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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
784.1.d.a \(2\) \(0.391\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+q^{9}+\beta q^{13}+\beta q^{17}+q^{25}+\cdots\)
784.1.k.a \(2\) \(0.391\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-iq^{9}+(1-i+\cdots)q^{11}+\cdots\)
784.1.r.a \(4\) \(0.391\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(-1-\beta _{2})q^{9}+\beta _{3}q^{13}+\cdots\)
784.1.v.a \(4\) \(0.391\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{8}+\zeta_{12}q^{9}+\cdots\)
784.1.y.a \(4\) \(0.391\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots\)
784.2.a.a \(1\) \(6.260\) \(\Q\) None None \(0\) \(-3\) \(-1\) \(0\) \(+\) \(q-3q^{3}-q^{5}+6q^{9}+q^{11}+2q^{13}+\cdots\)
784.2.a.b \(1\) \(6.260\) \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-2q^{3}+q^{9}+4q^{13}-6q^{17}+2q^{19}+\cdots\)
784.2.a.c \(1\) \(6.260\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{3}+q^{5}-2q^{9}-3q^{11}+6q^{13}+\cdots\)
784.2.a.d \(1\) \(6.260\) \(\Q\) None None \(0\) \(-1\) \(3\) \(0\) \(-\) \(q-q^{3}+3q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
784.2.a.e \(1\) \(6.260\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
784.2.a.f \(1\) \(6.260\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-3q^{9}-4q^{11}-8q^{23}-5q^{25}+2q^{29}+\cdots\)
784.2.a.g \(1\) \(6.260\) \(\Q\) None None \(0\) \(1\) \(-3\) \(0\) \(+\) \(q+q^{3}-3q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
784.2.a.h \(1\) \(6.260\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(+\) \(q+q^{3}-q^{5}-2q^{9}-3q^{11}-6q^{13}+\cdots\)
784.2.a.i \(1\) \(6.260\) \(\Q\) None None \(0\) \(2\) \(4\) \(0\) \(-\) \(q+2q^{3}+4q^{5}+q^{9}+8q^{15}+2q^{17}+\cdots\)
784.2.a.j \(1\) \(6.260\) \(\Q\) None None \(0\) \(3\) \(1\) \(0\) \(-\) \(q+3q^{3}+q^{5}+6q^{9}+q^{11}-2q^{13}+\cdots\)
784.2.a.k \(2\) \(6.260\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-q^{9}-6q^{11}+4\beta q^{13}+\cdots\)
784.2.a.l \(2\) \(6.260\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}+2\beta q^{5}-q^{9}+2q^{11}+4q^{15}+\cdots\)
784.2.a.m \(2\) \(6.260\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+2\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}+3\beta q^{13}+\cdots\)
784.2.a.n \(2\) \(6.260\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}+\beta q^{13}+\cdots\)
784.2.f.a \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+\zeta_{6}q^{5}-2q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots\)
784.2.f.b \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+\zeta_{6}q^{5}-2q^{9}+\zeta_{6}q^{11}+\zeta_{6}q^{15}+\cdots\)
784.2.f.c \(4\) \(6.260\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-3q^{9}+(\beta _{1}+\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
784.2.f.d \(4\) \(6.260\) \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+4q^{9}+\beta _{3}q^{11}+\cdots\)
784.2.f.e \(8\) \(6.260\) 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(3-3\beta _{1})q^{9}+\cdots\)
784.2.i.a \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-1\) \(0\) \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
784.2.i.b \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-4\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
784.2.i.c \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+\cdots\)
784.2.i.d \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
784.2.i.e \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
784.2.i.f \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+8\zeta_{6}q^{23}+\cdots\)
784.2.i.g \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
784.2.i.h \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
784.2.i.i \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(6+\cdots)q^{17}+\cdots\)
784.2.i.j \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(4\) \(0\) \(q+(2-2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+8q^{15}+\cdots\)
784.2.i.k \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+(-4+\cdots)q^{11}+\cdots\)
784.2.i.l \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
784.2.i.m \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
784.2.i.n \(4\) \(6.260\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
784.2.j.a \(56\) \(6.260\) None None \(4\) \(0\) \(0\) \(0\)
784.2.j.b \(96\) \(6.260\) None None \(0\) \(0\) \(0\) \(0\)
784.2.m.a \(2\) \(6.260\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1+i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots\)
784.2.m.b \(2\) \(6.260\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(2\) \(0\) \(q+(-1-i)q^{2}+(1-i)q^{3}+2iq^{4}+\cdots\)
784.2.m.c \(2\) \(6.260\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(4\) \(4\) \(0\) \(q+(-1+i)q^{2}+(2-2i)q^{3}-2iq^{4}+\cdots\)
784.2.m.d \(4\) \(6.260\) \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(-6\) \(0\) \(q+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+\cdots\)
784.2.m.e \(4\) \(6.260\) \(\Q(\zeta_{12})\) None None \(-2\) \(2\) \(6\) \(0\) \(q+(-1+\zeta_{12})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
784.2.m.f \(4\) \(6.260\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-2\beta _{3})q^{8}+\cdots\)
784.2.m.g \(8\) \(6.260\) 8.0.214798336.3 None None \(2\) \(0\) \(4\) \(0\) \(q-\beta _{3}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
784.2.m.h \(12\) \(6.260\) 12.0.\(\cdots\).1 None None \(2\) \(-4\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{10})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots\)
784.2.m.i \(20\) \(6.260\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{9}q^{3}-\beta _{17}q^{4}+\beta _{2}q^{5}+\cdots\)
784.2.m.j \(24\) \(6.260\) None None \(4\) \(0\) \(-4\) \(0\)
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