d.a \(4\) \(1.565\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots\)
196.2.d.b \(4\) \(1.565\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
196.2.d.c \(8\) \(1.565\) 8.0.\(\cdots\).10 None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots\)
196.2.e.a \(2\) \(1.565\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(0\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
196.2.e.b \(4\) \(1.565\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
196.2.f.a \(4\) \(1.565\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(6\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
196.2.f.b \(4\) \(1.565\) \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
196.2.f.c \(8\) \(1.565\) 8.0.339738624.1 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots\)
196.2.f.d \(16\) \(1.565\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(4\) \(0\) \(0\) \(0\) \(q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots\)
196.2.i.a \(24\) \(1.565\) None None \(0\) \(0\) \(0\) \(0\)
196.2.j.a \(156\) \(1.565\) None None \(-5\) \(0\) \(-14\) \(0\)
196.2.m.a \(60\) \(1.565\) None None \(0\) \(1\) \(3\) \(4\)
196.2.p.a \(312\) \(1.565\) None None \(-13\) \(0\) \(-22\) \(0\)
196.3.b.a \(2\) \(5.341\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+6q^{9}+15q^{11}+\cdots\)
196.3.b.b \(4\) \(5.341\) 4.0.2048.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-1-\beta _{3})q^{9}+\cdots\)
196.3.c.a \(2\) \(5.341\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}+9q^{9}+\cdots\)
196.3.c.b \(2\) \(5.341\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(0\) \(q+(1+\beta )q^{2}+(-1+3\beta )q^{4}+(-7+5\beta )q^{8}+\cdots\)
196.3.c.c \(2\) \(5.341\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+9q^{9}+\cdots\)
196.3.c.d \(4\) \(5.341\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.c.e \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.c.f \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-15})\) None None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1}+\cdots)q^{4}+\cdots\)
196.3.c.g \(6\) \(5.341\) 6.0.1539727.2 None None \(-1\) \(0\) \(4\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.c.h \(6\) \(5.341\) 6.0.15582448.1 None None \(2\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
196.3.c.i \(6\) \(5.341\) 6.0.15582448.1 None None \(2\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
196.3.g.a \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
196.3.g.b \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.g.c \(4\) \(5.341\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-4\beta _{2}q^{4}+\cdots\)
196.3.g.d \(4\) \(5.341\) \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(0\) \(q+(-2\beta _{2}+\beta _{3})q^{2}+(1-3\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.g.e \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
196.3.g.f \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(8\) \(0\) \(0\) \(0\) \(q+2q^{2}+(\beta _{1}-\beta _{3})q^{3}+4q^{4}+4\beta _{1}q^{5}+\cdots\)
196.3.g.g \(4\) \(5.341\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(8\) \(0\) \(0\) \(0\) \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
196.3.g.h \(8\) \(5.341\) 8.0.207360000.1 None None \(-2\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{3})q^{2}+(\beta _{1}-2\beta _{4}-2\beta _{5}-2\beta _{7})q^{3}+\cdots\)
196.3.g.i \(12\) \(5.341\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(2\) \(0\) \(q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)
196.3.g.j \(12\) \(5.341\) 12.0.\(\cdots\).1 None None \(1\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}-\beta _{4}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.g.k \(12\) \(5.341\) 12.0.\(\cdots\).1 None None \(1\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}-\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.h.a \(2\) \(5.341\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-3\) \(0\) \(q+(-1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}-6\zeta_{6}q^{9}+\cdots\)
196.3.h.b \(4\) \(5.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(15+15\beta _{1}+\cdots)q^{9}+\cdots\)
196.3.h.c \(8\) \(5.341\) 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2}-2\beta _{6})q^{5}+(1+\cdots)q^{9}+\cdots\)
196.3.k.a \(324\) \(5.341\) None None \(-5\) \(0\) \(-10\) \(0\)
196.3.l.a \(60\) \(5.341\) None None \(0\) \(0\) \(0\) \(-10\)
196.3.n.a \(108\) \(5.341\) None None \(0\) \(-3\) \(-3\) \(14\)
196.3.o.a \(648\) \(5.341\) None None \(-13\) \(0\) \(-26\) \(0\)
196.4.a.a \(1\) \(11.564\) \(\Q\) None None \(0\) \(-4\) \(-20\) \(0\) \(+\) \(q-4q^{3}-20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.b \(1\) \(11.564\) \(\Q\) None None \(0\) \(-4\) \(-6\) \(0\) \(+\) \(q-4q^{3}-6q^{5}-11q^{9}-12q^{11}+82q^{13}+\cdots\)
196.4.a.c \(1\) \(11.564\) \(\Q\) None None \(0\) \(4\) \(20\) \(0\) \(+\) \(q+4q^{3}+20q^{5}-11q^{9}+44q^{11}+\cdots\)
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