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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1224.1.m.a 1224.m 51.c $2$ $0.611$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-\beta q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
1224.1.m.b 1224.m 51.c $2$ $0.611$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-\beta q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)
1224.1.n.a 1224.n 136.e $1$ $0.611$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}+q^{17}-2q^{19}+\cdots\)
1224.1.n.b 1224.n 136.e $2$ $0.611$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots\)
1224.1.n.c 1224.n 136.e $2$ $0.611$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots\)
1224.1.s.a 1224.s 136.j $2$ $0.611$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+(-1-i)q^{11}+\cdots\)
1224.1.bb.a 1224.bb 1224.ab $2$ $0.611$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
1224.1.bb.b 1224.bb 1224.ab $2$ $0.611$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
1224.1.bu.a 1224.bu 408.ae $4$ $0.611$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
1224.1.bu.b 1224.bu 408.ae $4$ $0.611$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{3})q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
1224.1.bv.a 1224.bv 136.p $4$ $0.611$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(1-\zeta_{8}+\cdots)q^{11}+\cdots\)
1224.1.cb.a 1224.cb 1224.bb $4$ $0.611$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
1224.1.cb.b 1224.cb 1224.bb $4$ $0.611$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots\)
1224.1.cp.a 1224.cp 1224.bp $8$ $0.611$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{2}q^{6}+\cdots\)
1224.1.cp.b 1224.cp 1224.bp $8$ $0.611$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)
1224.1.cx.a 1224.cx 1224.bx $16$ $0.611$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{5}q^{2}+\zeta_{48}^{14}q^{3}+\zeta_{48}^{10}q^{4}+\cdots\)
1224.1.cx.b 1224.cx 1224.bx $16$ $0.611$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{5}q^{2}+\zeta_{48}^{17}q^{3}+\zeta_{48}^{10}q^{4}+\cdots\)
1224.2.a.a 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{11}+3q^{13}+q^{17}+q^{19}+\cdots\)
1224.2.a.b 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-4q^{11}+6q^{13}-q^{17}+\cdots\)
1224.2.a.c 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
1224.2.a.d 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{11}-6q^{13}+q^{17}+4q^{19}-4q^{23}+\cdots\)
1224.2.a.e 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+2q^{13}+q^{17}+4q^{19}-2q^{23}+\cdots\)
1224.2.a.f 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
1224.2.a.g 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}+6q^{11}+2q^{13}-q^{17}+\cdots\)
1224.2.a.h 1224.a 1.a $1$ $9.774$ \(\Q\) None None \(0\) \(0\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-4q^{7}-q^{11}-5q^{13}-q^{17}+\cdots\)
1224.2.a.i 1224.a 1.a $2$ $9.774$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
1224.2.a.j 1224.a 1.a $2$ $9.774$ \(\Q(\sqrt{17}) \) None None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+2\beta )q^{7}+(4+\beta )q^{11}+\cdots\)
1224.2.a.k 1224.a 1.a $2$ $9.774$ \(\Q(\sqrt{57}) \) None None \(0\) \(0\) \(1\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+4q^{7}+(2-\beta )q^{11}+\beta q^{13}+\cdots\)
1224.2.a.l 1224.a 1.a $3$ $9.774$ 3.3.1304.1 None None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
1224.2.a.m 1224.a 1.a $3$ $9.774$ 3.3.1304.1 None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1224.2.c.a 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{5}-4iq^{7}+iq^{11}-5q^{13}+\cdots\)
1224.2.c.b 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{5}+4iq^{7}+iq^{11}-5q^{13}+\cdots\)
1224.2.c.c 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+iq^{11}-2q^{13}+(-1-2i)q^{17}+\cdots\)
1224.2.c.d 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}-\beta q^{7}-2\beta q^{11}+2q^{13}+(-3+\cdots)q^{17}+\cdots\)
1224.2.c.e 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}-\beta q^{7}-2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots\)
1224.2.c.f 1224.c 17.b $2$ $9.774$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+\beta q^{7}-2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots\)
1224.2.c.g 1224.c 17.b $4$ $9.774$ \(\Q(i, \sqrt{33})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}-\beta _{1}q^{11}+\cdots\)
1224.2.c.h 1224.c 17.b $6$ $9.774$ 6.0.399424.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(\beta _{2}+\beta _{5})q^{7}-\beta _{5}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
1224.2.f.a 1224.f 8.b $2$ $9.774$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2iq^{4}+4iq^{5}-4q^{7}+\cdots\)
1224.2.f.b 1224.f 8.b $4$ $9.774$ \(\Q(i, \sqrt{5})\) None None \(-4\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1224.2.f.c 1224.f 8.b $8$ $9.774$ 8.0.4469724736.1 None None \(1\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{7})q^{5}+\cdots\)
1224.2.f.d 1224.f 8.b $8$ $9.774$ 8.0.1649659456.5 None None \(1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
1224.2.f.e 1224.f 8.b $12$ $9.774$ 12.0.\(\cdots\).1 None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{8}q^{4}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{5}+\cdots\)
1224.2.f.f 1224.f 8.b $14$ $9.774$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-4\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots\)
1224.2.f.g 1224.f 8.b $16$ $9.774$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{4}q^{5}+\beta _{5}q^{7}+\cdots\)
1224.2.f.h 1224.f 8.b $16$ $9.774$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}-\beta _{5}q^{4}+\beta _{4}q^{5}+\beta _{9}q^{7}+\cdots\)
1224.2.h.a 1224.h 408.h $8$ $9.774$ 8.0.\(\cdots\).11 \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-\beta _{4}q^{7}+2\beta _{1}q^{8}+\cdots\)
1224.2.h.b 1224.h 408.h $8$ $9.774$ 8.0.\(\cdots\).11 \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}+\beta _{4}q^{5}+\beta _{6}q^{7}-2\beta _{1}q^{8}+\cdots\)
1224.2.h.c 1224.h 408.h $56$ $9.774$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1224.2.j.a 1224.j 24.f $64$ $9.774$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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