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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.2.a.a 162.a 1.a $1$ $1.294$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
162.2.a.b 162.a 1.a $1$ $1.294$ \(\Q\) None \(-1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+3q^{11}+2q^{13}+\cdots\)
162.2.a.c 162.a 1.a $1$ $1.294$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots\)
162.2.a.d 162.a 1.a $1$ $1.294$ \(\Q\) None \(1\) \(0\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots\)
162.2.c.a 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
162.2.c.b 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
162.2.c.c 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
162.2.c.d 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
162.2.e.a 162.e 27.e $6$ $1.294$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
162.2.e.b 162.e 27.e $12$ $1.294$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}+\beta _{8})q^{2}-\beta _{6}q^{4}+(1-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots\)
162.2.g.a 162.g 81.g $72$ $1.294$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
162.2.g.b 162.g 81.g $90$ $1.294$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
162.3.b.a 162.b 3.b $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
162.3.b.b 162.b 3.b $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{3})q^{7}+\cdots\)
162.3.d.a 162.d 9.d $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-6\beta _{1}+6\beta _{3})q^{5}+\cdots\)
162.3.d.b 162.d 9.d $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{5}+\cdots\)
162.3.d.c 162.d 9.d $8$ $4.414$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{5}q^{2}+2\zeta_{24}q^{4}+(2\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
162.3.f.a 162.f 27.f $36$ $4.414$ None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
162.3.h.a 162.h 81.h $324$ $4.414$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{54}]$
162.4.a.a 162.a 1.a $1$ $9.558$ \(\Q\) None \(-2\) \(0\) \(9\) \(-31\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+9q^{5}-31q^{7}-8q^{8}+\cdots\)
162.4.a.b 162.a 1.a $1$ $9.558$ \(\Q\) None \(-2\) \(0\) \(21\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+21q^{5}+8q^{7}-8q^{8}+\cdots\)
162.4.a.c 162.a 1.a $1$ $9.558$ \(\Q\) None \(2\) \(0\) \(-21\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-21q^{5}+8q^{7}+8q^{8}+\cdots\)
162.4.a.d 162.a 1.a $1$ $9.558$ \(\Q\) None \(2\) \(0\) \(-9\) \(-31\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-9q^{5}-31q^{7}+8q^{8}+\cdots\)
162.4.a.e 162.a 1.a $2$ $9.558$ \(\Q(\sqrt{3}) \) None \(-4\) \(0\) \(-12\) \(16\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-6+\beta )q^{5}+(8-2\beta )q^{7}+\cdots\)
162.4.a.f 162.a 1.a $2$ $9.558$ \(\Q(\sqrt{105}) \) None \(-4\) \(0\) \(-9\) \(19\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-5-\beta )q^{5}+(9-\beta )q^{7}+\cdots\)
162.4.a.g 162.a 1.a $2$ $9.558$ \(\Q(\sqrt{105}) \) None \(4\) \(0\) \(9\) \(19\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(4-\beta )q^{5}+(10+\beta )q^{7}+\cdots\)
162.4.a.h 162.a 1.a $2$ $9.558$ \(\Q(\sqrt{3}) \) None \(4\) \(0\) \(12\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(6+\beta )q^{5}+(8+2\beta )q^{7}+\cdots\)
162.4.c.a 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-12\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-12\zeta_{6}q^{5}+\cdots\)
162.4.c.b 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
162.4.c.c 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+6\zeta_{6}q^{5}+\cdots\)
162.4.c.d 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(21\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots\)
162.4.c.e 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-21\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots\)
162.4.c.f 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-6\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-6\zeta_{6}q^{5}+\cdots\)
162.4.c.g 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
162.4.c.h 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(12\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+12\zeta_{6}q^{5}+\cdots\)
162.4.c.i 162.c 9.c $4$ $9.558$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-12\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(-6\zeta_{12}+\cdots)q^{5}+\cdots\)
162.4.c.j 162.c 9.c $4$ $9.558$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(12\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(6\zeta_{12}+\cdots)q^{5}+\cdots\)
162.4.e.a 162.e 27.e $24$ $9.558$ None \(0\) \(0\) \(12\) \(-33\) $\mathrm{SU}(2)[C_{9}]$
162.4.e.b 162.e 27.e $30$ $9.558$ None \(0\) \(0\) \(12\) \(33\) $\mathrm{SU}(2)[C_{9}]$
162.4.g.a 162.g 81.g $234$ $9.558$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
162.4.g.b 162.g 81.g $252$ $9.558$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
162.5.b.a 162.b 3.b $4$ $16.746$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-8q^{4}+(-17\beta _{1}+5\beta _{2}+\cdots)q^{5}+\cdots\)
162.5.b.b 162.b 3.b $4$ $16.746$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{1}q^{2}-8q^{4}+(-8\beta _{1}+\beta _{2})q^{5}+\cdots\)
162.5.b.c 162.b 3.b $8$ $16.746$ 8.0.\(\cdots\).4 None \(0\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-8q^{4}-\beta _{4}q^{5}+(6+\beta _{1})q^{7}+\cdots\)
162.5.d.a 162.d 9.d $4$ $16.746$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}+(8-8\beta _{2})q^{4}+6\beta _{1}q^{5}+\cdots\)
162.5.d.b 162.d 9.d $4$ $16.746$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(146\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{2})q^{4}+12\beta _{1}q^{5}+\cdots\)
162.5.d.c 162.d 9.d $8$ $16.746$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-68\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{5}q^{2}+8\zeta_{24}^{2}q^{4}+(\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
162.5.d.d 162.d 9.d $8$ $16.746$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{24}^{3}q^{2}+(8-8\zeta_{24})q^{4}+(22\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
162.5.d.e 162.d 9.d $8$ $16.746$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2\zeta_{24}^{3}+2\zeta_{24}^{5})q^{2}+(8-8\zeta_{24}+\cdots)q^{4}+\cdots\)
162.5.f.a 162.f 27.f $72$ $16.746$ None \(0\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
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