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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
200.1.e.a \(2\) \(0.100\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots\)
200.1.g.a \(1\) \(0.100\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
200.1.g.b \(1\) \(0.100\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)
200.2.a.a \(1\) \(1.597\) \(\Q\) None None \(0\) \(-3\) \(0\) \(2\) \(-\) \(q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
200.2.a.b \(1\) \(1.597\) \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
200.2.a.c \(1\) \(1.597\) \(\Q\) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
200.2.a.d \(1\) \(1.597\) \(\Q\) None None \(0\) \(2\) \(0\) \(2\) \(-\) \(q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
200.2.a.e \(1\) \(1.597\) \(\Q\) None None \(0\) \(3\) \(0\) \(-2\) \(-\) \(q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)
200.2.c.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots\)
200.2.c.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots\)
200.2.d.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots\)
200.2.d.b \(2\) \(1.597\) \(\Q(\sqrt{-7}) \) None None \(-1\) \(0\) \(0\) \(-8\) \(q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.c \(2\) \(1.597\) \(\Q(\sqrt{-7}) \) None None \(1\) \(0\) \(0\) \(8\) \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.d \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(4\) \(q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots\)
200.2.d.e \(4\) \(1.597\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.2.d.f \(4\) \(1.597\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.f.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(0\) \(0\) \(q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots\)
200.2.f.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(0\) \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
200.2.f.c \(4\) \(1.597\) \(\Q(\zeta_{12})\) None None \(-2\) \(4\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.f.d \(4\) \(1.597\) \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
200.2.f.e \(4\) \(1.597\) \(\Q(\zeta_{12})\) None None \(2\) \(-4\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.k.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(-4\) \(0\) \(0\) \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
200.2.k.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots\)
200.2.k.c \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(0\) \(4\) \(q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
200.2.k.d \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(4\) \(0\) \(0\) \(q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots\)
200.2.k.e \(4\) \(1.597\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(-4\) \(4\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
200.2.k.f \(4\) \(1.597\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(4\) \(-4\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots\)
200.2.k.g \(8\) \(1.597\) 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
200.2.k.h \(8\) \(1.597\) \(\Q(\zeta_{20})\) None None \(2\) \(4\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots\)
200.2.m.a \(4\) \(1.597\) \(\Q(\zeta_{10})\) None None \(0\) \(5\) \(-5\) \(6\) \(q+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
200.2.m.b \(8\) \(1.597\) 8.0.58140625.2 None None \(0\) \(-6\) \(5\) \(4\) \(q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
200.2.m.c \(16\) \(1.597\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(1\) \(-1\) \(-6\) \(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots\)
200.2.o.a \(112\) \(1.597\) None None \(-5\) \(0\) \(0\) \(0\)
200.2.q.a \(32\) \(1.597\) None None \(0\) \(0\) \(2\) \(0\)
200.2.t.a \(112\) \(1.597\) None None \(-3\) \(0\) \(0\) \(-16\)
200.2.v.a \(8\) \(1.597\) \(\Q(\zeta_{20})\) None None \(-8\) \(0\) \(10\) \(4\) \(q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.b \(8\) \(1.597\) \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(-10\) \(-4\) \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.c \(208\) \(1.597\) None None \(2\) \(-16\) \(0\) \(0\)
200.3.e.a \(2\) \(5.450\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+4q^{6}-4iq^{8}+\cdots\)
200.3.e.b \(4\) \(5.450\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.e.c \(12\) \(5.450\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6}+\beta _{9})q^{4}+\cdots\)
200.3.e.d \(16\) \(5.450\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{2}q^{3}+(1+\beta _{11})q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.g.a \(1\) \(5.450\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(0\) \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+8q^{8}+\cdots\)
200.3.g.b \(2\) \(5.450\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-2}) \) None \(-4\) \(2\) \(0\) \(0\) \(q-2q^{2}+(1+\beta )q^{3}+4q^{4}+(-2-2\beta )q^{6}+\cdots\)
200.3.g.c \(2\) \(5.450\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-4q^{4}-3iq^{7}-4iq^{8}-9q^{9}+\cdots\)
200.3.g.d \(2\) \(5.450\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-2}) \) None \(4\) \(-2\) \(0\) \(0\) \(q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.g.e \(6\) \(5.450\) 6.0.189974000.1 None None \(-3\) \(2\) \(0\) \(0\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
200.3.g.f \(6\) \(5.450\) 6.0.189974000.1 None None \(3\) \(-2\) \(0\) \(0\) \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
200.3.g.g \(8\) \(5.450\) 8.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.3.g.h \(8\) \(5.450\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(2+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots\)
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