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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.1.l.a 624.l 39.d $1$ $0.311$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots\)
624.1.bd.a 624.bd 156.l $2$ $0.311$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+(-1-i)q^{7}-q^{9}-iq^{13}+\cdots\)
624.1.bd.b 624.bd 156.l $2$ $0.311$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+(1+i)q^{7}-q^{9}-iq^{13}+(-1+\cdots)q^{19}+\cdots\)
624.1.bi.a 624.bi 624.ai $8$ $0.311$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
624.1.bs.a 624.bs 39.i $2$ $0.311$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots\)
624.1.cb.a 624.cb 39.h $2$ $0.311$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
624.1.cp.a 624.cp 156.v $4$ $0.311$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
624.1.cp.b 624.cp 156.v $4$ $0.311$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
624.2.a.a 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
624.2.a.b 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots\)
624.2.a.c 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-6q^{11}-q^{13}+2q^{17}+\cdots\)
624.2.a.d 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots\)
624.2.a.e 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
624.2.a.f 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
624.2.a.g 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
624.2.a.h 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
624.2.a.i 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
624.2.a.j 624.a 1.a $1$ $4.983$ \(\Q\) None None \(0\) \(1\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
624.2.a.k 624.a 1.a $2$ $4.983$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\)
624.2.c.a 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots\)
624.2.c.b 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
624.2.c.c 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
624.2.c.d 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots\)
624.2.c.e 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\)
624.2.c.f 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots\)
624.2.c.g 624.c 13.b $2$ $4.983$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots\)
624.2.d.a 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
624.2.d.b 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
624.2.d.c 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
624.2.d.d 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
624.2.d.e 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
624.2.d.f 624.d 12.b $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
624.2.d.g 624.d 12.b $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
624.2.d.h 624.d 12.b $4$ $4.983$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+3q^{9}+2\beta _{2}q^{11}+\cdots\)
624.2.d.i 624.d 12.b $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
624.2.n.a 624.n 156.h $2$ $4.983$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-4q^{7}-3q^{9}+(1+2\zeta_{6})q^{13}+\cdots\)
624.2.n.b 624.n 156.h $2$ $4.983$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+4q^{7}-3q^{9}+(1-2\zeta_{6})q^{13}+\cdots\)
624.2.n.c 624.n 156.h $4$ $4.983$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
624.2.n.d 624.n 156.h $4$ $4.983$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
624.2.n.e 624.n 156.h $8$ $4.983$ 8.0.170772624.1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
624.2.n.f 624.n 156.h $8$ $4.983$ 8.0.170772624.1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(\beta _{3}+\beta _{5})q^{7}+\cdots\)
624.2.q.a 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.b 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.c 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.d 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.e 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.f 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{9}+(3+\zeta_{6})q^{13}+\cdots\)
624.2.q.g 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.h 624.q 13.c $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(2\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
624.2.q.i 624.q 13.c $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(0\) \(2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{9}+\cdots\)
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