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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1617.1.h.a 1617.h 231.h $8$ $0.807$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}-q^{4}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
1617.1.k.a 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-231}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{6}-q^{8}+\cdots\)
1617.1.k.b 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-231}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}-q^{8}+\cdots\)
1617.1.k.c 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-231}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots\)
1617.1.k.d 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-231}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+q^{6}+q^{8}+\cdots\)
1617.1.k.e 1617.k 231.k $16$ $0.807$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+(\zeta_{48}-\zeta_{48}^{7}+\cdots)q^{5}+\cdots\)
1617.2.a.a 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(-2\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-q^{11}+\cdots\)
1617.2.a.b 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(-2\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-q^{11}+\cdots\)
1617.2.a.c 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(-1\) \(-1\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}+3q^{8}+\cdots\)
1617.2.a.d 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(-1\) \(1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}+3q^{8}+\cdots\)
1617.2.a.e 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(-1\) \(1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots\)
1617.2.a.f 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(1\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
1617.2.a.g 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
1617.2.a.h 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
1617.2.a.i 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
1617.2.a.j 1617.a 1.a $1$ $12.912$ \(\Q\) None None \(1\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots\)
1617.2.a.k 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{5}) \) None None \(-3\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1-2\beta )q^{5}+\cdots\)
1617.2.a.l 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{5}) \) None None \(-3\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
1617.2.a.m 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2q^{5}+\cdots\)
1617.2.a.n 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{2}) \) None None \(-2\) \(2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2q^{5}+\cdots\)
1617.2.a.o 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{21}) \) None None \(-1\) \(2\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(3+\beta )q^{4}-3q^{5}-\beta q^{6}+\cdots\)
1617.2.a.p 1617.a 1.a $2$ $12.912$ \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
1617.2.a.q 1617.a 1.a $3$ $12.912$ 3.3.229.1 None None \(0\) \(-3\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.r 1617.a 1.a $3$ $12.912$ 3.3.229.1 None None \(0\) \(3\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.s 1617.a 1.a $3$ $12.912$ 3.3.837.1 None None \(0\) \(3\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.t 1617.a 1.a $3$ $12.912$ 3.3.229.1 None None \(2\) \(-3\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1617.2.a.u 1617.a 1.a $4$ $12.912$ 4.4.2624.1 None None \(-2\) \(-4\) \(8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.v 1617.a 1.a $4$ $12.912$ 4.4.2624.1 None None \(-2\) \(4\) \(-8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1617.2.a.w 1617.a 1.a $4$ $12.912$ 4.4.2624.1 None None \(2\) \(-4\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.x 1617.a 1.a $4$ $12.912$ 4.4.11344.1 None None \(2\) \(-4\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.y 1617.a 1.a $4$ $12.912$ 4.4.2624.1 None None \(2\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.z 1617.a 1.a $4$ $12.912$ 4.4.11344.1 None None \(2\) \(4\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1617.2.a.ba 1617.a 1.a $5$ $12.912$ 5.5.3676752.1 None None \(2\) \(-5\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1617.2.a.bb 1617.a 1.a $5$ $12.912$ 5.5.3676752.1 None None \(2\) \(5\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
1617.2.c.a 1617.c 77.b $32$ $12.912$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1617.2.c.b 1617.c 77.b $48$ $12.912$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1617.4.a.a 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(-5\) \(-3\) \(14\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}-3q^{3}+17q^{4}+14q^{5}+15q^{6}+\cdots\)
1617.4.a.b 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(-3\) \(3\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+3q^{3}+q^{4}+4q^{5}-9q^{6}+\cdots\)
1617.4.a.c 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(-2\) \(-3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}-4q^{4}-q^{5}+6q^{6}+\cdots\)
1617.4.a.d 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(-1\) \(3\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}+4q^{5}-3q^{6}+\cdots\)
1617.4.a.e 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(2\) \(3\) \(-11\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}-4q^{4}-11q^{5}+6q^{6}+\cdots\)
1617.4.a.f 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(3\) \(-3\) \(14\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{2}-3q^{3}+q^{4}+14q^{5}-9q^{6}+\cdots\)
1617.4.a.g 1617.a 1.a $1$ $95.406$ \(\Q\) None None \(5\) \(-3\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+5q^{2}-3q^{3}+17q^{4}+6q^{5}-15q^{6}+\cdots\)
1617.4.a.h 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{17}) \) None None \(-3\) \(-6\) \(-25\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-3q^{3}+(-3+3\beta )q^{4}+\cdots\)
1617.4.a.i 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{17}) \) None None \(-3\) \(-6\) \(19\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-3q^{3}+(-3+3\beta )q^{4}+\cdots\)
1617.4.a.j 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{33}) \) None None \(1\) \(-6\) \(-16\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3q^{3}+\beta q^{4}+(-10+4\beta )q^{5}+\cdots\)
1617.4.a.k 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{97}) \) None None \(1\) \(6\) \(14\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(2^{4}+\beta )q^{4}+(6+2\beta )q^{5}+\cdots\)
1617.4.a.l 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{37}) \) None None \(3\) \(-6\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-3q^{3}+(2+3\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
1617.4.a.m 1617.a 1.a $2$ $95.406$ \(\Q(\sqrt{17}) \) None None \(3\) \(6\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots\)
1617.4.a.n 1617.a 1.a $5$ $95.406$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-1\) \(15\) \(-21\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
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