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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1792.1.c.a \(1\) \(0.894\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.b \(1\) \(0.894\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.c \(2\) \(0.894\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.c.d \(2\) \(0.894\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.o.a \(4\) \(0.894\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.o.b \(4\) \(0.894\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.v.a \(4\) \(0.894\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots\)
1792.1.v.b \(4\) \(0.894\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
1792.1.bf.a \(8\) \(0.894\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots\)
1792.1.bt.a \(32\) \(0.894\) \(\Q(\zeta_{64})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots\)
1792.2.a.a \(1\) \(14.309\) \(\Q\) None None \(0\) \(-2\) \(-4\) \(1\) \(+\) \(q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.b \(1\) \(14.309\) \(\Q\) None None \(0\) \(-2\) \(-2\) \(1\) \(+\) \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.c \(1\) \(14.309\) \(\Q\) None None \(0\) \(-2\) \(2\) \(-1\) \(+\) \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.d \(1\) \(14.309\) \(\Q\) None None \(0\) \(-2\) \(4\) \(-1\) \(-\) \(q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.e \(1\) \(14.309\) \(\Q\) None None \(0\) \(2\) \(-4\) \(-1\) \(+\) \(q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.f \(1\) \(14.309\) \(\Q\) None None \(0\) \(2\) \(-2\) \(-1\) \(-\) \(q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.g \(1\) \(14.309\) \(\Q\) None None \(0\) \(2\) \(2\) \(1\) \(-\) \(q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.h \(1\) \(14.309\) \(\Q\) None None \(0\) \(2\) \(4\) \(1\) \(-\) \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.i \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.j \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.k \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(2\) \(-\) \(q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.l \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(2\) \(2\) \(+\) \(q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.m \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots\)
1792.2.a.n \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.o \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(2\) \(+\) \(q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.a.p \(2\) \(14.309\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(2\) \(+\) \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.q \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(2\) \(+\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.r \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) \(-\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.s \(2\) \(14.309\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
1792.2.a.t \(2\) \(14.309\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1792.2.a.u \(4\) \(14.309\) \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.v \(4\) \(14.309\) 4.4.9248.1 None None \(0\) \(0\) \(0\) \(-4\) \(-\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.a.w \(4\) \(14.309\) \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.x \(4\) \(14.309\) 4.4.9248.1 None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.b.a \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-8q^{15}+\cdots\)
1792.2.b.b \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1792.2.b.c \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}+2iq^{13}+6q^{17}+\cdots\)
1792.2.b.d \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{5}-q^{7}+3q^{9}-2iq^{11}+iq^{13}+\cdots\)
1792.2.b.e \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+3q^{9}-iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.f \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1792.2.b.g \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}-2iq^{13}+6q^{17}+\cdots\)
1792.2.b.h \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}-2iq^{5}+q^{7}-q^{9}+8q^{15}+\cdots\)
1792.2.b.i \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-iq^{5}+q^{7}+3q^{9}+2iq^{11}+iq^{13}+\cdots\)
1792.2.b.j \(2\) \(14.309\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+3q^{9}+iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.k \(4\) \(14.309\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.l \(4\) \(14.309\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.m \(4\) \(14.309\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.n \(4\) \(14.309\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.o \(6\) \(14.309\) 6.0.399424.1 None None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
1792.2.b.p \(6\) \(14.309\) 6.0.399424.1 None None \(0\) \(0\) \(0\) \(6\) \(q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
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