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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
722.2.a.a 722.a 1.a $1$ $5.765$ \(\Q\) None \(-1\) \(-3\) \(2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-3q^{7}+\cdots\)
722.2.a.b 722.a 1.a $1$ $5.765$ \(\Q\) None \(-1\) \(1\) \(-4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
722.2.a.c 722.a 1.a $1$ $5.765$ \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
722.2.a.d 722.a 1.a $1$ $5.765$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
722.2.a.e 722.a 1.a $1$ $5.765$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
722.2.a.f 722.a 1.a $1$ $5.765$ \(\Q\) None \(1\) \(3\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}-3q^{7}+\cdots\)
722.2.a.g 722.a 1.a $2$ $5.765$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(1+\beta )q^{5}-\beta q^{6}+\cdots\)
722.2.a.h 722.a 1.a $2$ $5.765$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots\)
722.2.a.i 722.a 1.a $2$ $5.765$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-5\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots\)
722.2.a.j 722.a 1.a $2$ $5.765$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
722.2.a.k 722.a 1.a $3$ $5.765$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(6\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+2q^{5}-\beta _{1}q^{6}+\cdots\)
722.2.a.l 722.a 1.a $3$ $5.765$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(6\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+2q^{5}-\beta _{1}q^{6}+\cdots\)
722.2.a.m 722.a 1.a $4$ $5.765$ \(\Q(\zeta_{20})^+\) None \(-4\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
722.2.a.n 722.a 1.a $4$ $5.765$ \(\Q(\zeta_{20})^+\) None \(4\) \(2\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
722.2.c.a 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.b 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.c 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.d 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.e 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.f 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.g 722.c 19.c $2$ $5.765$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
722.2.c.h 722.c 19.c $4$ $5.765$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(2\) \(5\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+2\beta _{1}q^{3}+\beta _{3}q^{4}+\cdots\)
722.2.c.i 722.c 19.c $4$ $5.765$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(2\) \(-2\) \(5\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{2}-2\beta _{1}q^{3}+\beta _{3}q^{4}+(3+\cdots)q^{5}+\cdots\)
722.2.c.j 722.c 19.c $4$ $5.765$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
722.2.c.k 722.c 19.c $6$ $5.765$ \(\Q(\zeta_{18})\) None \(-3\) \(0\) \(-6\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+\cdots\)
722.2.c.l 722.c 19.c $6$ $5.765$ \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-6\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
722.2.c.m 722.c 19.c $8$ $5.765$ 8.0.324000000.2 None \(-4\) \(-2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
722.2.c.n 722.c 19.c $8$ $5.765$ 8.0.324000000.2 None \(4\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
722.2.e.a 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(-6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
722.2.e.b 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(-1+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots\)
722.2.e.c 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.d 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.e 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.f 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.g 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.h 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.i 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.j 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.k 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
722.2.e.l 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(1-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
722.2.e.m 722.e 19.e $6$ $5.765$ \(\Q(\zeta_{18})\) None \(0\) \(6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots\)
722.2.e.n 722.e 19.e $12$ $5.765$ 12.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
722.2.e.o 722.e 19.e $12$ $5.765$ 12.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
722.2.e.p 722.e 19.e $12$ $5.765$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{9}q^{2}-2\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
722.2.e.q 722.e 19.e $12$ $5.765$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{3}-\beta _{9})q^{2}-2\beta _{1}q^{3}+(-\beta _{5}+\beta _{11})q^{4}+\cdots\)
722.2.e.r 722.e 19.e $24$ $5.765$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$
722.2.e.s 722.e 19.e $24$ $5.765$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$
722.2.g.a 722.g 361.g $288$ $5.765$ None \(16\) \(-1\) \(1\) \(2\) $\mathrm{SU}(2)[C_{19}]$
722.2.g.b 722.g 361.g $306$ $5.765$ None \(-17\) \(16\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{19}]$
722.2.i.a 722.i 361.i $576$ $5.765$ None \(-16\) \(1\) \(-1\) \(10\) $\mathrm{SU}(2)[C_{57}]$
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