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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.1.c.a 196.c 4.b $1$ $0.098$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
196.1.g.a 196.g 28.g $2$ $0.098$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
196.2.a.a 196.a 1.a $1$ $1.565$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
196.2.a.b 196.a 1.a $1$ $1.565$ \(\Q\) None None \(0\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
196.2.a.c 196.a 1.a $2$ $1.565$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\)
196.2.d.a 196.d 28.d $4$ $1.565$ 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots\)
196.2.d.b 196.d 28.d $4$ $1.565$ \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
196.2.d.c 196.d 28.d $8$ $1.565$ 8.0.\(\cdots\).10 None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots\)
196.2.e.a 196.e 7.c $2$ $1.565$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
196.2.e.b 196.e 7.c $4$ $1.565$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
196.2.f.a 196.f 28.f $4$ $1.565$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
196.2.f.b 196.f 28.f $4$ $1.565$ \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
196.2.f.c 196.f 28.f $8$ $1.565$ 8.0.339738624.1 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots\)
196.2.f.d 196.f 28.f $16$ $1.565$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots\)
196.2.i.a 196.i 49.e $24$ $1.565$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{7}]$
196.2.j.a 196.j 196.j $156$ $1.565$ None None \(-5\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{14}]$
196.2.m.a 196.m 49.g $60$ $1.565$ None None \(0\) \(1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{21}]$
196.2.p.a 196.p 196.p $312$ $1.565$ None None \(-13\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{42}]$
196.3.b.a 196.b 7.b $2$ $5.341$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+6q^{9}+15q^{11}+\cdots\)
196.3.b.b 196.b 7.b $4$ $5.341$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-1-\beta _{3})q^{9}+\cdots\)
196.3.c.a 196.c 4.b $2$ $5.341$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}+9q^{9}+\cdots\)
196.3.c.b 196.c 4.b $2$ $5.341$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+\beta )q^{2}+(-1+3\beta )q^{4}+(-7+5\beta )q^{8}+\cdots\)
196.3.c.c 196.c 4.b $2$ $5.341$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+9q^{9}+\cdots\)
196.3.c.d 196.c 4.b $4$ $5.341$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.c.e 196.c 4.b $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.c.f 196.c 4.b $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-15})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1}+\cdots)q^{4}+\cdots\)
196.3.c.g 196.c 4.b $6$ $5.341$ 6.0.1539727.2 None None \(-1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.c.h 196.c 4.b $6$ $5.341$ 6.0.15582448.1 None None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
196.3.c.i 196.c 4.b $6$ $5.341$ 6.0.15582448.1 None None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
196.3.g.a 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
196.3.g.b 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.g.c 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-4\beta _{2}q^{4}+\cdots\)
196.3.g.d 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2\beta _{2}+\beta _{3})q^{2}+(1-3\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
196.3.g.e 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
196.3.g.f 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+(\beta _{1}-\beta _{3})q^{3}+4q^{4}+4\beta _{1}q^{5}+\cdots\)
196.3.g.g 196.g 28.g $4$ $5.341$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
196.3.g.h 196.g 28.g $8$ $5.341$ 8.0.207360000.1 None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{3})q^{2}+(\beta _{1}-2\beta _{4}-2\beta _{5}-2\beta _{7})q^{3}+\cdots\)
196.3.g.i 196.g 28.g $12$ $5.341$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)
196.3.g.j 196.g 28.g $12$ $5.341$ 12.0.\(\cdots\).1 None None \(1\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}-\beta _{4}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.g.k 196.g 28.g $12$ $5.341$ 12.0.\(\cdots\).1 None None \(1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}-\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
196.3.h.a 196.h 7.d $2$ $5.341$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}-6\zeta_{6}q^{9}+\cdots\)
196.3.h.b 196.h 7.d $4$ $5.341$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(15+15\beta _{1}+\cdots)q^{9}+\cdots\)
196.3.h.c 196.h 7.d $8$ $5.341$ 8.0.339738624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2}-2\beta _{6})q^{5}+(1+\cdots)q^{9}+\cdots\)
196.3.k.a 196.k 196.k $324$ $5.341$ None None \(-5\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{14}]$
196.3.l.a 196.l 49.f $60$ $5.341$ None None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{14}]$
196.3.n.a 196.n 49.h $108$ $5.341$ None None \(0\) \(-3\) \(-3\) \(14\) $\mathrm{SU}(2)[C_{42}]$
196.3.o.a 196.o 196.o $648$ $5.341$ None None \(-13\) \(0\) \(-26\) \(0\) $\mathrm{SU}(2)[C_{42}]$
196.4.a.a 196.a 1.a $1$ $11.564$ \(\Q\) None None \(0\) \(-4\) \(-20\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.b 196.a 1.a $1$ $11.564$ \(\Q\) None None \(0\) \(-4\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-6q^{5}-11q^{9}-12q^{11}+82q^{13}+\cdots\)
196.4.a.c 196.a 1.a $1$ $11.564$ \(\Q\) None None \(0\) \(4\) \(20\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+20q^{5}-11q^{9}+44q^{11}+\cdots\)
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