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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1078.2.a.a 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(-3\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{8}+\cdots\)
1078.2.a.b 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
1078.2.a.c 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.d 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-q^{8}-3q^{9}-4q^{10}+\cdots\)
1078.2.a.e 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.f 1078.a 1.a $1$ $8.608$ \(\Q\) None \(-1\) \(3\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}-q^{8}+\cdots\)
1078.2.a.g 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(-3\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-2q^{5}-3q^{6}+q^{8}+\cdots\)
1078.2.a.h 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots\)
1078.2.a.i 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.j 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1078.2.a.k 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.l 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{8}+\cdots\)
1078.2.a.m 1078.a 1.a $1$ $8.608$ \(\Q\) None \(1\) \(3\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{8}+\cdots\)
1078.2.a.n 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.o 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-3q^{9}-\beta q^{10}+\cdots\)
1078.2.a.p 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2\beta q^{5}-q^{8}-3q^{9}+2\beta q^{10}+\cdots\)
1078.2.a.q 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
1078.2.a.r 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+5q^{9}+\cdots\)
1078.2.a.s 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.t 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
1078.2.a.u 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+3\beta q^{5}+\beta q^{6}+\cdots\)
1078.2.a.v 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+q^{8}+\cdots\)
1078.2.a.w 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1078.2.a.x 1078.a 1.a $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots\)
1078.2.c.a 1078.c 77.b $8$ $8.608$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}q^{2}+(-\zeta_{16}^{2}-\zeta_{16}^{4})q^{3}-q^{4}+\cdots\)
1078.2.c.b 1078.c 77.b $16$ $8.608$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.c.c 1078.c 77.b $16$ $8.608$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.e.a 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.b 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1078.2.e.c 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1078.2.e.d 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.e 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.f 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.g 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.h 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.i 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1078.2.e.j 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
1078.2.e.k 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.l 1078.e 7.c $2$ $8.608$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.m 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.n 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.o 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1078.2.e.p 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.q 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1078.2.e.r 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)
1078.2.e.s 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.t 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.u 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.v 1078.e 7.c $4$ $8.608$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.i.a 1078.i 77.i $16$ $8.608$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{48}q^{2}+(-\zeta_{48}^{2}+\zeta_{48}^{7}-\zeta_{48}^{10}+\cdots)q^{3}+\cdots\)
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