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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
532.1.n.a 532.n 532.n $4$ $0.266$ \(\Q(\zeta_{12})\) None None 532.1.n.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
532.1.bc.a 532.bc 133.r $2$ $0.266$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 532.1.bc.a \(0\) \(0\) \(-2\) \(-1\) \(q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots\)
532.1.bc.b 532.bc 133.r $2$ $0.266$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None 532.1.bc.b \(0\) \(0\) \(1\) \(2\) \(q-\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots\)
532.1.bk.a 532.bk 532.ak $4$ $0.266$ \(\Q(\zeta_{12})\) None None 532.1.n.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
532.2.a.a 532.a 1.a $1$ $4.248$ \(\Q\) None None 532.2.a.a \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
532.2.a.b 532.a 1.a $2$ $4.248$ \(\Q(\sqrt{5}) \) None None 532.2.a.b \(0\) \(-3\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots\)
532.2.a.c 532.a 1.a $2$ $4.248$ \(\Q(\sqrt{21}) \) None None 532.2.a.c \(0\) \(-1\) \(6\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+3q^{5}+q^{7}+(2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
532.2.a.d 532.a 1.a $2$ $4.248$ \(\Q(\sqrt{5}) \) None None 532.2.a.d \(0\) \(1\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-2\beta )q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
532.2.a.e 532.a 1.a $3$ $4.248$ 3.3.733.1 None None 532.2.a.e \(0\) \(-1\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)
532.2.f.a 532.f 28.d $4$ $4.248$ \(\Q(i, \sqrt{5})\) None None 532.2.f.a \(-4\) \(-6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{2}+(-1+\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots\)
532.2.f.b 532.f 28.d $4$ $4.248$ \(\Q(i, \sqrt{5})\) None None 532.2.f.a \(-4\) \(6\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+2\beta _{3}q^{4}+\cdots\)
532.2.f.c 532.f 28.d $32$ $4.248$ None None 532.2.f.c \(3\) \(-6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$
532.2.f.d 532.f 28.d $32$ $4.248$ None None 532.2.f.c \(3\) \(6\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$
532.2.g.a 532.g 133.c $4$ $4.248$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None 532.2.g.a \(0\) \(0\) \(0\) \(3\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots\)
532.2.g.b 532.g 133.c $8$ $4.248$ 8.0.\(\cdots\).5 None None 532.2.g.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
532.2.h.a 532.h 76.d $4$ $4.248$ \(\Q(i, \sqrt{29})\) None None 532.2.h.a \(-4\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+2\beta _{2}q^{4}+\cdots\)
532.2.h.b 532.h 76.d $4$ $4.248$ \(\Q(i, \sqrt{29})\) None None 532.2.h.a \(4\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots\)
532.2.h.c 532.h 76.d $52$ $4.248$ None None 532.2.h.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$
532.2.i.a 532.i 7.c $4$ $4.248$ \(\Q(\zeta_{12})\) None None 532.2.i.a \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-2+3\zeta_{12}+\cdots)q^{7}+\cdots\)
532.2.i.b 532.i 7.c $6$ $4.248$ 6.0.4406832.1 None None 532.2.i.b \(0\) \(2\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
532.2.i.c 532.i 7.c $14$ $4.248$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None 532.2.i.c \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+\beta _{13}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
532.2.j.a 532.j 19.c $2$ $4.248$ \(\Q(\sqrt{-3}) \) None None 532.2.j.a \(0\) \(-1\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+q^{7}+\cdots\)
532.2.j.b 532.j 19.c $8$ $4.248$ 8.0.\(\cdots\).2 None None 532.2.j.b \(0\) \(2\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{6})q^{5}+\cdots\)
532.2.j.c 532.j 19.c $10$ $4.248$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 532.2.j.c \(0\) \(-3\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{4}-\beta _{9})q^{5}-q^{7}+\cdots\)
532.2.k.a 532.k 133.h $4$ $4.248$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None 532.2.k.a \(0\) \(-1\) \(-10\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-3+\beta _{3})q^{5}+(3+\beta _{2})q^{7}+\cdots\)
532.2.k.b 532.k 133.h $24$ $4.248$ None None 532.2.k.b \(0\) \(-1\) \(12\) \(-6\) $\mathrm{SU}(2)[C_{3}]$
532.2.l.a 532.l 133.g $4$ $4.248$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None 532.2.k.a \(0\) \(2\) \(5\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{3}+(1-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
532.2.l.b 532.l 133.g $24$ $4.248$ None None 532.2.k.b \(0\) \(2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{3}]$
532.2.q.a 532.q 133.i $28$ $4.248$ None None 532.2.q.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$
532.2.r.a 532.r 532.r $4$ $4.248$ \(\Q(\zeta_{12})\) None None 532.2.r.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
532.2.r.b 532.r 532.r $148$ $4.248$ None None 532.2.r.b \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.s.a 532.s 76.f $120$ $4.248$ None None 532.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.t.a 532.t 532.t $152$ $4.248$ None None 532.2.t.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.u.a 532.u 532.u $16$ $4.248$ 16.0.\(\cdots\).16 None None 532.2.u.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{5}+\beta _{7})q^{2}+(\beta _{1}-\beta _{13})q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
532.2.u.b 532.u 532.u $136$ $4.248$ None None 532.2.u.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.v.a 532.v 133.o $2$ $4.248$ \(\Q(\sqrt{-3}) \) None None 532.2.v.a \(0\) \(-2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
532.2.v.b 532.v 133.o $2$ $4.248$ \(\Q(\sqrt{-3}) \) None None 532.2.v.a \(0\) \(2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
532.2.v.c 532.v 133.o $4$ $4.248$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None 532.2.v.c \(0\) \(0\) \(0\) \(3\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1+2\beta _{1}+\beta _{2})q^{5}+(2\beta _{2}+\beta _{3})q^{7}+\cdots\)
532.2.v.d 532.v 133.o $4$ $4.248$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None 532.2.v.d \(0\) \(0\) \(3\) \(-6\) $\mathrm{U}(1)[D_{6}]$ \(q+(1-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
532.2.v.e 532.v 133.o $16$ $4.248$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 532.2.v.e \(0\) \(0\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{3}+(-\beta _{3}+\beta _{4}-\beta _{8}-\beta _{9})q^{5}+\cdots\)
532.2.w.a 532.w 28.f $72$ $4.248$ None None 532.2.w.a \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.w.b 532.w 28.f $72$ $4.248$ None None 532.2.w.a \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.x.a 532.x 133.p $24$ $4.248$ None None 532.2.x.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$
532.2.y.a 532.y 532.y $152$ $4.248$ None None 532.2.y.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.bl.a 532.bl 532.al $152$ $4.248$ None None 532.2.y.a \(-3\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.bm.a 532.bm 133.s $28$ $4.248$ None None 532.2.q.a \(0\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{6}]$
532.2.bn.a 532.bn 532.an $4$ $4.248$ \(\Q(\zeta_{12})\) None None 532.2.r.a \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
532.2.bn.b 532.bn 532.an $148$ $4.248$ None None 532.2.r.b \(3\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
532.2.bo.a 532.bo 19.e $30$ $4.248$ None None 532.2.bo.a \(0\) \(3\) \(-3\) \(-15\) $\mathrm{SU}(2)[C_{9}]$
532.2.bo.b 532.bo 19.e $30$ $4.248$ None None 532.2.bo.b \(0\) \(3\) \(3\) \(15\) $\mathrm{SU}(2)[C_{9}]$
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