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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1352.1.g.a 1352.g 8.d $2$ $0.675$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-26}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{7}+\cdots\)
1352.1.g.b 1352.g 8.d $3$ $0.675$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-2}) \) None \(-3\) \(-1\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots\)
1352.1.g.c 1352.g 8.d $3$ $0.675$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-2}) \) None \(3\) \(-1\) \(0\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots\)
1352.1.h.a 1352.h 104.h $6$ $0.675$ 6.0.153664.1 \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{4}q^{3}-q^{4}-\beta _{1}q^{6}-\beta _{5}q^{8}+\cdots\)
1352.1.n.a 1352.n 104.n $4$ $0.675$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-26}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1352.1.n.b 1352.n 104.n $6$ $0.675$ 6.0.64827.1 \(\Q(\sqrt{-2}) \) None \(-3\) \(1\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
1352.1.n.c 1352.n 104.n $6$ $0.675$ 6.0.64827.1 \(\Q(\sqrt{-2}) \) None \(3\) \(1\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
1352.1.p.a 1352.p 104.p $2$ $0.675$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-26}) \) None \(-1\) \(1\) \(-2\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1352.1.p.b 1352.p 104.p $2$ $0.675$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-26}) \) None \(1\) \(1\) \(2\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1352.1.p.c 1352.p 104.p $12$ $0.675$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots\)
1352.2.a.a 1352.a 1.a $1$ $10.796$ \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}-2q^{9}-q^{11}-2q^{15}+\cdots\)
1352.2.a.b 1352.a 1.a $1$ $10.796$ \(\Q\) None None \(0\) \(1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-5q^{7}-2q^{9}+2q^{11}+\cdots\)
1352.2.a.c 1352.a 1.a $1$ $10.796$ \(\Q\) None None \(0\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}-2q^{9}+q^{11}+2q^{15}+\cdots\)
1352.2.a.d 1352.a 1.a $2$ $10.796$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1352.2.a.e 1352.a 1.a $2$ $10.796$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+\beta q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1352.2.a.f 1352.a 1.a $2$ $10.796$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)
1352.2.a.g 1352.a 1.a $2$ $10.796$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots\)
1352.2.a.h 1352.a 1.a $2$ $10.796$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots\)
1352.2.a.i 1352.a 1.a $3$ $10.796$ \(\Q(\zeta_{14})^+\) None None \(0\) \(-4\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-1-\beta _{1})q^{5}-\beta _{1}q^{7}+\cdots\)
1352.2.a.j 1352.a 1.a $3$ $10.796$ \(\Q(\zeta_{14})^+\) None None \(0\) \(-4\) \(4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots\)
1352.2.a.k 1352.a 1.a $4$ $10.796$ 4.4.13968.1 None None \(0\) \(-2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1352.2.a.l 1352.a 1.a $4$ $10.796$ 4.4.13968.1 None None \(0\) \(-2\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1352.2.a.m 1352.a 1.a $6$ $10.796$ 6.6.3728753.1 None None \(0\) \(3\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1352.2.a.n 1352.a 1.a $6$ $10.796$ 6.6.3728753.1 None None \(0\) \(3\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
1352.2.f.a 1352.f 13.b $2$ $10.796$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}+iq^{7}-2q^{9}-iq^{11}+\cdots\)
1352.2.f.b 1352.f 13.b $2$ $10.796$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-iq^{5}-5iq^{7}-2q^{9}+2iq^{11}+\cdots\)
1352.2.f.c 1352.f 13.b $4$ $10.796$ \(\Q(i, \sqrt{17})\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
1352.2.f.d 1352.f 13.b $4$ $10.796$ \(\Q(i, \sqrt{17})\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1352.2.f.e 1352.f 13.b $6$ $10.796$ 6.0.153664.1 None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{2}+\beta _{4})q^{3}+(\beta _{3}-\beta _{5})q^{5}+\cdots\)
1352.2.f.f 1352.f 13.b $8$ $10.796$ 8.0.195105024.2 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{3}+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
1352.2.f.g 1352.f 13.b $12$ $10.796$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{4}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
1352.2.i.a 1352.i 13.c $2$ $10.796$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1352.2.i.b 1352.i 13.c $2$ $10.796$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1352.2.i.c 1352.i 13.c $2$ $10.796$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1352.2.i.d 1352.i 13.c $4$ $10.796$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-1\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-2-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1352.2.i.e 1352.i 13.c $4$ $10.796$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-1\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1352.2.i.f 1352.i 13.c $4$ $10.796$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-1\) \(6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(2+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
1352.2.i.g 1352.i 13.c $4$ $10.796$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1352.2.i.h 1352.i 13.c $4$ $10.796$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(1\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{7}+\cdots\)
1352.2.i.i 1352.i 13.c $6$ $10.796$ 6.0.64827.1 None None \(0\) \(4\) \(-8\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4}-\beta _{5})q^{3}+(-1+\beta _{3})q^{5}+\cdots\)
1352.2.i.j 1352.i 13.c $6$ $10.796$ 6.0.64827.1 None None \(0\) \(4\) \(8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4}-\beta _{5})q^{3}+(1-\beta _{3})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
1352.2.i.k 1352.i 13.c $8$ $10.796$ 8.0.195105024.2 None None \(0\) \(2\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1352.2.i.l 1352.i 13.c $8$ $10.796$ 8.0.195105024.2 None None \(0\) \(2\) \(8\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
1352.2.i.m 1352.i 13.c $12$ $10.796$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(-4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2}+\beta _{7}-\beta _{10})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1352.2.i.n 1352.i 13.c $12$ $10.796$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(4\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2}+\beta _{7}-\beta _{10})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1352.2.o.a 1352.o 13.e $4$ $10.796$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{3}q^{5}+(5\zeta_{12}+\cdots)q^{7}+\cdots\)
1352.2.o.b 1352.o 13.e $4$ $10.796$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
1352.2.o.c 1352.o 13.e $8$ $10.796$ 8.0.1731891456.1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{6}-\beta _{7})q^{5}+\cdots\)
1352.2.o.d 1352.o 13.e $8$ $10.796$ 8.0.1731891456.1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3}+\beta _{5})q^{3}+(-\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots\)
1352.2.o.e 1352.o 13.e $8$ $10.796$ 8.0.1731891456.1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{7})q^{3}+(\beta _{1}-\beta _{5})q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)
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