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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2592.1.b.a 2592.b 8.d $1$ $1.294$ \(\Q\) \(\Q(\sqrt{-2}) \) None 72.1.p.a \(0\) \(0\) \(0\) \(0\) \(q-q^{11}+q^{17}+q^{19}+q^{25}+q^{41}+\cdots\)
2592.1.b.b 2592.b 8.d $1$ $1.294$ \(\Q\) \(\Q(\sqrt{-2}) \) None 72.1.p.a \(0\) \(0\) \(0\) \(0\) \(q+q^{11}-q^{17}+q^{19}+q^{25}-q^{41}+\cdots\)
2592.1.e.a 2592.e 3.b $4$ $1.294$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-1}) \) None 2592.1.e.a \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{2}q^{13}-\beta _{3}q^{17}+(-1+\cdots)q^{25}+\cdots\)
2592.1.g.a 2592.g 4.b $2$ $1.294$ \(\Q(\sqrt{-1}) \) None None 288.1.o.a \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-iq^{7}+iq^{11}+q^{13}-iq^{23}+\cdots\)
2592.1.g.b 2592.g 4.b $2$ $1.294$ \(\Q(\sqrt{-1}) \) None None 288.1.o.a \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-iq^{7}-iq^{11}+q^{13}+iq^{23}+\cdots\)
2592.1.n.a 2592.n 72.j $2$ $1.294$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None 216.1.h.a \(0\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+\zeta_{6}q^{29}+\cdots\)
2592.1.n.b 2592.n 72.j $2$ $1.294$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None 216.1.h.a \(0\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{11}-\zeta_{6}q^{29}+\cdots\)
2592.1.q.a 2592.q 9.d $4$ $1.294$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None 288.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{17}+(1-\beta _{2})q^{25}+\cdots\)
2592.1.q.b 2592.q 9.d $8$ $1.294$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None 2592.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{5}+(-\zeta_{24}^{6}-\zeta_{24}^{10}+\cdots)q^{13}+\cdots\)
2592.1.bd.a 2592.bd 216.r $6$ $1.294$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None 216.1.r.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{18}^{6}+\zeta_{18}^{8})q^{11}+(\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{17}+\cdots\)
2592.1.bz.a 2592.bz 648.af $18$ $1.294$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-2}) \) None 648.1.bf.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{26}q^{3}-\zeta_{54}^{25}q^{9}+(\zeta_{54}^{3}+\zeta_{54}^{13}+\cdots)q^{11}+\cdots\)
2592.2.a.a 2592.a 1.a $1$ $20.697$ \(\Q\) None None 288.2.i.a \(0\) \(0\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}+5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.b 2592.a 1.a $1$ $20.697$ \(\Q\) None None 288.2.i.a \(0\) \(0\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}-5q^{11}-2q^{13}+3q^{17}+\cdots\)
2592.2.a.c 2592.a 1.a $1$ $20.697$ \(\Q\) None None 2592.2.a.c \(0\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.d 2592.a 1.a $1$ $20.697$ \(\Q\) None None 2592.2.a.c \(0\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}+q^{13}-3q^{17}+\cdots\)
2592.2.a.e 2592.a 1.a $1$ $20.697$ \(\Q\) None None 2592.2.a.c \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.f 2592.a 1.a $1$ $20.697$ \(\Q\) None None 2592.2.a.c \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
2592.2.a.g 2592.a 1.a $1$ $20.697$ \(\Q\) None None 288.2.i.a \(0\) \(0\) \(4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{7}-5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.h 2592.a 1.a $1$ $20.697$ \(\Q\) None None 288.2.i.a \(0\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}+5q^{11}-2q^{13}-3q^{17}+\cdots\)
2592.2.a.i 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None 2592.2.a.i \(0\) \(0\) \(-4\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+(-2+\beta )q^{5}+(3-2\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
2592.2.a.j 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 288.2.i.c \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.k 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None 2592.2.a.k \(0\) \(0\) \(-2\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+(-1+\beta )q^{5}+(-3-\beta )q^{13}+(1-2\beta )q^{17}+\cdots\)
2592.2.a.l 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) None None 288.2.i.d \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-\beta q^{11}-3q^{13}+4q^{17}+\cdots\)
2592.2.a.m 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 2592.2.a.m \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-\beta q^{11}+3q^{13}-5q^{17}+\cdots\)
