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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1176.1.e.a 1176.e 168.e $8$ $0.587$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}q^{3}-q^{4}+\zeta_{16}^{5}q^{6}+\cdots\)
1176.1.n.a 1176.n 24.h $1$ $0.587$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1176.1.n.b 1176.n 24.h $1$ $0.587$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
1176.1.n.c 1176.n 24.h $1$ $0.587$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1176.1.n.d 1176.n 24.h $1$ $0.587$ \(\Q\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1176.1.n.e 1176.n 24.h $4$ $0.587$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)
1176.1.s.a 1176.s 168.s $2$ $0.587$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.b 1176.s 168.s $2$ $0.587$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.c 1176.s 168.s $8$ $0.587$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
1176.1.be.a 1176.be 168.ae $16$ $0.587$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
1176.1.bj.a 1176.bj 1176.aj $6$ $0.587$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(-2\) \(-1\) \(q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
1176.1.bj.b 1176.bj 1176.aj $6$ $0.587$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(2\) \(-1\) \(q+\zeta_{14}^{3}q^{2}-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
1176.1.ck.a 1176.ck 1176.bk $12$ $0.587$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q+\zeta_{42}^{13}q^{2}+\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots\)
1176.1.ck.b 1176.ck 1176.bk $12$ $0.587$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(1\) \(q-\zeta_{42}^{13}q^{2}-\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots\)
1176.2.a.a 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1176.2.a.b 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots\)
1176.2.a.c 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
1176.2.a.d 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
1176.2.a.e 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
1176.2.a.f 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1176.2.a.g 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
1176.2.a.h 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots\)
1176.2.a.i 1176.a 1.a $1$ $9.390$ \(\Q\) None None \(0\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1176.2.a.j 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
1176.2.a.k 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{57}) \) None None \(0\) \(-2\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
1176.2.a.l 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
1176.2.a.m 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
1176.2.a.n 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{57}) \) None None \(0\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
1176.2.a.o 1176.a 1.a $2$ $9.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
1176.2.c.a 1176.c 8.b $2$ $9.390$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+2iq^{5}+\cdots\)
1176.2.c.b 1176.c 8.b $4$ $9.390$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1176.2.c.c 1176.c 8.b $8$ $9.390$ 8.0.386672896.3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
1176.2.c.d 1176.c 8.b $12$ $9.390$ 12.0.\(\cdots\).1 None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1176.2.c.e 1176.c 8.b $16$ $9.390$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots\)
1176.2.c.f 1176.c 8.b $16$ $9.390$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots\)
1176.2.c.g 1176.c 8.b $24$ $9.390$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1176.2.k.a 1176.k 21.c $16$ $9.390$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{5}q^{9}-\beta _{6}q^{11}+\cdots\)
1176.2.k.b 1176.k 21.c $24$ $9.390$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1176.2.p.a 1176.p 56.e $32$ $9.390$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1176.2.p.b 1176.p 56.e $48$ $9.390$ None None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1176.2.q.a 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.b 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.c 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
1176.2.q.d 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.e 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.f 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+6q^{13}+\cdots\)
1176.2.q.g 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
1176.2.q.h 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1176.2.q.i 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1176.2.q.j 1176.q 7.c $2$ $9.390$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots\)
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