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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.1.o.a 336.o 84.h $1$ $0.168$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(-1\) \(0\) \(1\) \(q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots\)
336.1.o.b 336.o 84.h $1$ $0.168$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}-2q^{19}-q^{21}-q^{25}+\cdots\)
336.1.z.a 336.z 84.j $2$ $0.168$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots\)
336.1.z.b 336.z 84.j $2$ $0.168$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots\)
336.1.bn.a 336.bn 21.h $2$ $0.168$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
336.2.a.a 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
336.2.a.b 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
336.2.a.c 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(-1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
336.2.a.d 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
336.2.a.e 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots\)
336.2.a.f 336.a 1.a $1$ $2.683$ \(\Q\) None None \(0\) \(1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
336.2.b.a 336.b 28.d $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-2-\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
336.2.b.b 336.b 28.d $2$ $2.683$ \(\Q(\sqrt{-6}) \) None None \(0\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
336.2.b.c 336.b 28.d $2$ $2.683$ \(\Q(\sqrt{-6}) \) None None \(0\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
336.2.b.d 336.b 28.d $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(2+\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
336.2.h.a 336.h 12.b $4$ $2.683$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
336.2.h.b 336.h 12.b $8$ $2.683$ 8.0.56070144.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\)
336.2.k.a 336.k 21.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
336.2.k.b 336.k 21.c $4$ $2.683$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
336.2.k.c 336.k 21.c $8$ $2.683$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
336.2.q.a 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
336.2.q.b 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.q.c 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
336.2.q.d 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
336.2.q.e 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.q.f 336.q 7.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
336.2.q.g 336.q 7.c $4$ $2.683$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(-2\) \(1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
336.2.s.a 336.s 48.k $4$ $2.683$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
336.2.s.b 336.s 48.k $4$ $2.683$ \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8})q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{4}+\cdots\)
336.2.s.c 336.s 48.k $40$ $2.683$ None None \(0\) \(4\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{4}]$
336.2.s.d 336.s 48.k $48$ $2.683$ None None \(0\) \(0\) \(0\) \(48\) $\mathrm{SU}(2)[C_{4}]$
336.2.u.a 336.u 112.j $64$ $2.683$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
336.2.w.a 336.w 16.e $20$ $2.683$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}-\beta _{7}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6}-\beta _{16}+\cdots)q^{4}+\cdots\)
336.2.w.b 336.w 16.e $28$ $2.683$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
336.2.y.a 336.y 336.y $120$ $2.683$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
336.2.bc.a 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(5\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.b 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.c 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.d 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.e 336.bc 21.g $4$ $2.683$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
336.2.bc.f 336.bc 21.g $16$ $2.683$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots\)
336.2.bj.a 336.bj 84.n $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-5\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
336.2.bj.b 336.bj 84.n $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.c 336.bj 84.n $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.d 336.bj 84.n $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(5\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.e 336.bj 84.n $8$ $2.683$ 8.0.8275904784.2 None None \(0\) \(-3\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
336.2.bj.f 336.bj 84.n $8$ $2.683$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+(1-2\beta _{2}+\beta _{4}+2\beta _{6})q^{5}+\cdots\)
336.2.bj.g 336.bj 84.n $8$ $2.683$ 8.0.8275904784.2 None None \(0\) \(3\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots\)
336.2.bl.a 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
336.2.bl.b 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
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