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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.1.h.a 224.h 56.h $1$ $0.112$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}-q^{9}-2q^{23}-q^{25}+q^{49}+\cdots\)
224.1.r.a 224.r 28.g $4$ $0.112$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
224.1.v.a 224.v 224.v $4$ $0.112$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
224.2.a.a 224.a 1.a $1$ $1.789$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
224.2.a.b 224.a 1.a $1$ $1.789$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
224.2.a.c 224.a 1.a $2$ $1.789$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
224.2.a.d 224.a 1.a $2$ $1.789$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
224.2.b.a 224.b 8.b $2$ $1.789$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+\beta q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots\)
224.2.b.b 224.b 8.b $4$ $1.789$ 4.0.2312.1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
224.2.e.a 224.e 56.e $2$ $1.789$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{7}+3q^{9}+4q^{11}+2\beta q^{23}-5q^{25}+\cdots\)
224.2.e.b 224.e 56.e $4$ $1.789$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
224.2.f.a 224.f 28.d $8$ $1.789$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots\)
224.2.i.a 224.i 7.c $4$ $1.789$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
224.2.i.b 224.i 7.c $4$ $1.789$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
224.2.i.c 224.i 7.c $4$ $1.789$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-3\beta _{2}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
224.2.i.d 224.i 7.c $4$ $1.789$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
224.2.p.a 224.p 28.f $16$ $1.789$ 16.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{14}q^{3}-\beta _{13}q^{5}-\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)
224.2.q.a 224.q 56.m $12$ $1.789$ 12.0.\(\cdots\).2 None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{3}+(-\beta _{4}-\beta _{7})q^{5}+(\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)
224.2.t.a 224.t 56.p $12$ $1.789$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{3}+(-\beta _{4}+\beta _{7})q^{5}+(\beta _{8}-\beta _{9}+\cdots)q^{7}+\cdots\)
224.2.u.a 224.u 32.g $4$ $1.789$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
224.2.u.b 224.u 32.g $40$ $1.789$ None None \(4\) \(4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$
224.2.u.c 224.u 32.g $52$ $1.789$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
224.2.x.a 224.x 224.x $8$ $1.789$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
224.2.x.b 224.x 224.x $112$ $1.789$ None None \(-8\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
224.2.bd.a 224.bd 224.ad $240$ $1.789$ None None \(-4\) \(-4\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{24}]$
224.2.be.a 224.be 224.ae $240$ $1.789$ None None \(-4\) \(-12\) \(-12\) \(-8\) $\mathrm{SU}(2)[C_{24}]$
224.3.c.a 224.c 7.b $8$ $6.104$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+\beta _{7}q^{5}+\beta _{2}q^{7}+(-7-\beta _{5}+\cdots)q^{9}+\cdots\)
224.3.c.b 224.c 7.b $8$ $6.104$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{5}q^{5}+\beta _{7}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
224.3.d.a 224.d 4.b $4$ $6.104$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}-\beta _{3}q^{7}+5q^{9}+\cdots\)
224.3.d.b 224.d 4.b $8$ $6.104$ 8.0.1997017344.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+(-5+\beta _{2}+\cdots)q^{9}+\cdots\)
224.3.g.a 224.g 8.d $4$ $6.104$ \(\Q(\sqrt{2}, \sqrt{-7})\) None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{1})q^{3}+(-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
224.3.g.b 224.g 8.d $8$ $6.104$ 8.0.\(\cdots\).3 None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)
224.3.h.a 224.h 56.h $2$ $6.104$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{U}(1)[D_{2}]$ \(q-7q^{7}-9q^{9}-\beta q^{11}-18q^{23}-5^{2}q^{25}+\cdots\)
224.3.h.b 224.h 56.h $2$ $6.104$ \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+\beta q^{5}-7q^{7}+19q^{9}+\beta q^{13}+\cdots\)
224.3.h.c 224.h 56.h $2$ $6.104$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(14\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+3\beta q^{5}+7q^{7}-q^{9}-9\beta q^{13}+\cdots\)
224.3.h.d 224.h 56.h $8$ $6.104$ 8.0.\(\cdots\).51 None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
224.3.n.a 224.n 56.j $28$ $6.104$ None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$
224.3.o.a 224.o 56.k $2$ $6.104$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{3}+(-3-3\zeta_{6})q^{5}+(-3+8\zeta_{6})q^{7}+\cdots\)
224.3.o.b 224.o 56.k $2$ $6.104$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(9\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{3}+(3+3\zeta_{6})q^{5}+(3-8\zeta_{6})q^{7}+\cdots\)
224.3.o.c 224.o 56.k $12$ $6.104$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2}-\beta _{8})q^{3}+(\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
224.3.o.d 224.o 56.k $12$ $6.104$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3}+\beta _{6}+\beta _{7}-\beta _{10})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
224.3.r.a 224.r 28.g $4$ $6.104$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+5\zeta_{12}q^{3}-9\zeta_{12}^{2}q^{5}+(8\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
224.3.r.b 224.r 28.g $4$ $6.104$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots\)
224.3.r.c 224.r 28.g $12$ $6.104$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{5}+(\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
224.3.r.d 224.r 28.g $12$ $6.104$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{7}+\beta _{9}-\beta _{10})q^{3}+(-3\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
224.3.s.a 224.s 7.d $16$ $6.104$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}+\beta _{10}q^{5}-\beta _{13}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
224.3.s.b 224.s 7.d $16$ $6.104$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{12})q^{7}+(-5\beta _{7}+\cdots)q^{9}+\cdots\)
224.3.v.a 224.v 224.v $8$ $6.104$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots\)
224.3.v.b 224.v 224.v $240$ $6.104$ None None \(-8\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
224.3.w.a 224.w 32.h $192$ $6.104$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
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