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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.1.d.a 95.d 95.d $1$ $0.047$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b 95.d 95.d $2$ $0.047$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
95.2.a.a 95.a 1.a $3$ $0.759$ 3.3.148.1 None None \(1\) \(2\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
95.2.a.b 95.a 1.a $4$ $0.759$ 4.4.11344.1 None None \(-2\) \(2\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
95.2.b.a 95.b 5.b $2$ $0.759$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1+2i)q^{5}-2iq^{7}+\cdots\)
95.2.b.b 95.b 5.b $6$ $0.759$ 6.0.16516096.1 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
95.2.e.a 95.e 19.c $2$ $0.759$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
95.2.e.b 95.e 19.c $6$ $0.759$ 6.0.3518667.1 None None \(-1\) \(-1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
95.2.e.c 95.e 19.c $8$ $0.759$ 8.0.4601315889.1 None None \(-1\) \(-3\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
95.2.g.a 95.g 95.g $4$ $0.759$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(6\) $\mathrm{U}(1)[D_{4}]$ \(q-2\beta _{2}q^{4}-\beta _{3}q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
95.2.g.b 95.g 95.g $12$ $0.759$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-4\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\)
95.2.i.a 95.i 95.i $4$ $0.759$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
95.2.i.b 95.i 95.i $12$ $0.759$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
95.2.k.a 95.k 19.e $18$ $0.759$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{4}+\beta _{15})q^{2}+(\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)
95.2.k.b 95.k 19.e $18$ $0.759$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{14}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{15}+\cdots)q^{3}+\cdots\)
95.2.l.a 95.l 95.l $4$ $0.759$ \(\Q(\zeta_{12})\) None None \(-6\) \(-6\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots\)
95.2.l.b 95.l 95.l $4$ $0.759$ \(\Q(\zeta_{12})\) None None \(0\) \(-6\) \(2\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\)
95.2.l.c 95.l 95.l $24$ $0.759$ None None \(0\) \(6\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
95.2.p.a 95.p 95.p $48$ $0.759$ None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{18}]$
95.2.r.a 95.r 95.r $96$ $0.759$ None None \(-12\) \(-12\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{36}]$
95.3.c.a 95.c 19.b $12$ $2.589$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
95.3.d.a 95.d 95.d $2$ $2.589$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-9\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{4}+(-4-\beta )q^{5}+(-3+6\beta )q^{7}+\cdots\)
95.3.d.b 95.d 95.d $4$ $2.589$ 4.4.462080.1 \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(4+\beta _{3})q^{4}+\cdots\)
95.3.d.c 95.d 95.d $4$ $2.589$ 4.4.7600.1 \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(4+3\beta _{3})q^{4}+\cdots\)
95.3.d.d 95.d 95.d $8$ $2.589$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+2\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
95.3.f.a 95.f 5.c $36$ $2.589$ None None \(-4\) \(-4\) \(-6\) \(-10\) $\mathrm{SU}(2)[C_{4}]$
95.3.h.a 95.h 95.h $36$ $2.589$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
95.3.j.a 95.j 19.d $24$ $2.589$ None None \(0\) \(12\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{6}]$
95.3.m.a 95.m 95.m $72$ $2.589$ None None \(-2\) \(-2\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{12}]$
95.3.n.a 95.n 19.f $84$ $2.589$ None None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
95.3.o.a 95.o 95.o $108$ $2.589$ None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{18}]$
95.3.q.a 95.q 95.q $216$ $2.589$ None None \(-12\) \(-12\) \(-12\) \(12\) $\mathrm{SU}(2)[C_{36}]$
95.4.a.a 95.a 1.a $1$ $5.605$ \(\Q\) None None \(0\) \(4\) \(-5\) \(-22\) $-$ $\mathrm{SU}(2)$ \(q+4q^{3}-8q^{4}-5q^{5}-22q^{7}-11q^{9}+\cdots\)
95.4.a.b 95.a 1.a $1$ $5.605$ \(\Q\) None None \(3\) \(-5\) \(-5\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{2}-5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots\)
95.4.a.c 95.a 1.a $1$ $5.605$ \(\Q\) None None \(3\) \(7\) \(5\) \(11\) $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+7q^{3}+q^{4}+5q^{5}+21q^{6}+\cdots\)
95.4.a.d 95.a 1.a $1$ $5.605$ \(\Q\) None None \(5\) \(4\) \(5\) \(-32\) $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+4q^{3}+17q^{4}+5q^{5}+20q^{6}+\cdots\)
95.4.a.e 95.a 1.a $3$ $5.605$ 3.3.1304.1 None None \(-3\) \(-11\) \(15\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
95.4.a.f 95.a 1.a $5$ $5.605$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-3\) \(-4\) \(25\) \(72\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
95.4.a.g 95.a 1.a $6$ $5.605$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(-1\) \(5\) \(-30\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)
95.4.b.a 95.b 5.b $12$ $5.605$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6})q^{3}+(-3+\beta _{2}+\cdots)q^{4}+\cdots\)
95.4.b.b 95.b 5.b $16$ $5.605$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-5+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
95.4.e.a 95.e 19.c $2$ $5.605$ \(\Q(\sqrt{-3}) \) None None \(1\) \(5\) \(-5\) \(44\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots\)
95.4.e.b 95.e 19.c $18$ $5.605$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(6\) \(2\) \(-45\) \(-90\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
95.4.e.c 95.e 19.c $20$ $5.605$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(-5\) \(50\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(4\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
95.4.g.a 95.g 95.g $4$ $5.605$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-28\) \(-72\) $\mathrm{U}(1)[D_{4}]$ \(q-8\beta _{1}q^{4}+(-7+2\beta _{3})q^{5}+(-18+\cdots)q^{7}+\cdots\)
95.4.g.b 95.g 95.g $52$ $5.605$ None None \(0\) \(0\) \(16\) \(64\) $\mathrm{SU}(2)[C_{4}]$
95.4.i.a 95.i 95.i $56$ $5.605$ None None \(0\) \(0\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{6}]$
95.4.k.a 95.k 19.e $60$ $5.605$ None None \(-9\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
95.4.k.b 95.k 19.e $60$ $5.605$ None None \(9\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
95.4.l.a 95.l 95.l $112$ $5.605$ None None \(-6\) \(-6\) \(6\) \(-16\) $\mathrm{SU}(2)[C_{12}]$
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