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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
816.1.m.a \(1\) \(0.407\) \(\Q\) \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{9}+q^{11}-q^{13}+q^{15}+\cdots\)
816.1.m.b \(1\) \(0.407\) \(\Q\) \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+q^{9}-q^{11}-q^{13}+q^{15}+\cdots\)
816.1.bc.a \(4\) \(0.407\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots\)
816.2.a.a \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(-3\) \(4\) \(-\) \(q-q^{3}-3q^{5}+4q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
816.2.a.b \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
816.2.a.c \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots\)
816.2.a.d \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots\)
816.2.a.e \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(+\) \(q-q^{3}+q^{5}+q^{9}-5q^{11}-5q^{13}+\cdots\)
816.2.a.f \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(2\) \(4\) \(-\) \(q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
816.2.a.g \(1\) \(6.516\) \(\Q\) None None \(0\) \(-1\) \(3\) \(4\) \(-\) \(q-q^{3}+3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots\)
816.2.a.h \(1\) \(6.516\) \(\Q\) None None \(0\) \(1\) \(-4\) \(2\) \(+\) \(q+q^{3}-4q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
816.2.a.i \(1\) \(6.516\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) \(+\) \(q+q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots\)
816.2.a.j \(1\) \(6.516\) \(\Q\) None None \(0\) \(1\) \(3\) \(0\) \(-\) \(q+q^{3}+3q^{5}+q^{9}+q^{11}+3q^{13}+\cdots\)
816.2.a.k \(2\) \(6.516\) \(\Q(\sqrt{57}) \) None None \(0\) \(-2\) \(-1\) \(-8\) \(-\) \(q-q^{3}-\beta q^{5}-4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
816.2.a.l \(2\) \(6.516\) \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(-1\) \(2\) \(-\) \(q+q^{3}-\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(4+\cdots)q^{11}+\cdots\)
816.2.a.m \(2\) \(6.516\) \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(3\) \(0\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots\)
816.2.c.a \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots\)
816.2.c.b \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots\)
816.2.c.c \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots\)
816.2.c.d \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots\)
816.2.c.e \(4\) \(6.516\) \(\Q(i, \sqrt{33})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots\)
816.2.c.f \(6\) \(6.516\) 6.0.399424.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
816.2.e.a \(4\) \(6.516\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{3}+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots\)
816.2.e.b \(8\) \(6.516\) 8.0.\(\cdots\).8 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+2\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
816.2.e.c \(20\) \(6.516\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{3}-\beta _{15}q^{5}-\beta _{16}q^{7}+(\beta _{9}+\cdots)q^{9}+\cdots\)
816.2.o.a \(4\) \(6.516\) \(\Q(\sqrt{-3}, \sqrt{17})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
816.2.o.b \(4\) \(6.516\) \(\Q(\sqrt{-3}, \sqrt{17})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}-3q^{9}-3\beta _{1}q^{11}+\cdots\)
816.2.o.c \(4\) \(6.516\) \(\Q(\sqrt{-3}, \sqrt{17})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{2}q^{3}+(1-\beta _{3})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
816.2.o.d \(8\) \(6.516\) 8.0.\(\cdots\).12 \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6})q^{7}-\beta _{2}q^{9}+\cdots\)
816.2.o.e \(16\) \(6.516\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+(1+\beta _{7}+\cdots)q^{9}+\cdots\)
816.2.r.a \(4\) \(6.516\) \(\Q(i, \sqrt{5})\) None None \(-4\) \(2\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots\)
816.2.r.b \(4\) \(6.516\) \(\Q(i, \sqrt{5})\) None None \(4\) \(2\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
816.2.r.c \(272\) \(6.516\) None None \(0\) \(-8\) \(0\) \(-8\)
816.2.s.a \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(-2\) \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
816.2.s.b \(2\) \(6.516\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(6\) \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
816.2.s.c \(68\) \(6.516\) None None \(-2\) \(68\) \(0\) \(-4\)
816.2.s.d \(72\) \(6.516\) None None \(-2\) \(-72\) \(0\) \(0\)
816.2.u.a \(64\) \(6.516\) None None \(0\) \(0\) \(0\) \(0\)
816.2.u.b \(64\) \(6.516\) None None \(0\) \(0\) \(0\) \(0\)
816.2.w.a \(280\) \(6.516\) None None \(0\) \(0\) \(0\) \(0\)
816.2.bd.a \(4\) \(6.516\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(-8\) \(q-\zeta_{8}q^{3}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
816.2.bd.b \(4\) \(6.516\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}q^{3}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots\)
816.2.bd.c \(4\) \(6.516\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{3}+(1+2\zeta_{8}+\zeta_{8}^{2})q^{5}-2\zeta_{8}^{3}q^{7}+\cdots\)
816.2.bd.d \(4\) \(6.516\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(8\) \(4\) \(q+\zeta_{8}q^{3}+(2+\zeta_{8}+2\zeta_{8}^{2})q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
816.2.bd.e \(8\) \(6.516\) 8.0.836829184.2 None None \(0\) \(0\) \(-4\) \(4\) \(q+\beta _{3}q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7})q^{5}+\cdots\)
816.2.bd.f \(12\) \(6.516\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{3}q^{3}+\beta _{6}q^{5}+(\beta _{4}+\beta _{10})q^{7}-\beta _{5}q^{9}+\cdots\)
816.2.bf.a \(8\) \(6.516\) 8.0.12960000.1 None None \(0\) \(-4\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{5})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+\cdots\)
816.2.bf.b \(8\) \(6.516\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}+(-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
816.2.bf.c \(8\) \(6.516\) 8.0.12960000.1 None None \(0\) \(4\) \(0\) \(0\) \(q+(1-\beta _{1}+\beta _{5})q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots\)
816.2.bf.d \(24\) \(6.516\) None None \(0\) \(0\) \(0\) \(0\)
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