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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.a.a 546.a 1.a $1$ $4.360$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
546.2.a.b 546.a 1.a $1$ $4.360$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.c 546.a 1.a $1$ $4.360$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.d 546.a 1.a $1$ $4.360$ \(\Q\) None \(-1\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.e 546.a 1.a $1$ $4.360$ \(\Q\) None \(1\) \(-1\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.f 546.a 1.a $1$ $4.360$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.g 546.a 1.a $1$ $4.360$ \(\Q\) None \(1\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.h 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{57}) \) None \(-2\) \(-2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.i 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{41}) \) None \(2\) \(-2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.j 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2-\beta )q^{5}+q^{6}+\cdots\)
546.2.c.a 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots\)
546.2.c.b 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
546.2.c.c 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
546.2.c.d 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots\)
546.2.c.e 546.c 13.b $4$ $4.360$ \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
546.2.e.a 546.e 273.g $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.b 546.e 273.g $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(0\) \(5\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.c 546.e 273.g $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(5\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
546.2.e.d 546.e 273.g $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+2\zeta_{6})q^{5}+\cdots\)
546.2.e.e 546.e 273.g $8$ $4.360$ 8.0.303595776.1 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+\cdots\)
546.2.e.f 546.e 273.g $8$ $4.360$ 8.0.\(\cdots\).11 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
546.2.e.g 546.e 273.g $8$ $4.360$ 8.0.303595776.1 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
546.2.e.h 546.e 273.g $8$ $4.360$ 8.0.\(\cdots\).11 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
546.2.g.a 546.g 21.c $4$ $4.360$ \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(4\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.g.b 546.g 21.c $4$ $4.360$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
546.2.g.c 546.g 21.c $12$ $4.360$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}+\beta _{6}q^{6}+\cdots\)
546.2.g.d 546.g 21.c $12$ $4.360$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots\)
546.2.i.a 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.b 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.c 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.d 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.e 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.f 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.g 546.i 7.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
546.2.i.h 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
546.2.i.i 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
546.2.i.j 546.i 7.c $4$ $4.360$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.i.k 546.i 7.c $6$ $4.360$ 6.0.21870000.1 None \(3\) \(3\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.j.a 546.j 91.h $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots\)
546.2.j.b 546.j 91.h $8$ $4.360$ 8.0.6498455769.2 None \(-8\) \(-4\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots\)
546.2.j.c 546.j 91.h $8$ $4.360$ 8.0.447703281.1 None \(8\) \(-4\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.j.d 546.j 91.h $8$ $4.360$ 8.0.447703281.1 None \(8\) \(4\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
546.2.j.e 546.j 91.h $10$ $4.360$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(5\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)
546.2.k.a 546.k 91.g $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}-q^{3}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{6}+\cdots\)
546.2.k.b 546.k 91.g $8$ $4.360$ 8.0.447703281.1 None \(-4\) \(-8\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-q^{3}+(-1-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
546.2.k.c 546.k 91.g $8$ $4.360$ 8.0.447703281.1 None \(-4\) \(8\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.k.d 546.k 91.g $8$ $4.360$ 8.0.6498455769.2 None \(4\) \(8\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}+\beta _{2}q^{5}+\cdots\)
546.2.k.e 546.k 91.g $10$ $4.360$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(5\) \(-10\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{5})q^{2}-q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
546.2.l.a 546.l 13.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
546.2.l.b 546.l 13.c $2$ $4.360$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
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