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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
637.2.a.a \(1\) \(5.086\) \(\Q\) None \(-2\) \(0\) \(3\) \(0\) \(+\) \(q-2q^{2}+2q^{4}+3q^{5}-3q^{9}-6q^{10}+\cdots\)
637.2.a.b \(1\) \(5.086\) \(\Q\) None \(0\) \(2\) \(3\) \(0\) \(-\) \(q+2q^{3}-2q^{4}+3q^{5}+q^{9}-4q^{12}+\cdots\)
637.2.a.c \(1\) \(5.086\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.d \(1\) \(5.086\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.e \(2\) \(5.086\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) \(+\) \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.f \(2\) \(5.086\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) \(+\) \(q+(-1-\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.g \(2\) \(5.086\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(0\) \(+\) \(q+\beta q^{2}+\beta q^{3}+(-3-\beta )q^{5}+2q^{6}+\cdots\)
637.2.a.h \(3\) \(5.086\) 3.3.404.1 None \(-2\) \(-4\) \(-5\) \(0\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
637.2.a.i \(3\) \(5.086\) 3.3.404.1 None \(-2\) \(4\) \(5\) \(0\) \(-\) \(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.a.j \(3\) \(5.086\) 3.3.316.1 None \(1\) \(2\) \(-2\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
637.2.a.k \(5\) \(5.086\) 5.5.746052.1 None \(4\) \(0\) \(-2\) \(0\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.l \(5\) \(5.086\) 5.5.746052.1 None \(4\) \(0\) \(2\) \(0\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.m \(6\) \(5.086\) 6.6.4507648.1 None \(0\) \(-8\) \(-6\) \(0\) \(+\) \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.n \(6\) \(5.086\) 6.6.4507648.1 None \(0\) \(8\) \(6\) \(0\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.c.a \(2\) \(5.086\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+2iq^{2}-2q^{3}-2q^{4}+iq^{5}-4iq^{6}+\cdots\)
637.2.c.b \(2\) \(5.086\) \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+\beta q^{5}-3q^{9}+\beta q^{13}+4q^{16}+\cdots\)
637.2.c.c \(2\) \(5.086\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2iq^{2}+2q^{3}-2q^{4}-iq^{5}+4iq^{6}+\cdots\)
637.2.c.d \(6\) \(5.086\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.c.e \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.c.f \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.c.g \(16\) \(5.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.e.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
637.2.e.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.c \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(3\) \(0\) \(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.d \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.e \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(0\) \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.f \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.g \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.h \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+(2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.e.i \(6\) \(5.086\) 6.0.2696112.1 None \(-1\) \(-2\) \(2\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
637.2.e.j \(6\) \(5.086\) 6.0.2696112.1 None \(-1\) \(2\) \(-2\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
637.2.e.k \(6\) \(5.086\) 6.0.4406832.1 None \(2\) \(-4\) \(-5\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.l \(6\) \(5.086\) 6.0.4406832.1 None \(2\) \(4\) \(5\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.m \(10\) \(5.086\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(2\) \(0\) \(q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
637.2.e.n \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(-6\) \(0\) \(q+(-\beta _{3}+\beta _{11})q^{2}+(\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.e.o \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(8\) \(6\) \(0\) \(q+(-\beta _{3}+\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.f.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.c \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-3\) \(-6\) \(0\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+\cdots\)
637.2.f.d \(4\) \(5.086\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.f.e \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.f \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.g \(8\) \(5.086\) 8.0.\(\cdots\).7 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.f.h \(8\) \(5.086\) 8.0.\(\cdots\).6 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2}-\beta _{6})q^{2}+(-\beta _{3}+\beta _{7})q^{3}+\cdots\)
637.2.f.i \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(1\) \(14\) \(0\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.j \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-1\) \(2\) \(0\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{11}q^{3}+\cdots\)
637.2.f.k \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(1\) \(-2\) \(0\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+\beta _{11}q^{3}+\cdots\)
637.2.f.l \(16\) \(5.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{4}+\beta _{10})q^{2}+(\beta _{8}-\beta _{15})q^{3}+\cdots\)
637.2.g.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(6\) \(3\) \(0\) \(q-\zeta_{6}q^{2}+3q^{3}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
637.2.g.b \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-6\) \(-3\) \(0\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+\cdots\)
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