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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1088.1.g.a 1088.g 68.d $1$ $0.543$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}+2q^{13}+q^{17}+q^{25}-q^{49}+\cdots\)
1088.1.g.b 1088.g 68.d $2$ $0.543$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots\)
1088.1.n.a 1088.n 136.j $2$ $0.543$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(-2\) \(q+(-1+i)q^{7}+iq^{9}+iq^{17}+(-1+\cdots)q^{23}+\cdots\)
1088.1.n.b 1088.n 136.j $2$ $0.543$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(2\) \(q+(1-i)q^{7}+iq^{9}+iq^{17}+(1-i+\cdots)q^{23}+\cdots\)
1088.1.p.a 1088.p 68.f $2$ $0.543$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-i)q^{5}-iq^{9}-q^{17}-iq^{25}+\cdots\)
1088.1.ba.a 1088.ba 68.g $4$ $0.543$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-\zeta_{8}q^{9}+(-\zeta_{8}+\cdots)q^{13}+\cdots\)
1088.1.co.a 1088.co 136.q $8$ $0.543$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}^{6}+\zeta_{16}^{7})q^{3}+(-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{9}+\cdots\)
1088.1.co.b 1088.co 136.q $8$ $0.543$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}^{6}-\zeta_{16}^{7})q^{3}+(-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{9}+\cdots\)
1088.1.cz.a 1088.cz 17.e $8$ $0.543$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}^{2}-\zeta_{16}^{7})q^{5}-\zeta_{16}^{5}q^{9}+\cdots\)
1088.2.a.a 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(-2\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
1088.2.a.b 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
1088.2.a.c 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-2q^{11}+6q^{13}-q^{17}+\cdots\)
1088.2.a.d 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(-2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1088.2.a.e 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(-2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
1088.2.a.f 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+4q^{11}-2q^{13}-q^{17}+\cdots\)
1088.2.a.g 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}-2q^{13}-q^{17}+\cdots\)
1088.2.a.h 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
1088.2.a.i 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
1088.2.a.j 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(2\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
1088.2.a.k 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
1088.2.a.l 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1088.2.a.m 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}+2q^{11}+6q^{13}-q^{17}+\cdots\)
1088.2.a.n 1088.a 1.a $1$ $8.688$ \(\Q\) None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots\)
1088.2.a.o 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-2q^{5}+(-1-\beta )q^{7}+\cdots\)
1088.2.a.p 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+(-1+\beta )q^{7}+\cdots\)
1088.2.a.q 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
1088.2.a.r 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}-\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
1088.2.a.s 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-2q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1088.2.a.t 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2\beta q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1088.2.a.u 1088.a 1.a $3$ $8.688$ 3.3.148.1 None None \(0\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
1088.2.a.v 1088.a 1.a $3$ $8.688$ 3.3.148.1 None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
1088.2.b.a 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.b 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.c 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+iq^{11}+2q^{13}+\cdots\)
1088.2.b.d 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+iq^{11}+2q^{13}+\cdots\)
1088.2.b.e 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
1088.2.b.f 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
1088.2.b.g 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.h 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1088.2.b.i 1088.b 17.b $2$ $8.688$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-iq^{5}+3q^{9}+6q^{13}+(1+i)q^{17}+\cdots\)
1088.2.b.j 1088.b 17.b $4$ $8.688$ 4.0.2312.1 \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-4-\beta _{3})q^{9}+\cdots\)
1088.2.b.k 1088.b 17.b $4$ $8.688$ 4.0.2312.1 \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1088.2.b.l 1088.b 17.b $4$ $8.688$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1088.2.b.m 1088.b 17.b $4$ $8.688$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
1088.2.c.a 1088.c 8.b $2$ $8.688$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{5}-4q^{7}+3q^{9}+2iq^{11}+2iq^{13}+\cdots\)
1088.2.c.b 1088.c 8.b $2$ $8.688$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots\)
1088.2.c.c 1088.c 8.b $4$ $8.688$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
1088.2.c.d 1088.c 8.b $12$ $8.688$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{3}-\beta _{6}q^{5}+\beta _{3}q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
1088.2.c.e 1088.c 8.b $12$ $8.688$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1088.2.h.a 1088.h 136.h $4$ $8.688$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{3}q^{3}+5q^{9}-\zeta_{8}^{3}q^{11}+(3+\zeta_{8}^{2}+\cdots)q^{17}+\cdots\)
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