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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1989.1.s.a 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{17}) \) \(-2\) \(0\) \(0\) \(0\) \(q+(-1+i)q^{2}-iq^{4}-q^{8}+iq^{13}+\cdots\)
1989.1.s.b 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{4}+(-1-i)q^{5}+(1-i)q^{11}+\cdots\)
1989.1.s.c 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{4}+(1+i)q^{5}+(-1+i)q^{11}+\cdots\)
1989.1.s.d 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{17}) \) \(2\) \(0\) \(0\) \(0\) \(q+(1-i)q^{2}-iq^{4}+q^{8}+iq^{13}+q^{16}+\cdots\)
1989.1.cn.a 1989.cn 663.al $8$ $0.993$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{4}-\zeta_{24}^{9}q^{5}-\zeta_{24}^{7}q^{11}+\cdots\)
1989.1.dg.a 1989.dg 221.w $4$ $0.993$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+(-1+\cdots)q^{11}+\cdots\)
1989.1.dg.b 1989.dg 221.w $4$ $0.993$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{5}q^{4}+(\zeta_{12}+\zeta_{12}^{2})q^{5}+(1+\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
1989.2.a.a 1989.a 1.a $1$ $15.882$ \(\Q\) None None \(-1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots\)
1989.2.a.b 1989.a 1.a $1$ $15.882$ \(\Q\) None None \(-1\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
1989.2.a.c 1989.a 1.a $1$ $15.882$ \(\Q\) None None \(1\) \(0\) \(-4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-2q^{7}-3q^{8}-4q^{10}+\cdots\)
1989.2.a.d 1989.a 1.a $1$ $15.882$ \(\Q\) None None \(1\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{7}-3q^{8}+2q^{11}+\cdots\)
1989.2.a.e 1989.a 1.a $1$ $15.882$ \(\Q\) None None \(1\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
1989.2.a.f 1989.a 1.a $2$ $15.882$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}+(1-\beta )q^{5}+2q^{7}-\beta q^{8}+\cdots\)
1989.2.a.g 1989.a 1.a $2$ $15.882$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
1989.2.a.h 1989.a 1.a $2$ $15.882$ \(\Q(\sqrt{21}) \) None None \(1\) \(0\) \(2\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3+\beta )q^{4}+q^{5}+(-3+\beta )q^{7}+\cdots\)
1989.2.a.i 1989.a 1.a $3$ $15.882$ 3.3.229.1 None None \(0\) \(0\) \(2\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1989.2.a.j 1989.a 1.a $3$ $15.882$ 3.3.148.1 None None \(1\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1989.2.a.k 1989.a 1.a $3$ $15.882$ 3.3.148.1 None None \(3\) \(0\) \(6\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+2q^{5}+\cdots\)
1989.2.a.l 1989.a 1.a $5$ $15.882$ 5.5.153424.1 None None \(-3\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{2}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
1989.2.a.m 1989.a 1.a $5$ $15.882$ 5.5.1004368.1 None None \(-1\) \(0\) \(-2\) \(8\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(2-\beta _{3}+\cdots)q^{7}+\cdots\)
1989.2.a.n 1989.a 1.a $6$ $15.882$ 6.6.15187408.1 None None \(-4\) \(0\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1989.2.a.o 1989.a 1.a $6$ $15.882$ 6.6.83831632.1 None None \(-2\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
1989.2.a.p 1989.a 1.a $6$ $15.882$ 6.6.28134208.1 None None \(-1\) \(0\) \(2\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+(1-\beta _{5})q^{7}+\cdots\)
1989.2.a.q 1989.a 1.a $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-4\) \(0\) \(-6\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1989.2.a.r 1989.a 1.a $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(-2\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{6})q^{5}+\cdots\)
1989.2.a.s 1989.a 1.a $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
1989.2.a.t 1989.a 1.a $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(4\) \(0\) \(6\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{6}+\cdots)q^{5}+\cdots\)
1989.2.b.a 1989.b 13.b $2$ $15.882$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
1989.2.b.b 1989.b 13.b $2$ $15.882$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+4iq^{7}+3iq^{8}+2iq^{11}+\cdots\)
1989.2.b.c 1989.b 13.b $2$ $15.882$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+(-1+2\zeta_{6})q^{5}+(3-6\zeta_{6})q^{11}+\cdots\)
1989.2.b.d 1989.b 13.b $4$ $15.882$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1989.2.b.e 1989.b 13.b $4$ $15.882$ 4.0.8112.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1989.2.b.f 1989.b 13.b $6$ $15.882$ 6.0.31337472.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1989.2.b.g 1989.b 13.b $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1989.2.b.h 1989.b 13.b $8$ $15.882$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
1989.2.b.i 1989.b 13.b $10$ $15.882$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{3}q^{7}+\cdots\)
1989.2.b.j 1989.b 13.b $10$ $15.882$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1989.2.b.k 1989.b 13.b $18$ $15.882$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots\)
1989.2.b.l 1989.b 13.b $18$ $15.882$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}+\beta _{7}q^{7}+\cdots\)
1989.2.f.a 1989.f 17.b $2$ $15.882$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}-2iq^{5}+3q^{8}+2iq^{10}+\cdots\)
1989.2.f.b 1989.f 17.b $2$ $15.882$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}-iq^{5}+3q^{8}+iq^{10}+\cdots\)
1989.2.f.c 1989.f 17.b $2$ $15.882$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}-iq^{5}+3q^{8}+iq^{10}+\cdots\)
1989.2.f.d 1989.f 17.b $2$ $15.882$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}+2iq^{5}-3q^{8}+2iq^{10}+\cdots\)
1989.2.f.e 1989.f 17.b $4$ $15.882$ 4.0.2312.1 None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
1989.2.f.f 1989.f 17.b $6$ $15.882$ 6.0.839056.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{3}+2\beta _{4}+\cdots)q^{5}+\cdots\)
1989.2.f.g 1989.f 17.b $6$ $15.882$ 6.0.49362048.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(2-\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
1989.2.f.h 1989.f 17.b $12$ $15.882$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(2-\beta _{2})q^{4}-\beta _{6}q^{5}+\beta _{8}q^{7}+\cdots\)
1989.2.f.i 1989.f 17.b $16$ $15.882$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(1-\beta _{5})q^{4}+(-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
1989.2.f.j 1989.f 17.b $18$ $15.882$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+(2+\beta _{1}+\beta _{9})q^{4}-\beta _{2}q^{5}+\cdots\)
1989.2.f.k 1989.f 17.b $20$ $15.882$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(1+\beta _{8})q^{4}+\beta _{7}q^{5}-\beta _{3}q^{7}+\cdots\)
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