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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
190.2.a.a 190.a 1.a $1$ $1.517$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.b 190.a 1.a $1$ $1.517$ \(\Q\) None \(1\) \(-3\) \(-1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
190.2.a.c 190.a 1.a $1$ $1.517$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
190.2.a.d 190.a 1.a $2$ $1.517$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
190.2.b.a 190.b 5.b $4$ $1.517$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
190.2.b.b 190.b 5.b $6$ $1.517$ 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
190.2.e.a 190.e 19.c $2$ $1.517$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
190.2.e.b 190.e 19.c $2$ $1.517$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
190.2.e.c 190.e 19.c $4$ $1.517$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(1\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
190.2.f.a 190.f 95.g $4$ $1.517$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots\)
190.2.f.b 190.f 95.g $16$ $1.517$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots\)
190.2.i.a 190.i 95.i $20$ $1.517$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
190.2.k.a 190.k 19.e $6$ $1.517$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b 190.k 19.e $12$ $1.517$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c 190.k 19.e $12$ $1.517$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d 190.k 19.e $18$ $1.517$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)
190.2.m.a 190.m 95.l $8$ $1.517$ \(\Q(\zeta_{24})\) None \(0\) \(12\) \(4\) \(-16\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
190.2.m.b 190.m 95.l $32$ $1.517$ None \(0\) \(-12\) \(0\) \(24\) $\mathrm{SU}(2)[C_{12}]$
190.2.p.a 190.p 95.p $60$ $1.517$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
190.2.r.a 190.r 95.r $120$ $1.517$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
190.3.c.a 190.c 19.b $16$ $5.177$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)
190.3.d.a 190.d 95.d $20$ $5.177$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
190.3.g.a 190.g 5.c $16$ $5.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(8\) \(2\) \(-10\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
190.3.g.b 190.g 5.c $20$ $5.177$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(0\) \(2\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots\)
190.3.h.a 190.h 95.h $4$ $5.177$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
190.3.h.b 190.h 95.h $36$ $5.177$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
190.3.j.a 190.j 19.d $32$ $5.177$ None \(0\) \(-12\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$
190.3.l.a 190.l 95.m $4$ $5.177$ \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(8\) \(32\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.b 190.l 95.m $4$ $5.177$ \(\Q(\zeta_{12})\) None \(2\) \(6\) \(10\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots\)
190.3.l.c 190.l 95.m $36$ $5.177$ None \(-18\) \(6\) \(-10\) \(-28\) $\mathrm{SU}(2)[C_{12}]$
190.3.l.d 190.l 95.m $36$ $5.177$ None \(18\) \(-6\) \(-12\) \(12\) $\mathrm{SU}(2)[C_{12}]$
190.3.n.a 190.n 19.f $72$ $5.177$ None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
190.3.o.a 190.o 95.o $120$ $5.177$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
190.3.q.a 190.q 95.q $120$ $5.177$ None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{36}]$
190.3.q.b 190.q 95.q $120$ $5.177$ None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{36}]$
190.4.a.a 190.a 1.a $1$ $11.210$ \(\Q\) None \(-2\) \(-2\) \(5\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
190.4.a.b 190.a 1.a $1$ $11.210$ \(\Q\) None \(-2\) \(2\) \(5\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots\)
190.4.a.c 190.a 1.a $1$ $11.210$ \(\Q\) None \(2\) \(-4\) \(5\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
190.4.a.d 190.a 1.a $2$ $11.210$ \(\Q(\sqrt{313}) \) None \(-4\) \(1\) \(10\) \(-27\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots\)
190.4.a.e 190.a 1.a $2$ $11.210$ \(\Q(\sqrt{3}) \) None \(-4\) \(2\) \(-10\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.f 190.a 1.a $2$ $11.210$ \(\Q(\sqrt{34}) \) None \(4\) \(0\) \(-10\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots\)
190.4.a.g 190.a 1.a $3$ $11.210$ 3.3.126168.1 None \(-6\) \(-1\) \(-15\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
190.4.a.h 190.a 1.a $3$ $11.210$ 3.3.5468.1 None \(6\) \(-9\) \(-15\) \(-11\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
190.4.a.i 190.a 1.a $3$ $11.210$ 3.3.15357.1 None \(6\) \(11\) \(15\) \(29\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
190.4.b.a 190.b 5.b $12$ $11.210$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
190.4.b.b 190.b 5.b $14$ $11.210$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
190.4.e.a 190.e 19.c $2$ $11.210$ \(\Q(\sqrt{-3}) \) None \(2\) \(2\) \(-5\) \(-56\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.b 190.e 19.c $2$ $11.210$ \(\Q(\sqrt{-3}) \) None \(2\) \(2\) \(5\) \(64\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
190.4.e.c 190.e 19.c $6$ $11.210$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(6\) \(3\) \(-15\) \(36\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
190.4.e.d 190.e 19.c $8$ $11.210$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(3\) \(20\) \(-82\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
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