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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
770.2.a.a 770.a 1.a $1$ $6.148$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
770.2.a.b 770.a 1.a $1$ $6.148$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
770.2.a.c 770.a 1.a $1$ $6.148$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
770.2.a.d 770.a 1.a $1$ $6.148$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
770.2.a.e 770.a 1.a $1$ $6.148$ \(\Q\) None \(-1\) \(2\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.f 770.a 1.a $1$ $6.148$ \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.g 770.a 1.a $1$ $6.148$ \(\Q\) None \(1\) \(-2\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
770.2.a.h 770.a 1.a $2$ $6.148$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
770.2.a.i 770.a 1.a $2$ $6.148$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots\)
770.2.a.j 770.a 1.a $2$ $6.148$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
770.2.a.k 770.a 1.a $2$ $6.148$ \(\Q(\sqrt{33}) \) None \(2\) \(4\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
770.2.a.l 770.a 1.a $3$ $6.148$ 3.3.892.1 None \(-3\) \(0\) \(-3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
770.2.a.m 770.a 1.a $3$ $6.148$ 3.3.316.1 None \(3\) \(2\) \(3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2})q^{6}+\cdots\)
770.2.c.a 770.c 5.b $2$ $6.148$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
770.2.c.b 770.c 5.b $2$ $6.148$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(1-2i)q^{5}-iq^{7}+iq^{8}+\cdots\)
770.2.c.c 770.c 5.b $2$ $6.148$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2-i)q^{5}+iq^{7}-iq^{8}+\cdots\)
770.2.c.d 770.c 5.b $4$ $6.148$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
770.2.c.e 770.c 5.b $8$ $6.148$ 8.0.1698758656.6 None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.c.f 770.c 5.b $10$ $6.148$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{7}q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.e.a 770.e 77.b $16$ $6.148$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{10}q^{5}+\cdots\)
770.2.e.b 770.e 77.b $16$ $6.148$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{10}q^{5}+\cdots\)
770.2.g.a 770.g 385.h $24$ $6.148$ None \(-24\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$
770.2.g.b 770.g 385.h $24$ $6.148$ None \(24\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$
770.2.i.a 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.b 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.c 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.d 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.e 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.f 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.g 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.h 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.i 770.i 7.c $2$ $6.148$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.j 770.i 7.c $6$ $6.148$ \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{18}^{3})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
770.2.i.k 770.i 7.c $6$ $6.148$ 6.0.64827.1 None \(3\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
770.2.i.l 770.i 7.c $8$ $6.148$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(1\) \(4\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{5})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{4}+(1+\cdots)q^{5}+\cdots\)
770.2.i.m 770.i 7.c $10$ $6.148$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(0\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{6})q^{2}+(\beta _{1}-\beta _{2})q^{3}-\beta _{6}q^{4}+\cdots\)
770.2.l.a 770.l 35.f $16$ $6.148$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{12}q^{2}+\beta _{1}q^{3}-\beta _{8}q^{4}+(\beta _{2}+\beta _{13}+\cdots)q^{5}+\cdots\)
770.2.l.b 770.l 35.f $24$ $6.148$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
770.2.l.c 770.l 35.f $40$ $6.148$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
770.2.m.a 770.m 55.e $4$ $6.148$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.b 770.m 55.e $4$ $6.148$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+2\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.c 770.m 55.e $4$ $6.148$ \(\Q(\zeta_{8})\) None \(0\) \(8\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(2+2\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
770.2.m.d 770.m 55.e $8$ $6.148$ 8.0.40960000.1 None \(0\) \(-4\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
770.2.m.e 770.m 55.e $16$ $6.148$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{10}q^{2}+(-1-\beta _{3}+\beta _{7}-\beta _{15})q^{3}+\cdots\)
770.2.m.f 770.m 55.e $36$ $6.148$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
770.2.n.a 770.n 11.c $4$ $6.148$ \(\Q(\zeta_{10})\) None \(-1\) \(-3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
770.2.n.b 770.n 11.c $4$ $6.148$ \(\Q(\zeta_{10})\) None \(1\) \(-4\) \(1\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.c 770.n 11.c $4$ $6.148$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.d 770.n 11.c $4$ $6.148$ \(\Q(\zeta_{10})\) None \(1\) \(2\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
770.2.n.e 770.n 11.c $8$ $6.148$ 8.0.682515625.5 None \(2\) \(-1\) \(2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+\beta _{3}q^{4}+\cdots\)
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