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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
260.1.g.a 260.g 260.g $1$ $0.130$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots\)
260.1.g.b 260.g 260.g $1$ $0.130$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots\)
260.1.l.a 260.l 260.l $2$ $0.130$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{9}-iq^{10}+\cdots\)
260.1.s.a 260.s 260.s $2$ $0.130$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots\)
260.1.w.a 260.w 260.w $2$ $0.130$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots\)
260.1.w.b 260.w 260.w $2$ $0.130$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots\)
260.1.be.a 260.be 260.ae $4$ $0.130$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
260.1.bl.a 260.bl 260.al $4$ $0.130$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
260.2.a.a 260.a 1.a $1$ $2.076$ \(\Q\) None None \(0\) \(2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
260.2.a.b 260.a 1.a $3$ $2.076$ 3.3.564.1 None None \(0\) \(2\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
260.2.c.a 260.c 5.b $6$ $2.076$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
260.2.d.a 260.d 65.d $8$ $2.076$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
260.2.f.a 260.f 13.b $6$ $2.076$ 6.0.9144576.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
260.2.i.a 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.b 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.c 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.d 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
260.2.j.a 260.j 52.f $56$ $2.076$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
260.2.m.a 260.m 65.k $2$ $2.076$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(-1+2i)q^{5}-4iq^{7}+\cdots\)
260.2.m.b 260.m 65.k $4$ $2.076$ \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
260.2.m.c 260.m 65.k $8$ $2.076$ 8.0.\(\cdots\).2 None None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(\beta _{3}-\beta _{6})q^{5}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
260.2.o.a 260.o 20.e $72$ $2.076$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
260.2.p.a 260.p 260.p $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(2+i)q^{5}+\cdots\)
260.2.p.b 260.p 260.p $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots\)
260.2.p.c 260.p 260.p $8$ $2.076$ 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
260.2.p.d 260.p 260.p $64$ $2.076$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
260.2.r.a 260.r 65.f $2$ $2.076$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+(2-i)q^{5}+4q^{7}+\cdots\)
260.2.r.b 260.r 65.f $4$ $2.076$ \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{9}+\cdots\)
260.2.r.c 260.r 65.f $8$ $2.076$ 8.0.\(\cdots\).2 None None \(0\) \(2\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{7})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
260.2.u.a 260.u 260.u $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-2+i)q^{5}+\cdots\)
260.2.u.b 260.u 260.u $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(1-2i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
260.2.u.c 260.u 260.u $72$ $2.076$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
260.2.x.a 260.x 13.e $8$ $2.076$ 8.0.22581504.2 None None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{2}-\beta _{4}-2\beta _{6}-\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
260.2.z.a 260.z 65.l $16$ $2.076$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{3}+\beta _{14}q^{5}-\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
260.2.ba.a 260.ba 65.n $12$ $2.076$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{10})q^{3}+(-\beta _{7}-\beta _{11})q^{5}+\cdots\)
260.2.bc.a 260.bc 260.ac $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bc.b 260.bc 260.ac $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bc.c 260.bc 260.ac $144$ $2.076$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{12}]$
260.2.bf.a 260.bf 65.t $4$ $2.076$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(8\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(2+\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bf.b 260.bf 65.t $4$ $2.076$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12})q^{3}+(-1+2\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bf.c 260.bf 65.t $20$ $2.076$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
260.2.bg.a 260.bg 260.ag $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots\)
260.2.bg.b 260.bg 260.ag $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots\)
260.2.bg.c 260.bg 260.ag $144$ $2.076$ None None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
260.2.bj.a 260.bj 260.aj $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bj.b 260.bj 260.aj $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bj.c 260.bj 260.aj $144$ $2.076$ None None \(-6\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{12}]$
260.2.bk.a 260.bk 65.o $4$ $2.076$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-2+\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bk.b 260.bk 65.o $4$ $2.076$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12})q^{3}+(-1-2\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bk.c 260.bk 65.o $20$ $2.076$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-2\) \(12\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+2\beta _{7}+\cdots)q^{3}+\cdots\)
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