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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.1.l.a 165.l 165.l $2$ $0.082$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots\)
165.1.l.b 165.l 165.l $2$ $0.082$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots\)
165.2.a.a 165.a 1.a $2$ $1.318$ \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
165.2.a.b 165.a 1.a $2$ $1.318$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+2q^{7}+\cdots\)
165.2.a.c 165.a 1.a $3$ $1.318$ 3.3.148.1 None None \(-1\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
165.2.c.a 165.c 5.b $6$ $1.318$ 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
165.2.c.b 165.c 5.b $6$ $1.318$ 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
165.2.d.a 165.d 165.d $2$ $1.318$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(3\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
165.2.d.b 165.d 165.d $2$ $1.318$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-3\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots\)
165.2.d.c 165.d 165.d $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
165.2.f.a 165.f 33.d $8$ $1.318$ 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
165.2.f.b 165.f 33.d $8$ $1.318$ 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
165.2.j.a 165.j 55.e $24$ $1.318$ None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
165.2.k.a 165.k 15.e $4$ $1.318$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
165.2.k.b 165.k 15.e $4$ $1.318$ \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
165.2.k.c 165.k 15.e $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(-2\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.k.d 165.k 15.e $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(4\) \(4\) \(8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots\)
165.2.m.a 165.m 11.c $8$ $1.318$ 8.0.13140625.1 None None \(0\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots\)
165.2.m.b 165.m 11.c $8$ $1.318$ 8.0.819390625.1 None None \(2\) \(2\) \(2\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
165.2.m.c 165.m 11.c $8$ $1.318$ \(\Q(\zeta_{15})\) None None \(2\) \(2\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
165.2.m.d 165.m 11.c $8$ $1.318$ 8.0.13140625.1 None None \(4\) \(-2\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots\)
165.2.p.a 165.p 33.f $16$ $1.318$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(8\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{2}-\beta _{5}+\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
165.2.p.b 165.p 33.f $48$ $1.318$ None None \(0\) \(-4\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$
165.2.r.a 165.r 165.r $80$ $1.318$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
165.2.s.a 165.s 55.j $48$ $1.318$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$
165.2.v.a 165.v 165.v $160$ $1.318$ None None \(0\) \(-8\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$
165.2.w.a 165.w 55.l $96$ $1.318$ None None \(0\) \(0\) \(-8\) \(-20\) $\mathrm{SU}(2)[C_{20}]$
165.3.b.a 165.b 11.b $16$ $4.496$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
165.3.e.a 165.e 3.b $28$ $4.496$ None None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$
165.3.g.a 165.g 15.d $2$ $4.496$ \(\Q(\sqrt{-11}) \) None None \(-2\) \(-5\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-2-\beta )q^{3}-3q^{4}-5q^{5}+\cdots\)
165.3.g.b 165.g 15.d $2$ $4.496$ \(\Q(\sqrt{-11}) \) None None \(2\) \(5\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(3-\beta )q^{3}-3q^{4}+5q^{5}+(3+\cdots)q^{6}+\cdots\)
165.3.g.c 165.g 15.d $36$ $4.496$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
165.3.h.a 165.h 55.d $24$ $4.496$ None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
165.3.i.a 165.i 5.c $40$ $4.496$ None None \(8\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$
165.3.l.a 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{10})\) None None \(0\) \(-12\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-4-3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.b 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}-\beta _{2}q^{4}+5\beta _{2}q^{5}+\cdots\)
165.3.l.c 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-3\beta _{2})q^{3}-4\beta _{2}q^{4}+(3\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.d 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+\beta _{2}q^{4}+(4+3\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.e 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(10\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(3+\beta _{3})q^{3}+4\beta _{2}q^{4}+(-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
165.3.l.f 165.l 165.l $4$ $4.496$ \(\Q(i, \sqrt{6})\) None None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3q^{3}-\beta _{2}q^{4}-5\beta _{2}q^{5}+\cdots\)
165.3.l.g 165.l 165.l $64$ $4.496$ None None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
165.3.n.a 165.n 55.h $96$ $4.496$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$
165.3.o.a 165.o 165.o $176$ $4.496$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
165.3.q.a 165.q 33.h $128$ $4.496$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
165.3.t.a 165.t 11.d $32$ $4.496$ None None \(0\) \(0\) \(40\) \(20\) $\mathrm{SU}(2)[C_{10}]$
165.3.t.b 165.t 11.d $32$ $4.496$ None None \(0\) \(0\) \(-40\) \(-20\) $\mathrm{SU}(2)[C_{10}]$
165.3.u.a 165.u 165.u $352$ $4.496$ None None \(0\) \(-4\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$
165.3.x.a 165.x 55.k $192$ $4.496$ None None \(0\) \(0\) \(-8\) \(52\) $\mathrm{SU}(2)[C_{20}]$
165.4.a.a 165.a 1.a $1$ $9.735$ \(\Q\) None None \(0\) \(-3\) \(-5\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-8q^{4}-5q^{5}+2q^{7}+9q^{9}+\cdots\)
165.4.a.b 165.a 1.a $1$ $9.735$ \(\Q\) None None \(1\) \(3\) \(-5\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
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