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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
66.2.a.a 66.a 1.a $1$ $0.527$ \(\Q\) None 66.2.a.a \(-1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
66.2.a.b 66.a 1.a $1$ $0.527$ \(\Q\) None 66.2.a.b \(1\) \(-1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
66.2.a.c 66.a 1.a $1$ $0.527$ \(\Q\) None 66.2.a.c \(1\) \(1\) \(-4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
66.2.b.a 66.b 33.d $2$ $0.527$ \(\Q(\sqrt{-2}) \) None 66.2.b.a \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
66.2.b.b 66.b 33.d $2$ $0.527$ \(\Q(\sqrt{-2}) \) None 66.2.b.a \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
66.2.e.a 66.e 11.c $4$ $0.527$ \(\Q(\zeta_{10})\) None 66.2.e.a \(-1\) \(1\) \(8\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
66.2.e.b 66.e 11.c $4$ $0.527$ \(\Q(\zeta_{10})\) None 66.2.e.b \(1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
66.2.h.a 66.h 33.f $8$ $0.527$ 8.0.185640625.1 None 66.2.h.a \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
66.2.h.b 66.h 33.f $8$ $0.527$ 8.0.185640625.1 None 66.2.h.a \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
66.3.c.a 66.c 3.b $8$ $1.798$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 66.3.c.a \(0\) \(-2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-2q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
66.3.d.a 66.d 11.b $4$ $1.798$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 66.3.d.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-2-4\beta _{2}+\cdots)q^{5}+\cdots\)
66.3.f.a 66.f 11.d $16$ $1.798$ 16.0.\(\cdots\).7 None 66.3.f.a \(0\) \(0\) \(8\) \(60\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{6}q^{2}-\beta _{9}q^{3}+(2-2\beta _{4}-2\beta _{8}+\cdots)q^{4}+\cdots\)
66.3.g.a 66.g 33.h $32$ $1.798$ None 66.3.g.a \(0\) \(2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{10}]$
66.4.a.a 66.a 1.a $1$ $3.894$ \(\Q\) None 66.4.a.a \(-2\) \(3\) \(0\) \(14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+14q^{7}+\cdots\)
66.4.a.b 66.a 1.a $1$ $3.894$ \(\Q\) None 66.4.a.b \(2\) \(-3\) \(10\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+10q^{5}-6q^{6}+\cdots\)
66.4.a.c 66.a 1.a $2$ $3.894$ \(\Q(\sqrt{97}) \) None 66.4.a.c \(4\) \(6\) \(10\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(5-\beta )q^{5}+6q^{6}+\cdots\)
66.4.b.a 66.b 33.d $6$ $3.894$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 66.4.b.a \(-12\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}-\beta _{5}q^{5}-2\beta _{1}q^{6}+\cdots\)
66.4.b.b 66.b 33.d $6$ $3.894$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 66.4.b.a \(12\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}-\beta _{5}q^{5}+2\beta _{1}q^{6}+\cdots\)
66.4.e.a 66.e 11.c $4$ $3.894$ \(\Q(\zeta_{10})\) None 66.4.e.a \(-2\) \(3\) \(-15\) \(-31\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\zeta_{10}q^{2}+3\zeta_{10}^{3}q^{3}+4\zeta_{10}^{2}q^{4}+\cdots\)
66.4.e.b 66.e 11.c $4$ $3.894$ \(\Q(\zeta_{10})\) None 66.4.e.b \(2\) \(-3\) \(15\) \(-19\) $\mathrm{SU}(2)[C_{5}]$ \(q+2\zeta_{10}q^{2}-3\zeta_{10}^{3}q^{3}+4\zeta_{10}^{2}q^{4}+\cdots\)
66.4.e.c 66.e 11.c $8$ $3.894$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 66.4.e.c \(-4\) \(-6\) \(-5\) \(-13\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\beta _{3}q^{2}-3\beta _{2}q^{3}+(-4+4\beta _{2}+4\beta _{3}+\cdots)q^{4}+\cdots\)
66.4.e.d 66.e 11.c $8$ $3.894$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 66.4.e.d \(4\) \(6\) \(-27\) \(27\) $\mathrm{SU}(2)[C_{5}]$ \(q+2\beta _{2}q^{2}+(3-3\beta _{2}+3\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
66.4.h.a 66.h 33.f $24$ $3.894$ None 66.4.h.a \(-12\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
66.4.h.b 66.h 33.f $24$ $3.894$ None 66.4.h.a \(12\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
66.5.c.a 66.c 3.b $12$ $6.822$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 66.5.c.a \(0\) \(10\) \(0\) \(-184\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}-8q^{4}+\cdots\)
66.5.d.a 66.d 11.b $8$ $6.822$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 66.5.d.a \(0\) \(0\) \(72\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}-8q^{4}+(9+2\beta _{1}+\cdots)q^{5}+\cdots\)
