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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.1.b.a 592.b 148.b $1$ $0.295$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-37}) \) \(\Q(\sqrt{37}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+q^{25}-q^{37}-2q^{41}+q^{49}+\cdots\)
592.1.b.b 592.b 148.b $2$ $0.295$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{37}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
592.1.k.a 592.k 37.d $2$ $0.295$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(2\) \(q+iq^{3}+(-1-i)q^{5}+q^{7}+iq^{11}+\cdots\)
592.1.k.b 592.k 37.d $2$ $0.295$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+q^{7}+iq^{11}+(-1-i)q^{17}+\cdots\)
592.1.z.a 592.z 148.i $4$ $0.295$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{5}+(1-\beta _{2})q^{9}+\cdots\)
592.1.bb.a 592.bb 148.j $2$ $0.295$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+(-1+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)
592.1.bt.a 592.bt 148.o $6$ $0.295$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+(-\zeta_{18}^{2}-\zeta_{18}^{3})q^{5}+\zeta_{18}^{8}q^{9}+\cdots\)
592.2.a.a 592.a 1.a $1$ $4.727$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots\)
592.2.a.b 592.a 1.a $1$ $4.727$ \(\Q\) None None \(0\) \(1\) \(-4\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
592.2.a.c 592.a 1.a $1$ $4.727$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
592.2.a.d 592.a 1.a $1$ $4.727$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots\)
592.2.a.e 592.a 1.a $1$ $4.727$ \(\Q\) None None \(0\) \(3\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
592.2.a.f 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{13}) \) None None \(0\) \(-3\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots\)
592.2.a.g 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
592.2.a.h 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}-\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
592.2.a.i 592.a 1.a $3$ $4.727$ 3.3.229.1 None None \(0\) \(-2\) \(-1\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
592.2.a.j 592.a 1.a $4$ $4.727$ 4.4.48389.1 None None \(0\) \(-2\) \(5\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
592.2.g.a 592.g 37.b $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots\)
592.2.g.b 592.g 37.b $2$ $4.727$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}-3q^{7}-2q^{9}+3q^{11}+\cdots\)
592.2.g.c 592.g 37.b $4$ $4.727$ \(\Q(i, \sqrt{21})\) None None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3-\beta _{3})q^{9}+\cdots\)
592.2.g.d 592.g 37.b $10$ $4.727$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
592.2.i.a 592.i 37.c $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{3}-3\zeta_{6}q^{5}-4\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots\)
592.2.i.b 592.i 37.c $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
592.2.i.c 592.i 37.c $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+2q^{11}+\cdots\)
592.2.i.d 592.i 37.c $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{9}+\cdots\)
592.2.i.e 592.i 37.c $6$ $4.727$ 6.0.4406832.1 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots\)
592.2.i.f 592.i 37.c $6$ $4.727$ 6.0.27870912.1 None None \(0\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
592.2.i.g 592.i 37.c $6$ $4.727$ 6.0.591408.1 None None \(0\) \(2\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
592.2.i.h 592.i 37.c $10$ $4.727$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(1\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)
592.2.m.a 592.m 592.m $148$ $4.727$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
592.2.n.a 592.n 592.n $148$ $4.727$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
592.2.o.a 592.o 16.e $144$ $4.727$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
592.2.s.a 592.s 592.s $148$ $4.727$ None None \(-4\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
592.2.t.a 592.t 148.g $2$ $4.727$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{5}-3q^{9}+(-1+i)q^{13}+\cdots\)
592.2.t.b 592.t 148.g $4$ $4.727$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+4q^{9}+\cdots\)
592.2.t.c 592.t 148.g $4$ $4.727$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{12}^{3}q^{3}+(2-2\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
592.2.t.d 592.t 148.g $28$ $4.727$ None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
592.2.w.a 592.w 37.e $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}-2\zeta_{6}q^{7}+\cdots\)
592.2.w.b 592.w 37.e $2$ $4.727$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{5}+\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
592.2.w.c 592.w 37.e $4$ $4.727$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{5}+\cdots\)
592.2.w.d 592.w 37.e $4$ $4.727$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(-6\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-2+\zeta_{12})q^{5}+\cdots\)
592.2.w.e 592.w 37.e $4$ $4.727$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(2-\zeta_{12})q^{5}-2\zeta_{12}q^{7}+\cdots\)
592.2.w.f 592.w 37.e $20$ $4.727$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(2\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{5}+\beta _{14})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{10}+\cdots)q^{7}+\cdots\)
592.2.bc.a 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None None \(0\) \(-3\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-2\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
592.2.bc.b 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{3})q^{3}+(1+\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
592.2.bc.c 592.bc 37.f $6$ $4.727$ \(\Q(\zeta_{18})\) None None \(0\) \(6\) \(6\) \(12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}^{4})q^{3}+(1+\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
592.2.bc.d 592.bc 37.f $12$ $4.727$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{1}+\beta _{5})q^{5}+\cdots\)
592.2.bc.e 592.bc 37.f $24$ $4.727$ None None \(0\) \(-3\) \(-3\) \(9\) $\mathrm{SU}(2)[C_{9}]$
592.2.bc.f 592.bc 37.f $24$ $4.727$ None None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{9}]$
592.2.bc.g 592.bc 37.f $30$ $4.727$ None None \(0\) \(0\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$
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