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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1232.1.m.a 1232.m 308.g $2$ $0.615$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-77}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
1232.1.m.b 1232.m 308.g $2$ $0.615$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-77}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{3}+q^{7}+q^{9}-q^{11}+\beta q^{13}+\cdots\)
1232.1.u.a 1232.u 1232.u $2$ $0.615$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+iq^{9}+\cdots\)
1232.1.u.b 1232.u 1232.u $2$ $0.615$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+iq^{9}+\cdots\)
1232.1.cd.a 1232.cd 77.j $4$ $0.615$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\zeta_{10}q^{11}+\cdots\)
1232.1.cq.a 1232.cq 1232.bq $8$ $0.615$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{7}+\cdots\)
1232.1.cq.b 1232.cq 1232.bq $8$ $0.615$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{7}+\zeta_{20}^{3}q^{8}+\cdots\)
1232.1.cr.a 1232.cr 1232.br $8$ $0.615$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+\zeta_{20}^{7}q^{7}+\cdots\)
1232.1.cr.b 1232.cr 1232.br $8$ $0.615$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}-\zeta_{20}^{7}q^{7}+\cdots\)
1232.2.a.a 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
1232.2.a.b 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(-2\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}+q^{11}-4q^{15}+\cdots\)
1232.2.a.c 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(-2\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
1232.2.a.d 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(-1\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots\)
1232.2.a.e 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(0\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
1232.2.a.f 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
1232.2.a.g 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+q^{11}-6q^{13}+2q^{19}+\cdots\)
1232.2.a.h 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
1232.2.a.i 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}-q^{15}+\cdots\)
1232.2.a.j 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots\)
1232.2.a.k 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(2\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
1232.2.a.l 1232.a 1.a $1$ $9.838$ \(\Q\) None None \(0\) \(3\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)
1232.2.a.m 1232.a 1.a $2$ $9.838$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-2q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1232.2.a.n 1232.a 1.a $2$ $9.838$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+q^{7}+3q^{9}+q^{11}+\cdots\)
1232.2.a.o 1232.a 1.a $2$ $9.838$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
1232.2.a.p 1232.a 1.a $2$ $9.838$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1232.2.a.q 1232.a 1.a $3$ $9.838$ 3.3.229.1 None None \(0\) \(-1\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1})q^{9}+\cdots\)
1232.2.a.r 1232.a 1.a $3$ $9.838$ 3.3.1016.1 None None \(0\) \(1\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
1232.2.a.s 1232.a 1.a $4$ $9.838$ 4.4.11348.1 None None \(0\) \(-1\) \(5\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
1232.2.e.a 1232.e 77.b $2$ $9.838$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{7}+3q^{9}+(-2-\beta )q^{11}+8q^{23}+\cdots\)
1232.2.e.b 1232.e 77.b $4$ $9.838$ \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\)
1232.2.e.c 1232.e 77.b $4$ $9.838$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}-2q^{9}+\cdots\)
1232.2.e.d 1232.e 77.b $4$ $9.838$ \(\Q(\sqrt{-2}, \sqrt{-7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1232.2.e.e 1232.e 77.b $8$ $9.838$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{6}q^{5}+(\beta _{1}-\beta _{3}-\beta _{7})q^{7}+\cdots\)
1232.2.e.f 1232.e 77.b $24$ $9.838$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1232.2.f.a 1232.f 44.c $6$ $9.838$ 6.0.10323968.1 None None \(0\) \(0\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1232.2.f.b 1232.f 44.c $6$ $9.838$ 6.0.10323968.1 None None \(0\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1232.2.f.c 1232.f 44.c $12$ $9.838$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{5}q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1232.2.f.d 1232.f 44.c $12$ $9.838$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(2\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{5}q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1232.2.j.a 1232.j 28.d $16$ $9.838$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{15}q^{3}-\beta _{12}q^{5}-\beta _{13}q^{7}+(1+\beta _{6}+\cdots)q^{9}+\cdots\)
1232.2.j.b 1232.j 28.d $24$ $9.838$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1232.2.q.a 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.b 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1232.2.q.c 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.d 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1232.2.q.e 1232.q 7.c $2$ $9.838$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1232.2.q.f 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1232.2.q.g 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1232.2.q.h 1232.q 7.c $4$ $9.838$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1232.2.q.i 1232.q 7.c $6$ $9.838$ 6.0.64827.1 None None \(0\) \(-5\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(1+\cdots)q^{5}+\cdots\)
1232.2.q.j 1232.q 7.c $6$ $9.838$ 6.0.1783323.2 None None \(0\) \(-3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
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