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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.1.f.a 1620.f 20.d $1$ $0.808$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1620.1.f.b 1620.f 20.d $1$ $0.808$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1620.1.f.c 1620.f 20.d $1$ $0.808$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
1620.1.f.d 1620.f 20.d $1$ $0.808$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1620.1.f.e 1620.f 20.d $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.l.a 1620.l 5.c $2$ $0.808$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}+(-1+i)q^{7}-q^{11}+(-1+\cdots)q^{17}+\cdots\)
1620.1.l.b 1620.l 5.c $2$ $0.808$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{5}+(-1+i)q^{7}+q^{11}+(1-i+\cdots)q^{17}+\cdots\)
1620.1.m.a 1620.m 60.l $8$ $0.808$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+\zeta_{24}^{3}q^{8}+\cdots\)
1620.1.p.a 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.b 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.c 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.p.d 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
1620.1.p.e 1620.p 180.p $4$ $0.808$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1620.1.v.a 1620.v 45.k $4$ $0.808$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.v.b 1620.v 45.k $4$ $0.808$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{4}q^{11}+\cdots\)
1620.1.w.a 1620.w 180.v $8$ $0.808$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{9}q^{5}+\cdots\)
1620.1.w.b 1620.w 180.v $8$ $0.808$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}q^{5}+\cdots\)
1620.1.w.c 1620.w 180.v $8$ $0.808$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{5}q^{5}+\cdots\)
1620.1.bf.a 1620.bf 540.af $6$ $0.808$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
1620.1.bf.b 1620.bf 540.af $6$ $0.808$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(-\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
1620.1.bp.a 1620.bp 1620.ap $18$ $0.808$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{54}^{25}q^{2}-\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)
1620.1.bp.b 1620.bp 1620.ap $18$ $0.808$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{25}q^{2}+\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots\)
1620.2.a.a 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.b 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots\)
1620.2.a.c 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+3q^{11}-4q^{13}+6q^{17}+\cdots\)
1620.2.a.d 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.e 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots\)
1620.2.a.f 1620.a 1.a $1$ $12.936$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots\)
1620.2.a.g 1620.a 1.a $2$ $12.936$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.h 1620.a 1.a $2$ $12.936$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.i 1620.a 1.a $3$ $12.936$ 3.3.564.1 None None \(0\) \(0\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1-\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)
1620.2.a.j 1620.a 1.a $3$ $12.936$ 3.3.564.1 None None \(0\) \(0\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)
1620.2.d.a 1620.d 5.b $2$ $12.936$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots\)
1620.2.d.b 1620.d 5.b $2$ $12.936$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{5}+iq^{7}-q^{11}+iq^{17}+\cdots\)
1620.2.d.c 1620.d 5.b $6$ $12.936$ 6.0.301925376.2 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots\)
1620.2.d.d 1620.d 5.b $6$ $12.936$ 6.0.301925376.2 None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots\)
1620.2.d.e 1620.d 5.b $8$ $12.936$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
1620.2.e.a 1620.e 12.b $48$ $12.936$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1620.2.e.b 1620.e 12.b $48$ $12.936$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1620.2.i.a 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.b 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.c 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.d 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.e 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.f 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.g 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.h 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.i 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.j 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.k 1620.i 9.c $2$ $12.936$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
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