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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.1.c.a 76.c 19.b $1$ $0.038$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
76.2.a.a 76.a 1.a $1$ $0.607$ \(\Q\) None None \(0\) \(2\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
76.2.d.a 76.d 76.d $8$ $0.607$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
76.2.e.a 76.e 19.c $2$ $0.607$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
76.2.f.a 76.f 76.f $16$ $0.607$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)
76.2.i.a 76.i 19.e $12$ $0.607$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)
76.2.k.a 76.k 76.k $48$ $0.607$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.3.b.a 76.b 4.b $4$ $2.071$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(-4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b 76.b 4.b $14$ $2.071$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)
76.3.c.a 76.c 19.b $2$ $2.071$ \(\Q(\sqrt{-29}) \) None None \(0\) \(0\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b 76.c 19.b $2$ $2.071$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(5\) $\mathrm{U}(1)[D_{2}]$ \(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)
76.3.g.a 76.g 76.g $4$ $2.071$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None None \(-4\) \(6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b 76.g 76.g $4$ $2.071$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None None \(8\) \(-6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c 76.g 76.g $28$ $2.071$ None None \(-5\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
76.3.h.a 76.h 19.d $8$ $2.071$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(6\) \(-1\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
76.3.j.a 76.j 19.f $18$ $2.071$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(-6\) \(0\) \(9\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots\)
76.3.l.a 76.l 76.l $108$ $2.071$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.4.a.a 76.a 1.a $2$ $4.484$ \(\Q(\sqrt{33}) \) None None \(0\) \(-5\) \(-5\) \(-30\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b 76.a 1.a $3$ $4.484$ 3.3.35529.1 None None \(0\) \(1\) \(9\) \(44\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)
76.4.d.a 76.d 76.d $28$ $4.484$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
76.4.e.a 76.e 19.c $10$ $4.484$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(7\) \(-4\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.4.f.a 76.f 76.f $56$ $4.484$ None None \(-3\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
76.4.i.a 76.i 19.e $30$ $4.484$ None None \(0\) \(-3\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$
76.4.k.a 76.k 76.k $168$ $4.484$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.5.b.a 76.b 4.b $36$ $7.856$ None None \(6\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
76.5.c.a 76.c 19.b $2$ $7.856$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-31\) \(73\) $\mathrm{U}(1)[D_{2}]$ \(q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots\)
76.5.c.b 76.c 19.b $4$ $7.856$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None None \(0\) \(0\) \(22\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots\)
76.5.g.a 76.g 76.g $76$ $7.856$ None None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
76.5.h.a 76.h 19.d $12$ $7.856$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-12\) \(9\) \(-52\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
76.5.j.a 76.j 19.f $42$ $7.856$ None None \(0\) \(12\) \(0\) \(-45\) $\mathrm{SU}(2)[C_{18}]$
76.5.l.a 76.l 76.l $228$ $7.856$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.6.a.a 76.a 1.a $3$ $12.189$ 3.3.272193.1 None None \(0\) \(-8\) \(-9\) \(-13\) $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b 76.a 1.a $4$ $12.189$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(10\) \(-110\) \(30\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)
76.6.d.a 76.d 76.d $48$ $12.189$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
76.6.e.a 76.e 19.c $18$ $12.189$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(-11\) \(11\) \(336\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.6.f.a 76.f 76.f $96$ $12.189$ None None \(-3\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
76.6.i.a 76.i 19.e $48$ $12.189$ None None \(0\) \(33\) \(0\) \(-177\) $\mathrm{SU}(2)[C_{9}]$
76.6.k.a 76.k 76.k $288$ $12.189$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.7.b.a 76.b 4.b $54$ $17.484$ None None \(-10\) \(0\) \(-44\) \(0\) $\mathrm{SU}(2)[C_{2}]$
76.7.c.a 76.c 19.b $2$ $17.484$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(54\) \(-610\) $\mathrm{U}(1)[D_{2}]$ \(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b 76.c 19.b $8$ $17.484$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(2\) \(362\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
76.7.g.a 76.g 76.g $116$ $17.484$ None None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
76.7.h.a 76.h 19.d $20$ $17.484$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-30\) \(-56\) \(464\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots\)
76.7.j.a 76.j 19.f $60$ $17.484$ None None \(0\) \(30\) \(0\) \(-216\) $\mathrm{SU}(2)[C_{18}]$
76.7.l.a 76.l 76.l $348$ $17.484$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
76.8.a.a 76.a 1.a $5$ $23.741$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-14\) \(-280\) \(414\) $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
76.8.a.b 76.a 1.a $6$ $23.741$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(40\) \(279\) \(-1565\) $+$ $\mathrm{SU}(2)$ \(q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots\)
76.8.d.a 76.d 76.d $68$ $23.741$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
76.8.e.a 76.e 19.c $22$ $23.741$ None None \(0\) \(13\) \(1\) \(560\) $\mathrm{SU}(2)[C_{3}]$
76.8.f.a 76.f 76.f $136$ $23.741$ None None \(-3\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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