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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.2.a.a 289.a 1.a $1$ $2.308$ \(\Q\) None \(-1\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
289.2.a.b 289.a 1.a $2$ $2.308$ \(\Q(\sqrt{13}) \) None \(-1\) \(-1\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
289.2.a.c 289.a 1.a $2$ $2.308$ \(\Q(\sqrt{13}) \) None \(-1\) \(1\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
289.2.a.d 289.a 1.a $3$ $2.308$ \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
289.2.a.e 289.a 1.a $3$ $2.308$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.a.f 289.a 1.a $4$ $2.308$ \(\Q(\zeta_{16})^+\) None \(4\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.a 289.b 17.b $2$ $2.308$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
289.2.b.b 289.b 17.b $4$ $2.308$ 4.0.2048.2 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.c 289.b 17.b $4$ $2.308$ \(\Q(i, \sqrt{13})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.b.d 289.b 17.b $6$ $2.308$ 6.0.419904.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)
289.2.c.a 289.c 17.c $4$ $2.308$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
289.2.c.b 289.c 17.c $8$ $2.308$ 8.0.1871773696.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.c.c 289.c 17.c $8$ $2.308$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\)
289.2.c.d 289.c 17.c $12$ $2.308$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
289.2.d.a 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(-4\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c 289.d 17.d $4$ $2.308$ \(\Q(\zeta_{8})\) None \(4\) \(4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d 289.d 17.d $8$ $2.308$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
289.2.d.e 289.d 17.d $16$ $2.308$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f 289.d 17.d $24$ $2.308$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
289.2.f.a 289.f 289.f $384$ $2.308$ None \(-13\) \(-13\) \(-43\) \(-13\) $\mathrm{SU}(2)[C_{17}]$
289.2.g.a 289.g 289.g $384$ $2.308$ None \(-17\) \(-17\) \(17\) \(-17\) $\mathrm{SU}(2)[C_{34}]$
289.2.h.a 289.h 289.h $768$ $2.308$ None \(-34\) \(-34\) \(-34\) \(-34\) $\mathrm{SU}(2)[C_{68}]$
289.2.i.a 289.i 289.i $1600$ $2.308$ None \(-64\) \(-64\) \(-68\) \(-64\) $\mathrm{SU}(2)[C_{136}]$
289.3.e.a 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(-8\) \(-16\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.b 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.c 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(-8\) \(8\) \(-16\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.d 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(-8\) \(8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.e 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(-8\) \(16\) \(8\) \(16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.f 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(0\) \(-8\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
289.3.e.g 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(24\) \(16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
289.3.e.h 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(0\) \(8\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.i 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(-8\) \(-16\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.j 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(-8\) \(16\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.k 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(0\) \(-16\) \(40\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.l 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(0\) \(16\) \(-40\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.m 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(8\) \(16\) \(-8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.n 289.e 17.e $8$ $7.875$ \(\Q(\zeta_{16})\) None \(8\) \(8\) \(-16\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.o 289.e 17.e $16$ $7.875$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$ \(q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
289.3.e.p 289.e 17.e $32$ $7.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
289.3.e.q 289.e 17.e $48$ $7.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
289.3.e.r 289.e 17.e $96$ $7.875$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
289.3.j.a 289.j 289.j $6400$ $7.875$ None \(-128\) \(-128\) \(-128\) \(-128\) $\mathrm{SU}(2)[C_{272}]$
289.4.a.a 289.a 1.a $1$ $17.052$ \(\Q\) None \(-3\) \(8\) \(-6\) \(28\) $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
289.4.a.b 289.a 1.a $3$ $17.052$ 3.3.2636.1 None \(1\) \(-4\) \(8\) \(-22\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
289.4.a.c 289.a 1.a $4$ $17.052$ 4.4.2555057.1 None \(1\) \(-2\) \(14\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.d 289.a 1.a $4$ $17.052$ 4.4.2555057.1 None \(1\) \(2\) \(-14\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.e 289.a 1.a $4$ $17.052$ 4.4.4669632.2 None \(2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots\)
289.4.a.f 289.a 1.a $8$ $17.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
289.4.a.g 289.a 1.a $12$ $17.052$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots\)
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