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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
833.1.h.a 833.h 119.h $4$ $0.416$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-119}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\cdots\)
833.1.h.b 833.h 119.h $4$ $0.416$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-119}) \) None \(1\) \(1\) \(1\) \(0\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
833.2.a.a 833.a 1.a $1$ $6.652$ \(\Q\) None None \(-1\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
833.2.a.b 833.a 1.a $3$ $6.652$ \(\Q(\zeta_{14})^+\) None None \(-1\) \(-1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.a.c 833.a 1.a $3$ $6.652$ \(\Q(\zeta_{14})^+\) None None \(-1\) \(1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.a.d 833.a 1.a $4$ $6.652$ 4.4.1957.1 None None \(-1\) \(-4\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.a.e 833.a 1.a $4$ $6.652$ 4.4.9301.1 None None \(-1\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.a.f 833.a 1.a $4$ $6.652$ 4.4.1957.1 None None \(-1\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.a.g 833.a 1.a $5$ $6.652$ 5.5.453749.1 None None \(2\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots\)
833.2.a.h 833.a 1.a $7$ $6.652$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(3\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.i 833.a 1.a $7$ $6.652$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(3\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.j 833.a 1.a $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(-8\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.k 833.a 1.a $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(8\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.b.a 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{1}-\beta _{2})q^{4}+\cdots\)
833.2.b.b 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) \(\Q(\sqrt{-119}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{8})q^{4}-\beta _{5}q^{5}+\cdots\)
833.2.b.c 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots\)
833.2.b.d 833.b 17.b $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots\)
833.2.b.e 833.b 17.b $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-\beta _{1}q^{3}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+\cdots\)
833.2.e.a 833.e 7.c $2$ $6.652$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.b 833.e 7.c $2$ $6.652$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.c 833.e 7.c $6$ $6.652$ 6.0.64827.1 None None \(1\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.d 833.e 7.c $8$ $6.652$ 8.0.310217769.2 None None \(1\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
833.2.e.e 833.e 7.c $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{3}+\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.f 833.e 7.c $8$ $6.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{7})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.g 833.e 7.c $8$ $6.652$ 8.0.310217769.2 None None \(1\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
833.2.e.h 833.e 7.c $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{3}-\beta _{7}-\beta _{8})q^{3}+(\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
833.2.e.i 833.e 7.c $10$ $6.652$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{7}+\beta _{8})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
833.2.e.j 833.e 7.c $14$ $6.652$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-3\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{13}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.k 833.e 7.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(2\) \(-8\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{6}+\beta _{10}+\beta _{14}+\cdots)q^{3}+\cdots\)
833.2.e.l 833.e 7.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(2\) \(8\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{6}-\beta _{10}-\beta _{14})q^{3}+\cdots\)
833.2.g.a 833.g 17.c $2$ $6.652$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(-2-2i)q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
833.2.g.b 833.g 17.c $2$ $6.652$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(2+2i)q^{3}+q^{4}+(1+i)q^{5}+\cdots\)
833.2.g.c 833.g 17.c $4$ $6.652$ \(\Q(i, \sqrt{11})\) None None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.g.d 833.g 17.c $4$ $6.652$ \(\Q(i, \sqrt{11})\) None None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
833.2.g.e 833.g 17.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{8}-\beta _{13})q^{2}+\beta _{9}q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
833.2.g.f 833.g 17.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
833.2.g.g 833.g 17.c $16$ $6.652$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
833.2.g.h 833.g 17.c $20$ $6.652$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{14}q^{3}+(-2+\beta _{17}+\beta _{18}+\cdots)q^{4}+\cdots\)
833.2.g.i 833.g 17.c $32$ $6.652$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
833.2.j.a 833.j 119.j $20$ $6.652$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{15}q^{2}-\beta _{1}q^{3}+(-1+\beta _{11}+\beta _{14}+\cdots)q^{4}+\cdots\)
833.2.j.b 833.j 119.j $20$ $6.652$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-119}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{12}q^{2}+\beta _{1}q^{3}+(\beta _{3}+\beta _{6}+2\beta _{8}+\cdots)q^{4}+\cdots\)
833.2.j.c 833.j 119.j $20$ $6.652$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{13}q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.j.d 833.j 119.j $20$ $6.652$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{3})q^{2}-\beta _{13}q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.j.e 833.j 119.j $32$ $6.652$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
833.2.k.a 833.k 49.e $6$ $6.652$ \(\Q(\zeta_{14})\) None None \(-3\) \(5\) \(-4\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
833.2.k.b 833.k 49.e $216$ $6.652$ None None \(2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{7}]$
833.2.k.c 833.k 49.e $234$ $6.652$ None None \(1\) \(-7\) \(2\) \(-13\) $\mathrm{SU}(2)[C_{7}]$
833.2.l.a 833.l 17.d $4$ $6.652$ \(\Q(\zeta_{8})\) None None \(-4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
833.2.l.b 833.l 17.d $32$ $6.652$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
833.2.l.c 833.l 17.d $32$ $6.652$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
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