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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
798.2.a.a 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
798.2.a.b 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.c 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.d 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
798.2.a.e 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.f 798.a 1.a $1$ $6.372$ \(\Q\) None \(-1\) \(1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.g 798.a 1.a $1$ $6.372$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.h 798.a 1.a $1$ $6.372$ \(\Q\) None \(1\) \(1\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.i 798.a 1.a $1$ $6.372$ \(\Q\) None \(1\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.j 798.a 1.a $2$ $6.372$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
798.2.a.k 798.a 1.a $2$ $6.372$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.l 798.a 1.a $2$ $6.372$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.m 798.a 1.a $2$ $6.372$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
798.2.b.a 798.b 57.d $2$ $6.372$ \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
798.2.b.b 798.b 57.d $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{6}-q^{7}+\cdots\)
798.2.b.c 798.b 57.d $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}-q^{7}+\cdots\)
798.2.b.d 798.b 57.d $2$ $6.372$ \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(1-\beta )q^{6}+\cdots\)
798.2.b.e 798.b 57.d $8$ $6.372$ 8.0.\(\cdots\).1 None \(-8\) \(-1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
798.2.b.f 798.b 57.d $8$ $6.372$ 8.0.5240022544.1 None \(-8\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{5}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{5}q^{6}+\cdots\)
798.2.b.g 798.b 57.d $8$ $6.372$ 8.0.5240022544.1 None \(8\) \(-1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{5}q^{6}+\cdots\)
798.2.b.h 798.b 57.d $8$ $6.372$ 8.0.\(\cdots\).1 None \(8\) \(1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
798.2.e.a 798.e 133.c $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{4}q^{6}+\cdots\)
798.2.e.b 798.e 133.c $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{4}q^{6}+\cdots\)
798.2.f.a 798.f 21.c $24$ $6.372$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$
798.2.f.b 798.f 21.c $24$ $6.372$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$
798.2.i.a 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-7\) \(-14\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{8})q^{2}-q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
798.2.i.b 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-7\) \(14\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+q^{3}+\beta _{3}q^{4}-\beta _{1}q^{5}+\cdots\)
798.2.i.c 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(-14\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
798.2.i.d 798.i 133.g $14$ $6.372$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(7\) \(14\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{6})q^{2}+q^{3}-\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots\)
798.2.j.a 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.b 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.c 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.d 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.e 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.f 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.g 798.j 7.c $4$ $6.372$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
798.2.j.h 798.j 7.c $4$ $6.372$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
798.2.j.i 798.j 7.c $6$ $6.372$ 6.0.4406832.1 None \(-3\) \(-3\) \(5\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
798.2.j.j 798.j 7.c $6$ $6.372$ 6.0.4406832.1 None \(3\) \(3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
798.2.j.k 798.j 7.c $8$ $6.372$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
798.2.j.l 798.j 7.c $8$ $6.372$ 8.0.856615824.2 None \(4\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
798.2.k.a 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.b 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.c 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.d 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.e 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.f 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.g 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.h 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
798.2.k.i 798.k 19.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
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