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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
845.2.a.a \(1\) \(6.747\) \(\Q\) None \(1\) \(-2\) \(1\) \(4\) \(-\) \(q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}+4q^{7}+\cdots\)
845.2.a.b \(2\) \(6.747\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(-4\) \(+\) \(q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
845.2.a.c \(2\) \(6.747\) \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(-2\) \(-2\) \(+\) \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
845.2.a.d \(2\) \(6.747\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-4\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(3+\beta )q^{6}+\cdots\)
845.2.a.e \(2\) \(6.747\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(4\) \(-\) \(q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
845.2.a.f \(2\) \(6.747\) \(\Q(\sqrt{13}) \) None \(1\) \(2\) \(2\) \(2\) \(-\) \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
845.2.a.g \(2\) \(6.747\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-4\) \(+\) \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
845.2.a.h \(3\) \(6.747\) \(\Q(\zeta_{14})^+\) None \(-1\) \(-5\) \(3\) \(-5\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.a.i \(3\) \(6.747\) 3.3.564.1 None \(-1\) \(-2\) \(3\) \(-2\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
845.2.a.j \(3\) \(6.747\) \(\Q(\zeta_{14})^+\) None \(1\) \(-5\) \(-3\) \(5\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.a.k \(3\) \(6.747\) 3.3.564.1 None \(1\) \(-2\) \(-3\) \(2\) \(-\) \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
845.2.a.l \(4\) \(6.747\) 4.4.4752.1 None \(-2\) \(-2\) \(4\) \(-10\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
845.2.a.m \(4\) \(6.747\) 4.4.4752.1 None \(2\) \(-2\) \(-4\) \(10\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
845.2.a.n \(9\) \(6.747\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(7\) \(-9\) \(-7\) \(-\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(1-\beta _{4})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)
845.2.a.o \(9\) \(6.747\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(7\) \(9\) \(7\) \(-\) \(q+(\beta _{1}+\beta _{6})q^{2}+(1-\beta _{4})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)
845.2.b.a \(2\) \(6.747\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
845.2.b.b \(2\) \(6.747\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+2iq^{3}+q^{4}+(2+i)q^{5}-2q^{6}+\cdots\)
845.2.b.c \(6\) \(6.747\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
845.2.b.d \(6\) \(6.747\) 6.0.49843600.1 None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.b.e \(6\) \(6.747\) 6.0.49843600.1 None \(0\) \(0\) \(3\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.b.f \(8\) \(6.747\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
845.2.b.g \(18\) \(6.747\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
845.2.b.h \(18\) \(6.747\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
845.2.c.a \(2\) \(6.747\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}+iq^{5}-2iq^{6}+\cdots\)
845.2.c.b \(4\) \(6.747\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
845.2.c.c \(4\) \(6.747\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
845.2.c.d \(4\) \(6.747\) \(\Q(i, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
845.2.c.e \(4\) \(6.747\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{3})q^{3}-q^{4}+\zeta_{12}q^{5}+\cdots\)
845.2.c.f \(6\) \(6.747\) 6.0.153664.1 None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
845.2.c.g \(8\) \(6.747\) 8.0.22581504.2 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.c.h \(18\) \(6.747\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(14\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{2}+(1+\beta _{11})q^{3}+(-2+\cdots)q^{4}+\cdots\)
845.2.d.a \(6\) \(6.747\) 6.0.350464.1 None \(-6\) \(0\) \(-2\) \(4\) \(q+(-1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
845.2.d.b \(6\) \(6.747\) 6.0.350464.1 None \(6\) \(0\) \(2\) \(-4\) \(q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
845.2.d.c \(8\) \(6.747\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+\beta _{3}q^{3}-\beta _{4}q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
845.2.d.d \(12\) \(6.747\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{11})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.d.e \(36\) \(6.747\) None \(0\) \(0\) \(0\) \(0\)
845.2.e.a \(2\) \(6.747\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.b \(2\) \(6.747\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-2\) \(4\) \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
845.2.e.c \(4\) \(6.747\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(-4\) \(4\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.d \(4\) \(6.747\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(-2\) \(4\) \(-2\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.e \(4\) \(6.747\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-4\) \(-4\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
845.2.e.f \(4\) \(6.747\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(4\) \(4\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
845.2.e.g \(4\) \(6.747\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(0\) \(-4\) \(4\) \(q+\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
845.2.e.h \(4\) \(6.747\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(-4\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.i \(6\) \(6.747\) 6.0.954288.1 None \(-1\) \(2\) \(-6\) \(-2\) \(q+(\beta _{4}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.j \(6\) \(6.747\) 6.0.64827.1 None \(-1\) \(5\) \(-6\) \(-5\) \(q-\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.k \(6\) \(6.747\) 6.0.954288.1 None \(1\) \(2\) \(6\) \(2\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
845.2.e.l \(6\) \(6.747\) 6.0.64827.1 None \(1\) \(5\) \(6\) \(5\) \(q+\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.e.m \(8\) \(6.747\) 8.0.22581504.2 None \(-2\) \(2\) \(-8\) \(-10\) \(q+(-1+\beta _{1}+\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
845.2.e.n \(8\) \(6.747\) 8.0.22581504.2 None \(2\) \(2\) \(8\) \(10\) \(q+(1-\beta _{1}-\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
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