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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1083.1.b.a 1083.b 3.b $1$ $0.540$ \(\Q\) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}+q^{9}-q^{12}+q^{13}+\cdots\)
1083.1.b.b 1083.b 3.b $1$ $0.540$ \(\Q\) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}-q^{13}+\cdots\)
1083.1.h.a 1083.h 57.h $2$ $0.540$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(1\) \(0\) \(-2\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
1083.1.l.a 1083.l 57.l $6$ $0.540$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)
1083.1.l.b 1083.l 57.l $6$ $0.540$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\)
1083.1.p.a 1083.p 1083.p $18$ $0.540$ \(\Q(\zeta_{38})\) \(\Q(\sqrt{-3}) \) None 1083.1.p.a \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{38}^{6}q^{3}+\zeta_{38}^{2}q^{4}+(\zeta_{38}^{6}-\zeta_{38}^{9}+\cdots)q^{7}+\cdots\)
1083.1.r.a 1083.r 1083.r $36$ $0.540$ \(\Q(\zeta_{57})\) \(\Q(\sqrt{-3}) \) None 1083.1.r.a \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{114}^{13}q^{3}-\zeta_{114}^{17}q^{4}+(\zeta_{114}^{10}+\cdots)q^{7}+\cdots\)
1083.2.a.a 1083.a 1.a $1$ $8.648$ \(\Q\) None None 57.2.a.c \(-1\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
1083.2.a.b 1083.a 1.a $1$ $8.648$ \(\Q\) None None 57.2.e.a \(-1\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
1083.2.a.c 1083.a 1.a $1$ $8.648$ \(\Q\) None None 57.2.e.a \(1\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
1083.2.a.d 1083.a 1.a $1$ $8.648$ \(\Q\) None None 57.2.a.b \(2\) \(-1\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
1083.2.a.e 1083.a 1.a $1$ $8.648$ \(\Q\) None None 57.2.a.a \(2\) \(1\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
1083.2.a.f 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None None 1083.2.a.f \(-3\) \(2\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
1083.2.a.g 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{17}) \) None None 1083.2.a.g \(-1\) \(-2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.h 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None None 1083.2.a.h \(-1\) \(2\) \(-1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.i 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None None 1083.2.a.h \(1\) \(-2\) \(-1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.j 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{17}) \) None None 1083.2.a.g \(1\) \(2\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.k 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None None 1083.2.a.f \(3\) \(-2\) \(1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1083.2.a.l 1083.a 1.a $3$ $8.648$ 3.3.564.1 None None 57.2.e.b \(-1\) \(3\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.m 1083.a 1.a $3$ $8.648$ \(\Q(\zeta_{18})^+\) None None 57.2.i.a \(0\) \(-3\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.n 1083.a 1.a $3$ $8.648$ \(\Q(\zeta_{18})^+\) None None 57.2.i.a \(0\) \(3\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.o 1083.a 1.a $3$ $8.648$ 3.3.564.1 None None 57.2.e.b \(1\) \(-3\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.p 1083.a 1.a $6$ $8.648$ 6.6.6357609.1 None None 57.2.i.b \(0\) \(-6\) \(9\) \(9\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.q 1083.a 1.a $6$ $8.648$ 6.6.6357609.1 None None 57.2.i.b \(0\) \(6\) \(9\) \(9\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.r 1083.a 1.a $8$ $8.648$ 8.8.9764000000.1 None None 1083.2.a.r \(-4\) \(-8\) \(-2\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1083.2.a.s 1083.a 1.a $8$ $8.648$ 8.8.9764000000.1 None None 1083.2.a.r \(4\) \(8\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1083.2.d.a 1083.d 57.d $6$ $8.648$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 57.2.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{18}q^{3}-2q^{4}-\zeta_{18}^{3}q^{7}-3q^{9}+\cdots\)
1083.2.d.b 1083.d 57.d $8$ $8.648$ \(\Q(\zeta_{24})\) None None 57.2.f.a \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{6}q^{2}+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
1083.2.d.c 1083.d 57.d $12$ $8.648$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 1083.2.d.c \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{2}+\beta _{1}q^{3}+(1-\beta _{3}-\beta _{9})q^{4}+\cdots\)
1083.2.d.d 1083.d 57.d $24$ $8.648$ None None 57.2.j.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$
1083.2.d.e 1083.d 57.d $48$ $8.648$ None None 1083.2.d.e \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
1083.4.a.a 1083.a 1.a $1$ $63.899$ \(\Q\) None None 57.4.a.a \(1\) \(-3\) \(-12\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}-7q^{4}-12q^{5}-3q^{6}+\cdots\)
1083.4.a.b 1083.a 1.a $2$ $63.899$ \(\Q(\sqrt{33}) \) None None 57.4.a.b \(-1\) \(6\) \(22\) \(36\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{3}+\beta q^{4}+(10+2\beta )q^{5}+\cdots\)
1083.4.a.c 1083.a 1.a $3$ $63.899$ 3.3.2700.1 None None 57.4.a.c \(3\) \(9\) \(-12\) \(-18\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+3q^{3}+(3+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
1083.4.a.d 1083.a 1.a $4$ $63.899$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None 57.4.a.d \(-3\) \(-12\) \(-6\) \(38\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(6+\beta _{2})q^{4}+\cdots\)
1083.4.a.e 1083.a 1.a $4$ $63.899$ 4.4.5682368.1 None None 1083.4.a.e \(-2\) \(12\) \(18\) \(-10\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1083.4.a.f 1083.a 1.a $4$ $63.899$ 4.4.5682368.1 None None 1083.4.a.e \(2\) \(-12\) \(18\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1083.4.a.g 1083.a 1.a $5$ $63.899$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None 57.4.e.a \(-1\) \(15\) \(4\) \(15\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
1083.4.a.h 1083.a 1.a $5$ $63.899$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None 57.4.e.b \(-1\) \(15\) \(-12\) \(-27\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1083.4.a.i 1083.a 1.a $5$ $63.899$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None 57.4.e.a \(1\) \(-15\) \(4\) \(15\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
1083.4.a.j 1083.a 1.a $5$ $63.899$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None 57.4.e.b \(1\) \(-15\) \(-12\) \(-27\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1083.4.a.k 1083.a 1.a $10$ $63.899$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 1083.4.a.k \(-9\) \(-30\) \(5\) \(21\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(7-\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
1083.4.a.l 1083.a 1.a $10$ $63.899$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 1083.4.a.l \(-1\) \(30\) \(19\) \(21\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1083.4.a.m 1083.a 1.a $10$ $63.899$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 1083.4.a.l \(1\) \(-30\) \(19\) \(21\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1083.4.a.n 1083.a 1.a $10$ $63.899$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 1083.4.a.k \(9\) \(30\) \(5\) \(21\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
1083.4.a.o 1083.a 1.a $12$ $63.899$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 57.4.i.a \(0\) \(-36\) \(-42\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots\)
1083.4.a.p 1083.a 1.a $12$ $63.899$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None 57.4.i.a \(0\) \(36\) \(-42\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots\)
1083.4.a.q 1083.a 1.a $16$ $63.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1083.4.a.q \(-8\) \(48\) \(2\) \(-70\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(2+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1083.4.a.r 1083.a 1.a $16$ $63.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1083.4.a.q \(8\) \(-48\) \(2\) \(-70\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(2+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1083.4.a.s 1083.a 1.a $18$ $63.899$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None 57.4.i.b \(0\) \(-54\) \(18\) \(48\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
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