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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3969.1.b.a 3969.b 3.b $4$ $1.981$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(2\beta _{1}-\beta _{3})q^{8}+\cdots\)
3969.1.j.a 3969.j 63.j $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\zeta_{6}q^{13}+q^{16}+\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots\)
3969.1.j.b 3969.j 63.j $4$ $1.981$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}+(-\beta _{1}+\beta _{3})q^{11}-q^{16}+\cdots\)
3969.1.j.c 3969.j 63.j $8$ $1.981$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{11})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
3969.1.k.a 3969.k 63.k $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}+q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.b 3969.k 63.k $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{16}+q^{25}+\zeta_{6}q^{37}+\cdots\)
3969.1.k.c 3969.k 63.k $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(1+\zeta_{6})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.d 3969.k 63.k $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}-q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.e 3969.k 63.k $4$ $1.981$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.l.a 3969.l 63.l $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.l.b 3969.l 63.l $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.a 3969.m 7.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.b 3969.m 7.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.c 3969.m 7.d $4$ $1.981$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.n.a 3969.n 63.n $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{13}-\zeta_{6}q^{16}-\zeta_{6}^{2}q^{19}+\cdots\)
3969.1.n.b 3969.n 63.n $4$ $1.981$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{11}+\cdots\)
3969.1.n.c 3969.n 63.n $8$ $1.981$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.q.a 3969.q 21.h $8$ $1.981$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.r.a 3969.r 9.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}-q^{19}+\cdots\)
3969.1.r.b 3969.r 9.d $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+q^{19}+\cdots\)
3969.1.r.c 3969.r 9.d $4$ $1.981$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
3969.1.r.d 3969.r 9.d $8$ $1.981$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.t.a 3969.t 63.t $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}-\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.b 3969.t 63.t $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+(-1-\zeta_{6})q^{13}+q^{16}+\zeta_{6}^{2}q^{25}+\cdots\)
3969.1.t.c 3969.t 63.t $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{16}+\zeta_{6}^{2}q^{25}-\zeta_{6}^{2}q^{37}+\cdots\)
3969.1.t.d 3969.t 63.t $2$ $1.981$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{8}+\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.e 3969.t 63.t $4$ $1.981$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{5})q^{2}+(1+\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.br.a 3969.br 441.ac $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{18}q^{4}-\zeta_{42}^{2}q^{7}+(-\zeta_{42}^{3}+\cdots)q^{13}+\cdots\)
3969.1.bt.a 3969.bt 441.ae $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+(\zeta_{42}^{8}-\zeta_{42}^{17}+\cdots)q^{13}+\cdots\)
3969.1.bx.a 3969.bx 441.ai $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{42}q^{4}+\zeta_{42}^{4}q^{7}+(-\zeta_{42}^{9}-\zeta_{42}^{13}+\cdots)q^{13}+\cdots\)
3969.1.bz.a 3969.bz 441.ak $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{16}q^{4}-\zeta_{42}^{8}q^{7}+(-\zeta_{42}^{4}+\cdots)q^{13}+\cdots\)
3969.1.ca.a 3969.ca 441.al $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{10}q^{4}+\zeta_{42}^{19}q^{7}+(\zeta_{42}^{4}-\zeta_{42}^{6}+\cdots)q^{13}+\cdots\)
3969.1.cb.a 3969.cb 441.am $12$ $1.981$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{42}^{18}q^{4}+\zeta_{42}^{16}q^{7}+(-\zeta_{42}+\cdots)q^{13}+\cdots\)
3969.2.a.a 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-5q^{11}+\cdots\)
3969.2.a.b 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-2q^{11}+\cdots\)
3969.2.a.c 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(-1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-5q^{11}+\cdots\)
3969.2.a.d 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+5q^{11}+\cdots\)
3969.2.a.e 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots\)
3969.2.a.f 3969.a 1.a $1$ $31.693$ \(\Q\) None None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+5q^{11}+\cdots\)
3969.2.a.g 3969.a 1.a $2$ $31.693$ \(\Q(\sqrt{15}) \) None None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots\)
3969.2.a.h 3969.a 1.a $2$ $31.693$ \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots\)
3969.2.a.i 3969.a 1.a $2$ $31.693$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots\)
3969.2.a.j 3969.a 1.a $2$ $31.693$ \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}+(1+\cdots)q^{11}+\cdots\)
3969.2.a.k 3969.a 1.a $2$ $31.693$ \(\Q(\sqrt{15}) \) None None \(2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+\beta q^{10}+\cdots\)
3969.2.a.l 3969.a 1.a $3$ $31.693$ \(\Q(\zeta_{18})^+\) None None \(-3\) \(0\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
3969.2.a.m 3969.a 1.a $3$ $31.693$ 3.3.321.1 None None \(-1\) \(0\) \(5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots\)
3969.2.a.n 3969.a 1.a $3$ $31.693$ 3.3.621.1 None None \(0\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3969.2.a.o 3969.a 1.a $3$ $31.693$ 3.3.621.1 None None \(0\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3969.2.a.p 3969.a 1.a $3$ $31.693$ 3.3.321.1 None None \(1\) \(0\) \(-5\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
3969.2.a.q 3969.a 1.a $3$ $31.693$ \(\Q(\zeta_{18})^+\) None None \(3\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
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