66.5.f.a 66.f 11.d $32$ $6.822$ None 66.5.f.a \(0\) \(0\) \(-72\) \(-300\) $\mathrm{SU}(2)[C_{10}]$
66.5.g.a 66.g 33.h $64$ $6.822$ None 66.5.g.a \(0\) \(2\) \(0\) \(80\) $\mathrm{SU}(2)[C_{10}]$
66.6.a.a 66.a 1.a $1$ $10.585$ \(\Q\) None 66.6.a.a \(-4\) \(-9\) \(-14\) \(-112\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-14q^{5}+6^{2}q^{6}+\cdots\)
66.6.a.b 66.a 1.a $1$ $10.585$ \(\Q\) None 66.6.a.b \(-4\) \(-9\) \(-14\) \(130\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-14q^{5}+6^{2}q^{6}+\cdots\)
66.6.a.c 66.a 1.a $1$ $10.585$ \(\Q\) None 66.6.a.c \(-4\) \(9\) \(-14\) \(-130\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-14q^{5}-6^{2}q^{6}+\cdots\)
66.6.a.d 66.a 1.a $1$ $10.585$ \(\Q\) None 66.6.a.d \(4\) \(-9\) \(50\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+50q^{5}-6^{2}q^{6}+\cdots\)
66.6.a.e 66.a 1.a $2$ $10.585$ \(\Q(\sqrt{8761}) \) None 66.6.a.e \(-8\) \(18\) \(-14\) \(210\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-7-\beta )q^{5}+\cdots\)
66.6.a.f 66.a 1.a $2$ $10.585$ \(\Q(\sqrt{2161}) \) None 66.6.a.f \(8\) \(18\) \(50\) \(96\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(5^{2}-\beta )q^{5}+\cdots\)
66.6.b.a 66.b 33.d $10$ $10.585$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 66.6.b.a \(-40\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4q^{2}+(1-\beta _{3})q^{3}+2^{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
66.6.b.b 66.b 33.d $10$ $10.585$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 66.6.b.a \(40\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{2}+(1-\beta _{3})q^{3}+2^{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
66.6.e.a 66.e 11.c $8$ $10.585$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 66.6.e.a \(-8\) \(-18\) \(150\) \(474\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{2}q^{2}+(-9+9\beta _{2}-9\beta _{3}+9\beta _{5}+\cdots)q^{3}+\cdots\)
66.6.e.b 66.e 11.c $8$ $10.585$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 66.6.e.b \(8\) \(18\) \(118\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{2}q^{2}+(9+9\beta _{2}+9\beta _{3}+9\beta _{5}+\cdots)q^{3}+\cdots\)
66.6.e.c 66.e 11.c $12$ $10.585$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 66.6.e.c \(-12\) \(27\) \(-118\) \(216\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{5}q^{2}+9\beta _{2}q^{3}+(-2^{4}+2^{4}\beta _{2}+\cdots)q^{4}+\cdots\)
66.6.e.d 66.e 11.c $12$ $10.585$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 66.6.e.d \(12\) \(-27\) \(-62\) \(-60\) $\mathrm{SU}(2)[C_{5}]$ \(q+(4+4\beta _{2}-4\beta _{3}-4\beta _{4})q^{2}-9\beta _{4}q^{3}+\cdots\)
66.6.h.a 66.h 33.f $40$ $10.585$ None 66.6.h.a \(-40\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
66.6.h.b 66.h 33.f $40$ $10.585$ None 66.6.h.a \(40\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
66.7.c.a 66.c 3.b $20$ $15.184$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 66.7.c.a \(0\) \(-32\) \(0\) \(400\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-2-\beta _{1})q^{3}-2^{5}q^{4}+(4\beta _{2}+\cdots)q^{5}+\cdots\)
66.7.d.a 66.d 11.b $12$ $15.184$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 66.7.d.a \(0\) \(0\) \(-448\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}-2^{5}q^{4}+(-37+\beta _{2}+\cdots)q^{5}+\cdots\)
66.7.f.a 66.f 11.d $48$ $15.184$ None 66.7.f.a \(0\) \(0\) \(448\) \(-1440\) $\mathrm{SU}(2)[C_{10}]$
66.7.g.a 66.g 33.h $96$ $15.184$ None 66.7.g.a \(0\) \(-52\) \(0\) \(-408\) $\mathrm{SU}(2)[C_{10}]$
66.8.a.a 66.a 1.a $1$ $20.617$ \(\Q\) None 66.8.a.a \(-8\) \(27\) \(-70\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-70q^{5}-6^{3}q^{6}+\cdots\)
66.8.a.b 66.a 1.a $1$ $20.617$ \(\Q\) None 66.8.a.b \(8\) \(-27\) \(0\) \(-286\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-6^{3}q^{6}-286q^{7}+\cdots\)
66.8.a.c 66.a 1.a $2$ $20.617$ \(\Q(\sqrt{3193}) \) None 66.8.a.c \(-16\) \(-54\) \(-70\) \(-762\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-35-7\beta )q^{5}+\cdots\)
66.8.a.d 66.a 1.a $2$ $20.617$ \(\Q(\sqrt{97}) \) None 66.8.a.d \(-16\) \(-54\) \(-70\) \(-278\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-35-5\beta )q^{5}+\cdots\)
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