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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
896.1.h.a \(2\) \(0.447\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-\beta q^{5}-q^{7}+q^{9}+\beta q^{13}+\cdots\)
896.1.h.b \(2\) \(0.447\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}-\beta q^{5}+q^{7}+q^{9}+\beta q^{13}+\cdots\)
896.1.l.a \(2\) \(0.447\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+iq^{9}+(-1+i)q^{11}-iq^{25}+\cdots\)
896.1.l.b \(2\) \(0.447\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+iq^{9}+(1-i)q^{11}-iq^{25}+\cdots\)
896.1.v.a \(4\) \(0.447\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots\)
896.1.bm.a \(16\) \(0.447\) \(\Q(\zeta_{32})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{13}q^{2}-\zeta_{32}^{10}q^{4}-\zeta_{32}^{9}q^{7}+\cdots\)
896.2.a.a \(1\) \(7.155\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{9}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
896.2.a.b \(1\) \(7.155\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{9}+2q^{11}-4q^{13}-2q^{17}+\cdots\)
896.2.a.c \(1\) \(7.155\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-3q^{9}-2q^{11}-4q^{13}-2q^{17}+\cdots\)
896.2.a.d \(1\) \(7.155\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-3q^{9}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
896.2.a.e \(2\) \(7.155\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(2\) \(+\) \(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots\)
896.2.a.f \(2\) \(7.155\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(q+(-1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
896.2.a.g \(2\) \(7.155\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
896.2.a.h \(2\) \(7.155\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(2\) \(-\) \(q+(1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)
896.2.a.i \(3\) \(7.155\) 3.3.316.1 None None \(0\) \(-2\) \(-2\) \(-3\) \(+\) \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}-q^{7}+\cdots\)
896.2.a.j \(3\) \(7.155\) 3.3.316.1 None None \(0\) \(-2\) \(2\) \(3\) \(-\) \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots\)
896.2.a.k \(3\) \(7.155\) 3.3.316.1 None None \(0\) \(2\) \(-2\) \(3\) \(-\) \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+q^{7}+\cdots\)
896.2.a.l \(3\) \(7.155\) 3.3.316.1 None None \(0\) \(2\) \(2\) \(-3\) \(-\) \(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
896.2.b.a \(2\) \(7.155\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-iq^{5}-q^{7}-q^{9}-iq^{13}+\cdots\)
896.2.b.b \(2\) \(7.155\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}-q^{7}+3q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)
896.2.b.c \(2\) \(7.155\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+iq^{5}+q^{7}-q^{9}+iq^{13}+\cdots\)
896.2.b.d \(2\) \(7.155\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{5}+q^{7}+3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
896.2.b.e \(4\) \(7.155\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
896.2.b.f \(4\) \(7.155\) 4.0.2048.2 None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(-1-\beta _{3})q^{9}+\cdots\)
896.2.b.g \(4\) \(7.155\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
896.2.b.h \(4\) \(7.155\) 4.0.2048.2 None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(-1-\beta _{3})q^{9}+\cdots\)
896.2.e.a \(4\) \(7.155\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(-8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.b \(4\) \(7.155\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.c \(4\) \(7.155\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2-\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.d \(4\) \(7.155\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.e \(4\) \(7.155\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(-8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.f \(4\) \(7.155\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.g \(8\) \(7.155\) 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)
896.2.f.a \(8\) \(7.155\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{1}q^{5}+(\beta _{4}+\beta _{7})q^{7}+\beta _{2}q^{9}+\cdots\)
896.2.f.b \(8\) \(7.155\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{1}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+\cdots\)
896.2.f.c \(8\) \(7.155\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
896.2.f.d \(8\) \(7.155\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
896.2.i.a \(8\) \(7.155\) 8.0.3010058496.1 None None \(0\) \(-2\) \(-2\) \(2\) \(q-\beta _{4}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
896.2.i.b \(8\) \(7.155\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-2\) \(-2\) \(2\) \(q+(-\beta _{4}+\beta _{6})q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
896.2.i.c \(8\) \(7.155\) 8.0.3010058496.1 None None \(0\) \(-2\) \(2\) \(-2\) \(q-\beta _{4}q^{3}+(\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
896.2.i.d \(8\) \(7.155\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-2\) \(2\) \(-2\) \(q+(-\beta _{4}+\beta _{6})q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots\)
896.2.i.e \(8\) \(7.155\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(2\) \(-2\) \(-2\) \(q+(\beta _{4}-\beta _{6})q^{3}+(-1+\beta _{4}+\beta _{5}+\beta _{7})q^{5}+\cdots\)
896.2.i.f \(8\) \(7.155\) 8.0.3010058496.1 None None \(0\) \(2\) \(-2\) \(-2\) \(q+\beta _{4}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
896.2.i.g \(8\) \(7.155\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(2\) \(2\) \(2\) \(q+(\beta _{4}-\beta _{6})q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots\)
896.2.i.h \(8\) \(7.155\) 8.0.3010058496.1 None None \(0\) \(2\) \(2\) \(2\) \(q+\beta _{4}q^{3}+(\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
896.2.j.a \(4\) \(7.155\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.j.b \(4\) \(7.155\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots\)
896.2.j.c \(4\) \(7.155\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
896.2.j.d \(4\) \(7.155\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
896.2.j.e \(4\) \(7.155\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(4\) \(q+(-\beta _{2}-\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots\)
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