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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
650.2.a.a 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(-3\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
650.2.a.b 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
650.2.a.c 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(-2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots\)
650.2.a.d 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-3q^{9}-q^{13}+q^{16}+\cdots\)
650.2.a.e 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
650.2.a.f 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(2\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-5q^{7}-q^{8}+\cdots\)
650.2.a.g 650.a 1.a $1$ $5.190$ \(\Q\) None \(-1\) \(3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{7}-q^{8}+\cdots\)
650.2.a.h 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(-2\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+5q^{7}+q^{8}+\cdots\)
650.2.a.i 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
650.2.a.j 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
650.2.a.k 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
650.2.a.l 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+4q^{7}+q^{8}+\cdots\)
650.2.a.m 650.a 1.a $1$ $5.190$ \(\Q\) None \(1\) \(3\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
650.2.a.n 650.a 1.a $3$ $5.190$ 3.3.940.1 None \(-3\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
650.2.a.o 650.a 1.a $3$ $5.190$ 3.3.940.1 None \(3\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
650.2.b.a 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}+iq^{7}+\cdots\)
650.2.b.b 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+5iq^{7}+\cdots\)
650.2.b.c 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-4iq^{7}+\cdots\)
650.2.b.d 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
650.2.b.e 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-iq^{13}+\cdots\)
650.2.b.f 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+4iq^{7}+\cdots\)
650.2.b.g 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots\)
650.2.b.h 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots\)
650.2.b.i 650.b 5.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3iq^{3}-q^{4}+3q^{6}-iq^{8}+\cdots\)
650.2.c.a 650.c 65.d $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-3q^{7}-q^{8}+\cdots\)
650.2.c.b 650.c 65.d $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots\)
650.2.c.c 650.c 65.d $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{6}+q^{8}-q^{9}+\cdots\)
650.2.c.d 650.c 65.d $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{6}+3q^{7}+q^{8}+\cdots\)
650.2.c.e 650.c 65.d $6$ $5.190$ 6.0.126157824.1 None \(-6\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
650.2.c.f 650.c 65.d $6$ $5.190$ 6.0.126157824.1 None \(6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
650.2.d.a 650.d 13.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-2q^{3}-q^{4}+2iq^{6}+iq^{8}+\cdots\)
650.2.d.b 650.d 13.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots\)
650.2.d.c 650.d 13.b $6$ $5.190$ 6.0.126157824.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
650.2.d.d 650.d 13.b $6$ $5.190$ 6.0.126157824.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
650.2.d.e 650.d 13.b $8$ $5.190$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{1}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
650.2.e.a 650.e 13.c $2$ $5.190$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
650.2.e.b 650.e 13.c $2$ $5.190$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{7}-q^{8}+\cdots\)
650.2.e.c 650.e 13.c $2$ $5.190$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{7}-q^{8}+\cdots\)
650.2.e.d 650.e 13.c $4$ $5.190$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-2\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
650.2.e.e 650.e 13.c $4$ $5.190$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-2\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
650.2.e.f 650.e 13.c $4$ $5.190$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
650.2.e.g 650.e 13.c $4$ $5.190$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(2\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
650.2.e.h 650.e 13.c $4$ $5.190$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
650.2.e.i 650.e 13.c $4$ $5.190$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(2\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
650.2.e.j 650.e 13.c $6$ $5.190$ 6.0.591408.1 None \(-3\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4})q^{2}-\beta _{5}q^{3}-\beta _{4}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
650.2.e.k 650.e 13.c $6$ $5.190$ 6.0.591408.1 None \(3\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(\beta _{3}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
650.2.g.a 650.g 65.k $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+q^{4}+2iq^{7}-q^{8}-3iq^{9}+\cdots\)
650.2.g.b 650.g 65.k $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(1+i)q^{3}+q^{4}+(-1-i)q^{6}+\cdots\)
650.2.g.c 650.g 65.k $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(-1-i)q^{3}+q^{4}+(-1-i)q^{6}+\cdots\)
650.2.g.d 650.g 65.k $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+q^{4}-2iq^{7}+q^{8}-3iq^{9}+\cdots\)
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