2592.2.a.n 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 288.2.i.c \(0\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-1+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.a.o 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 288.2.i.c \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
2592.2.a.p 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) None None 288.2.i.d \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}-3q^{13}-4q^{17}+\cdots\)
2592.2.a.q 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None 2592.2.a.k \(0\) \(0\) \(2\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{5}+(-3+\beta )q^{13}+(-1-2\beta )q^{17}+\cdots\)
2592.2.a.r 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 2592.2.a.m \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}+3q^{13}+5q^{17}+\cdots\)
2592.2.a.s 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{6}) \) None None 288.2.i.c \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1+2\beta )q^{13}+\cdots\)
2592.2.a.t 2592.a 1.a $2$ $20.697$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None 2592.2.a.i \(0\) \(0\) \(4\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+(2+\beta )q^{5}+(3+2\beta )q^{13}+(4+\beta )q^{17}+\cdots\)
2592.2.a.u 2592.a 1.a $4$ $20.697$ 4.4.13068.1 None None 288.2.i.f \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+\cdots\)
2592.2.a.v 2592.a 1.a $4$ $20.697$ \(\Q(\sqrt{3}, \sqrt{7})\) None None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{3})q^{11}+\cdots\)
2592.2.a.w 2592.a 1.a $4$ $20.697$ \(\Q(\sqrt{3}, \sqrt{7})\) None None 2592.2.a.v \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)
2592.2.a.x 2592.a 1.a $4$ $20.697$ 4.4.13068.1 None None 288.2.i.f \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
2592.2.c.a 2592.c 12.b $8$ $20.697$ \(\Q(\zeta_{24})\) None None 2592.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}-\zeta_{24}^{3})q^{5}-\zeta_{24}^{5}q^{7}+(-2\zeta_{24}^{6}+\cdots)q^{11}+\cdots\)
2592.2.c.b 2592.c 12.b $16$ $20.697$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 2592.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+\beta _{8}q^{7}+\beta _{11}q^{11}+(-1+\cdots)q^{13}+\cdots\)
2592.2.c.c 2592.c 12.b $24$ $20.697$ None None 288.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2592.2.d.a 2592.d 8.b $2$ $20.697$ \(\Q(\sqrt{-1}) \) None None 72.2.n.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{5}-4q^{7}-3iq^{11}+2iq^{13}+\cdots\)
2592.2.d.b 2592.d 8.b $2$ $20.697$ \(\Q(\sqrt{-1}) \) None None 72.2.n.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{5}-4q^{7}-3iq^{11}-2iq^{13}+\cdots\)
2592.2.d.c 2592.d 8.b $2$ $20.697$ \(\Q(\sqrt{-7}) \) None None 648.2.d.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}+2q^{7}+\beta q^{13}-7q^{17}-2\beta q^{19}+\cdots\)
2592.2.d.d 2592.d 8.b $2$ $20.697$ \(\Q(\sqrt{-7}) \) None None 648.2.d.b \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}+2q^{7}-\beta q^{13}+7q^{17}+2\beta q^{19}+\cdots\)
2592.2.d.e 2592.d 8.b $4$ $20.697$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 648.2.d.g \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.d.f 2592.d 8.b $4$ $20.697$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 648.2.d.g \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.d.g 2592.d 8.b $4$ $20.697$ \(\Q(\zeta_{12})\) None None 648.2.d.e \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-1+\zeta_{12}^{3})q^{7}+\cdots\)
2592.2.d.h 2592.d 8.b $4$ $20.697$ \(\Q(\zeta_{12})\) None None 648.2.d.e \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-1+\zeta_{12}^{3})q^{7}+\cdots\)
2592.2.d.i 2592.d 8.b $4$ $20.697$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None 648.2.d.f \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+4q^{7}+2\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
2592.2.d.j 2592.d 8.b $8$ $20.697$ 8.0.\(\cdots\).1 None None 72.2.n.b \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{6})q^{5}+(1-\beta _{5})q^{7}-\beta _{7}q^{11}+\cdots\)
2592.2.d.k 2592.d 8.b $8$ $20.697$ 8.0.\(\cdots\).1 None None 72.2.n.b \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{6})q^{5}+(1-\beta _{5})q^{7}-\beta _{7}q^{11}+\cdots\)
2592.2.f.a 2592.f 24.f $4$ $20.697$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None 72.2.l.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{11}+(-2\beta _{1}-\beta _{2})q^{17}+\cdots\)
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