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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
768.1.e.a \(1\) \(0.383\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots\)
768.1.e.b \(1\) \(0.383\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots\)
768.1.e.c \(2\) \(0.383\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots\)
768.1.i.a \(4\) \(0.383\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
768.1.i.b \(4\) \(0.383\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
768.2.a.a \(1\) \(6.133\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}-4q^{13}+\cdots\)
768.2.a.b \(1\) \(6.133\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(q-q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
768.2.a.c \(1\) \(6.133\) \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) \(-\) \(q-q^{3}+4q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
768.2.a.d \(1\) \(6.133\) \(\Q\) None None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(q-q^{3}+2q^{5}-2q^{7}+q^{9}+4q^{13}+\cdots\)
768.2.a.e \(1\) \(6.133\) \(\Q\) None None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(q+q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{13}+\cdots\)
768.2.a.f \(1\) \(6.133\) \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) \(+\) \(q+q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
768.2.a.g \(1\) \(6.133\) \(\Q\) None None \(0\) \(1\) \(0\) \(4\) \(-\) \(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
768.2.a.h \(1\) \(6.133\) \(\Q\) None None \(0\) \(1\) \(2\) \(2\) \(-\) \(q+q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{13}+\cdots\)
768.2.a.i \(2\) \(6.133\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-4q^{11}+\cdots\)
768.2.a.j \(2\) \(6.133\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\)
768.2.a.k \(2\) \(6.133\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(0\) \(-\) \(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\)
768.2.a.l \(2\) \(6.133\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) \(-\) \(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+4q^{11}+\cdots\)
768.2.c.a \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.c.b \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.c.c \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta )q^{3}+(-1+2\beta )q^{9}+6q^{11}+\cdots\)
768.2.c.d \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-6q^{11}+\cdots\)
768.2.c.e \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+(1-\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.c.f \(2\) \(6.133\) \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.c.g \(4\) \(6.133\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-3q^{9}+\zeta_{12}^{3}q^{13}+\cdots\)
768.2.c.h \(4\) \(6.133\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8}^{3})q^{9}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
768.2.c.i \(4\) \(6.133\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+3q^{9}+\cdots\)
768.2.c.j \(4\) \(6.133\) \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+3q^{9}-2\beta _{2}q^{11}+\cdots\)
768.2.d.a \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
768.2.d.b \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}-2q^{7}-q^{9}-4iq^{11}-6iq^{13}+\cdots\)
768.2.d.c \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q-iq^{3}+4iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots\)
768.2.d.d \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots\)
768.2.d.e \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots\)
768.2.d.f \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}+4iq^{5}+2q^{7}-q^{9}+4iq^{11}+\cdots\)
768.2.d.g \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) \(q-iq^{3}+2q^{7}-q^{9}+4iq^{11}-6iq^{13}+\cdots\)
768.2.d.h \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+2iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)
768.2.f.a \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+\cdots\)
768.2.f.b \(4\) \(6.133\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1+\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots\)
768.2.f.c \(4\) \(6.133\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+\cdots\)
768.2.f.d \(4\) \(6.133\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{7}+3q^{9}+\zeta_{12}^{3}q^{13}+\cdots\)
768.2.f.e \(4\) \(6.133\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(-4\) \(0\) \(q+(1-\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots\)
768.2.f.f \(4\) \(6.133\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(4\) \(0\) \(q+(1+\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
768.2.f.g \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.j.a \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-8\) \(0\) \(q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots\)
768.2.j.b \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
768.2.j.c \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
768.2.j.d \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{8}q^{3}+(2-2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots\)
768.2.j.e \(8\) \(6.133\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-8\) \(0\) \(q-\zeta_{24}q^{3}+(-1+\zeta_{24}^{2}-\zeta_{24}^{6})q^{5}+\cdots\)
768.2.j.f \(8\) \(6.133\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(8\) \(0\) \(q-\zeta_{24}q^{3}+(1-\zeta_{24}^{2}+\zeta_{24}^{6})q^{5}+\cdots\)
768.2.k.a \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots\)
768.2.k.b \(4\) \(6.133\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots\)
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