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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.1.m.a 189.m 7.d $2$ $0.094$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{6}q^{4}-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)
189.1.q.a 189.q 21.h $2$ $0.094$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots\)
189.2.a.a 189.a 1.a $1$ $1.509$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.b 189.a 1.a $1$ $1.509$ \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}+q^{7}-6q^{11}-4q^{13}+\cdots\)
189.2.a.c 189.a 1.a $1$ $1.509$ \(\Q\) None None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+q^{7}+6q^{11}-4q^{13}+\cdots\)
189.2.a.d 189.a 1.a $1$ $1.509$ \(\Q\) None None \(2\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
189.2.a.e 189.a 1.a $2$ $1.509$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{5}+q^{7}-\beta q^{8}+3q^{10}+\cdots\)
189.2.a.f 189.a 1.a $2$ $1.509$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-\beta q^{5}-q^{7}+3\beta q^{8}+\cdots\)
189.2.c.a 189.c 21.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots\)
189.2.c.b 189.c 21.c $4$ $1.509$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c 189.c 21.c $4$ $1.509$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)
189.2.e.a 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.b 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots\)
189.2.e.c 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.d 189.e 7.c $4$ $1.509$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
189.2.e.e 189.e 7.c $6$ $1.509$ 6.0.309123.1 None None \(-2\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
189.2.e.f 189.e 7.c $6$ $1.509$ 6.0.309123.1 None None \(2\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
189.2.f.a 189.f 9.c $6$ $1.509$ 6.0.309123.1 None None \(-1\) \(0\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
189.2.f.b 189.f 9.c $6$ $1.509$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
189.2.g.a 189.g 63.g $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b 189.g 63.g $10$ $1.509$ 10.0.\(\cdots\).1 None None \(-2\) \(0\) \(8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
189.2.h.a 189.h 63.h $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
189.2.h.b 189.h 63.h $10$ $1.509$ 10.0.\(\cdots\).1 None None \(4\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(1+\beta _{3})q^{4}+(\beta _{6}-\beta _{9})q^{5}+\cdots\)
189.2.i.a 189.i 63.i $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
189.2.i.b 189.i 63.i $10$ $1.509$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
189.2.o.a 189.o 63.o $12$ $1.509$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(6\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
189.2.p.a 189.p 21.g $2$ $1.509$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+2\zeta_{6})q^{4}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.p.b 189.p 21.g $4$ $1.509$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
189.2.p.c 189.p 21.g $4$ $1.509$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-3+2\beta _{2})q^{7}+\cdots\)
189.2.p.d 189.p 21.g $12$ $1.509$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(1-\beta _{3}-\beta _{7}+\beta _{9})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
189.2.s.a 189.s 63.s $2$ $1.509$ \(\Q(\sqrt{-3}) \) None None \(3\) \(0\) \(6\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+3q^{5}+(-3+\cdots)q^{7}+\cdots\)
189.2.s.b 189.s 63.s $10$ $1.509$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
189.2.u.a 189.u 189.u $132$ $1.509$ None None \(-3\) \(-3\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
189.2.v.a 189.v 27.e $54$ $1.509$ None None \(0\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
189.2.v.b 189.v 27.e $54$ $1.509$ None None \(0\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
189.2.w.a 189.w 189.w $132$ $1.509$ None None \(-3\) \(-3\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
189.2.ba.a 189.ba 189.aa $132$ $1.509$ None None \(-3\) \(-9\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
189.2.bd.a 189.bd 189.ad $132$ $1.509$ None None \(-3\) \(-9\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
189.2.be.a 189.be 189.ae $132$ $1.509$ None None \(-12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
189.3.b.a 189.b 3.b $4$ $5.150$ 4.0.1166592.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-6+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
189.3.b.b 189.b 3.b $4$ $5.150$ \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots\)
189.3.b.c 189.b 3.b $8$ $5.150$ 8.0.1997017344.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{3})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
189.3.d.a 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}+(-7+7\zeta_{6})q^{7}+\cdots\)
189.3.d.b 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(13\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{4}+(6+\zeta_{6})q^{7}+(-5+10\zeta_{6})q^{13}+\cdots\)
189.3.d.c 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
189.3.d.d 189.d 7.b $8$ $5.150$ 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(3+\beta _{5})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
189.3.d.e 189.d 7.b $8$ $5.150$ 8.0.\(\cdots\).14 None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(5-\beta _{1})q^{4}+\beta _{2}q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
189.3.j.a 189.j 63.j $6$ $5.150$ 6.0.63369648.1 None None \(0\) \(0\) \(15\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{4}-\beta _{5})q^{2}+(-4-\beta _{1})q^{4}+\cdots\)
189.3.j.b 189.j 63.j $22$ $5.150$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
189.3.k.a 189.k 63.k $28$ $5.150$ None None \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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