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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13
8281.2.a.a 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-2\) \(-2\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.b 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-2\) \(2\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.c 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(-3\) \(-3\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots\)
8281.2.a.d 8281.a 1.a $1$ $66.124$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
8281.2.a.e 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.f 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.g 8281.a 1.a $1$ $66.124$ \(\Q\) None \(-1\) \(3\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots\)
8281.2.a.h 8281.a 1.a $1$ $66.124$ \(\Q\) None \(0\) \(2\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots\)
8281.2.a.i 8281.a 1.a $1$ $66.124$ \(\Q\) None \(1\) \(-3\) \(3\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots\)
8281.2.a.j 8281.a 1.a $1$ $66.124$ \(\Q\) None \(1\) \(3\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots\)
8281.2.a.k 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(-2\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.l 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(0\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots\)
8281.2.a.m 8281.a 1.a $1$ $66.124$ \(\Q\) None \(2\) \(2\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.n 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.o 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.p 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.q 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8281.2.a.r 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.s 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.t 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.u 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots\)
8281.2.a.v 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
8281.2.a.w 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.x 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.y 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.z 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.ba 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.bb 8281.a 1.a $2$ $66.124$ \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.bc 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-4\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bd 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
8281.2.a.be 8281.a 1.a $3$ $66.124$ 3.3.148.1 None \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bf 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) None \(-2\) \(2\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bg 8281.a 1.a $3$ $66.124$ 3.3.316.1 None \(-1\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.bh 8281.a 1.a $3$ $66.124$ 3.3.404.1 None \(2\) \(-4\) \(5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bi 8281.a 1.a $3$ $66.124$ 3.3.148.1 None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bj 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) None \(2\) \(2\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bk 8281.a 1.a $3$ $66.124$ 3.3.404.1 None \(2\) \(4\) \(-5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bl 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(3\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots\)
8281.2.a.bm 8281.a 1.a $3$ $66.124$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(4\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots\)
8281.2.a.bn 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{2}, \sqrt{23})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
8281.2.a.bo 8281.a 1.a $4$ $66.124$ 4.4.105456.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
8281.2.a.bp 8281.a 1.a $4$ $66.124$ 4.4.27004.1 None \(-1\) \(-1\) \(7\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bq 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
8281.2.a.br 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots\)
8281.2.a.bs 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
8281.2.a.bt 8281.a 1.a $4$ $66.124$ 4.4.27004.1 None \(1\) \(-1\) \(-7\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bu 8281.a 1.a $4$ $66.124$ 4.4.105456.1 None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
8281.2.a.bv 8281.a 1.a $4$ $66.124$ \(\Q(\sqrt{2}, \sqrt{23})\) None \(4\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8281.2.a.bw 8281.a 1.a $5$ $66.124$ 5.5.746052.1 None \(-4\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.bx 8281.a 1.a $5$ $66.124$ 5.5.746052.1 None \(-4\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
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