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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2268.1.h.a 2268.h 84.h $8$ $1.132$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)
2268.1.m.a 2268.m 63.n $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots\)
2268.1.m.b 2268.m 63.n $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots\)
2268.1.p.a 2268.p 63.k $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(1+\zeta_{6})q^{19}+q^{25}+(1+\zeta_{6}+\cdots)q^{31}+\cdots\)
2268.1.p.b 2268.p 63.k $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots\)
2268.1.s.a 2268.s 252.s $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.b 2268.s 252.s $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.c 2268.s 252.s $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.d 2268.s 252.s $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.e 2268.s 252.s $8$ $1.132$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.f 2268.s 252.s $8$ $1.132$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.g 2268.s 252.s $8$ $1.132$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.bc.a 2268.bc 63.l $2$ $1.132$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(-3\) \(1\) \(q+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
2268.1.bc.b 2268.bc 63.l $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(1-\zeta_{6}^{2})q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.c 2268.bc 63.l $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.d 2268.bc 63.l $2$ $1.132$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(3\) \(1\) \(q+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)
2268.1.bd.a 2268.bd 63.t $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+(-1+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bd.b 2268.bd 63.t $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{19}-\zeta_{6}q^{25}+\cdots\)
2268.1.bh.a 2268.bh 63.j $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
2268.1.bh.b 2268.bh 63.j $2$ $1.132$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
2268.2.a.a 2268.a 1.a $1$ $18.110$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-q^{11}+2q^{17}+2q^{19}+\cdots\)
2268.2.a.b 2268.a 1.a $1$ $18.110$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
2268.2.a.c 2268.a 1.a $1$ $18.110$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+3q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
2268.2.a.d 2268.a 1.a $1$ $18.110$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+q^{11}-2q^{17}+2q^{19}+\cdots\)
2268.2.a.e 2268.a 1.a $2$ $18.110$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}+q^{7}+\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots\)
2268.2.a.f 2268.a 1.a $2$ $18.110$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots\)
2268.2.a.g 2268.a 1.a $3$ $18.110$ 3.3.321.1 None None \(0\) \(0\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
2268.2.a.h 2268.a 1.a $3$ $18.110$ 3.3.321.1 None None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}-q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
2268.2.a.i 2268.a 1.a $3$ $18.110$ 3.3.321.1 None None \(0\) \(0\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2268.2.a.j 2268.a 1.a $3$ $18.110$ 3.3.321.1 None None \(0\) \(0\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
2268.2.a.k 2268.a 1.a $4$ $18.110$ \(\Q(\sqrt{3}, \sqrt{19})\) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
2268.2.f.a 2268.f 21.c $16$ $18.110$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+\beta _{10}q^{7}-\beta _{4}q^{11}+\beta _{13}q^{13}+\cdots\)
2268.2.f.b 2268.f 21.c $16$ $18.110$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{15}q^{5}+\beta _{9}q^{7}+\beta _{1}q^{11}+\beta _{7}q^{13}+\cdots\)
2268.2.i.a 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
2268.2.i.b 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
2268.2.i.c 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{3}]$ \(q+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.d 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+(-2+3\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.e 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+(1-3\zeta_{6})q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.f 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{3}]$ \(q+(3-\zeta_{6})q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.g 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
2268.2.i.h 2268.i 63.h $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
2268.2.i.i 2268.i 63.h $4$ $18.110$ \(\Q(\sqrt{-3}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
2268.2.i.j 2268.i 63.h $6$ $18.110$ 6.0.309123.1 None None \(0\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.k 2268.i 63.h $6$ $18.110$ 6.0.309123.1 None None \(0\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.l 2268.i 63.h $8$ $18.110$ 8.0.310217769.2 None None \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{5}q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2268.2.i.m 2268.i 63.h $8$ $18.110$ 8.0.310217769.2 None None \(0\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{5}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2268.2.i.n 2268.i 63.h $16$ $18.110$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{13}q^{5}+\beta _{3}q^{7}-\beta _{12}q^{11}+(2-2\beta _{4}+\cdots)q^{13}+\cdots\)
2268.2.j.a 2268.j 9.c $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2268.2.j.b 2268.j 9.c $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2268.2.j.c 2268.j 9.c $2$ $18.110$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
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