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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
560.1.p.a 560.p 35.c $1$ $0.279$ \(\Q\) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-q^{3}-q^{5}+q^{7}+q^{11}+q^{13}+q^{15}+\cdots\)
560.1.p.b 560.p 35.c $1$ $0.279$ \(\Q\) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}+q^{11}-q^{13}+q^{15}+\cdots\)
560.1.bt.a 560.bt 140.p $4$ $0.279$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
560.2.a.a 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(-3\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.b 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots\)
560.2.a.c 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
560.2.a.d 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
560.2.a.e 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots\)
560.2.a.f 560.a 1.a $1$ $4.472$ \(\Q\) None None \(0\) \(3\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.g 560.a 1.a $2$ $4.472$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}-q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
560.2.a.h 560.a 1.a $2$ $4.472$ \(\Q(\sqrt{33}) \) None None \(0\) \(1\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+q^{7}+(5+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
560.2.a.i 560.a 1.a $2$ $4.472$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
560.2.e.a 560.e 140.c $4$ $4.472$ \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots\)
560.2.e.b 560.e 140.c $4$ $4.472$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+q^{9}+\cdots\)
560.2.e.c 560.e 140.c $8$ $4.472$ 8.0.121550625.1 \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
560.2.e.d 560.e 140.c $8$ $4.472$ 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots\)
560.2.g.a 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots\)
560.2.g.b 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2-i)q^{5}+iq^{7}+2q^{9}+\cdots\)
560.2.g.c 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots\)
560.2.g.d 560.g 5.b $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots\)
560.2.g.e 560.g 5.b $4$ $4.472$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
560.2.g.f 560.g 5.b $6$ $4.472$ 6.0.5161984.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
560.2.k.a 560.k 28.d $8$ $4.472$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
560.2.k.b 560.k 28.d $8$ $4.472$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}+\beta _{3}q^{5}+(\beta _{4}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
560.2.q.a 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.b 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
560.2.q.c 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
560.2.q.d 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
560.2.q.e 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.f 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
560.2.q.g 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
560.2.q.h 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
560.2.q.i 560.q 7.c $2$ $4.472$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.j 560.q 7.c $4$ $4.472$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.k 560.q 7.c $4$ $4.472$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.l 560.q 7.c $6$ $4.472$ 6.0.11337408.1 None None \(0\) \(0\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
560.2.r.a 560.r 560.r $184$ $4.472$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.t.a 560.t 80.j $144$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.x.a 560.x 20.e $12$ $4.472$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{4}-\beta _{8})q^{3}+(-\beta _{6}+\beta _{9})q^{5}+\cdots\)
560.2.x.b 560.x 20.e $24$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.bb.a 560.bb 80.q $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
560.2.bb.b 560.bb 80.q $2$ $4.472$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+(1+i)q^{3}+2iq^{4}+(2+\cdots)q^{5}+\cdots\)
560.2.bb.c 560.bb 80.q $70$ $4.472$ None None \(-2\) \(-2\) \(-4\) \(-70\) $\mathrm{SU}(2)[C_{4}]$
560.2.bb.d 560.bb 80.q $70$ $4.472$ None None \(2\) \(2\) \(2\) \(70\) $\mathrm{SU}(2)[C_{4}]$
560.2.bc.a 560.bc 112.j $128$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.bd.a 560.bd 16.e $44$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.bd.b 560.bd 16.e $52$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.be.a 560.be 560.ae $184$ $4.472$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
560.2.bj.a 560.bj 35.f $4$ $4.472$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
560.2.bj.b 560.bj 35.f $8$ $4.472$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(\beta _{2}-\beta _{6})q^{5}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots\)
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