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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
644.1.h.a 644.h 644.h $1$ $0.321$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-161}) \) \(\Q(\sqrt{23}) \) \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}+2q^{11}+\cdots\)
644.1.h.b 644.h 644.h $1$ $0.321$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-161}) \) \(\Q(\sqrt{23}) \) \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}-2q^{11}+\cdots\)
644.1.h.c 644.h 644.h $2$ $0.321$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-161}) \) None \(-2\) \(0\) \(0\) \(-2\) \(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots\)
644.1.h.d 644.h 644.h $2$ $0.321$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-161}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots\)
644.1.r.a 644.r 644.r $10$ $0.321$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}-\zeta_{22}^{9}q^{7}-\zeta_{22}^{7}q^{8}+\cdots\)
644.1.r.b 644.r 644.r $10$ $0.321$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{22}^{4}q^{2}+\zeta_{22}^{8}q^{4}+\zeta_{22}^{9}q^{7}+\cdots\)
644.2.a.a 644.a 1.a $1$ $5.142$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-2q^{11}-3q^{13}+\cdots\)
644.2.a.b 644.a 1.a $1$ $5.142$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots\)
644.2.a.c 644.a 1.a $5$ $5.142$ 5.5.8580816.1 None None \(0\) \(1\) \(4\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
644.2.a.d 644.a 1.a $5$ $5.142$ 5.5.6963152.1 None None \(0\) \(3\) \(2\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
644.2.c.a 644.c 92.b $36$ $5.142$ None None \(1\) \(0\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{2}]$
644.2.c.b 644.c 92.b $36$ $5.142$ None None \(1\) \(0\) \(0\) \(36\) $\mathrm{SU}(2)[C_{2}]$
644.2.d.a 644.d 161.c $16$ $5.142$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{8}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
644.2.f.a 644.f 28.d $4$ $5.142$ \(\Q(i, \sqrt{14})\) None None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}-q^{3}-2\beta _{2}q^{4}-2\beta _{2}q^{5}+\cdots\)
644.2.f.b 644.f 28.d $4$ $5.142$ \(\Q(i, \sqrt{14})\) None None \(-4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+q^{3}-2\beta _{2}q^{4}+2\beta _{2}q^{5}+\cdots\)
644.2.f.c 644.f 28.d $80$ $5.142$ None None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
644.2.i.a 644.i 7.c $14$ $5.142$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(-3\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{10}q^{3}+(-\beta _{2}-\beta _{11})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
644.2.i.b 644.i 7.c $14$ $5.142$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(5\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\cdots\)
644.2.k.a 644.k 28.f $176$ $5.142$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
644.2.m.a 644.m 161.g $32$ $5.142$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
644.2.p.a 644.p 644.p $184$ $5.142$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
644.2.q.a 644.q 23.c $60$ $5.142$ None None \(0\) \(-4\) \(-11\) \(6\) $\mathrm{SU}(2)[C_{11}]$
644.2.q.b 644.q 23.c $60$ $5.142$ None None \(0\) \(0\) \(7\) \(-6\) $\mathrm{SU}(2)[C_{11}]$
644.2.t.a 644.t 644.t $20$ $5.142$ 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{22}]$ \(q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots\)
644.2.t.b 644.t 644.t $20$ $5.142$ 20.0.\(\cdots\).2 \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{22}]$ \(q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots\)
644.2.t.c 644.t 644.t $880$ $5.142$ None None \(-22\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
644.2.v.a 644.v 161.k $160$ $5.142$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
644.2.w.a 644.w 92.h $360$ $5.142$ None None \(-1\) \(0\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{22}]$
644.2.w.b 644.w 92.h $360$ $5.142$ None None \(-1\) \(0\) \(0\) \(36\) $\mathrm{SU}(2)[C_{22}]$
644.2.y.a 644.y 161.m $320$ $5.142$ None None \(0\) \(0\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{33}]$
644.2.z.a 644.z 644.z $1840$ $5.142$ None None \(-11\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{66}]$
644.2.bc.a 644.bc 161.o $320$ $5.142$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{66}]$
644.2.be.a 644.be 644.ae $1840$ $5.142$ None None \(-7\) \(0\) \(-54\) \(0\) $\mathrm{SU}(2)[C_{66}]$
644.3.b.a 644.b 7.b $28$ $17.548$ None None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$
644.3.g.a 644.g 23.b $24$ $17.548$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
644.3.l.a 644.l 161.f $64$ $17.548$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
644.3.o.a 644.o 7.d $60$ $17.548$ None None \(0\) \(-6\) \(0\) \(22\) $\mathrm{SU}(2)[C_{6}]$
644.4.a.a 644.a 1.a $6$ $37.997$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-6\) \(-10\) \(42\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{1}-\beta _{4})q^{5}+\cdots\)
644.4.a.b 644.a 1.a $6$ $37.997$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(2\) \(0\) \(-42\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-7q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
644.4.a.c 644.a 1.a $10$ $37.997$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(10\) \(70\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+7q^{7}+(12+\beta _{2}+\cdots)q^{9}+\cdots\)
644.4.a.d 644.a 1.a $10$ $37.997$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(8\) \(20\) \(-70\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2-\beta _{4})q^{5}-7q^{7}+(12+\cdots)q^{9}+\cdots\)
644.4.d.a 644.d 161.c $48$ $37.997$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
644.4.i.a 644.i 7.c $44$ $37.997$ None None \(0\) \(-12\) \(-10\) \(-38\) $\mathrm{SU}(2)[C_{3}]$
644.4.i.b 644.i 7.c $44$ $37.997$ None None \(0\) \(12\) \(10\) \(-6\) $\mathrm{SU}(2)[C_{3}]$
644.4.m.a 644.m 161.g $96$ $37.997$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
644.5.b.a 644.b 7.b $60$ $66.570$ None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$
644.5.g.a 644.g 23.b $48$ $66.570$ None None \(0\) \(20\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
644.6.a.a 644.a 1.a $12$ $103.287$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-25\) \(-64\) \(-588\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{3}+(-5+\beta _{5})q^{5}-7^{2}q^{7}+\cdots\)
644.6.a.b 644.a 1.a $12$ $103.287$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-15\) \(-14\) \(588\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+7^{2}q^{7}+\cdots\)
644.6.a.c 644.a 1.a $16$ $103.287$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-7\) \(36\) \(-784\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(2-\beta _{3})q^{5}-7^{2}q^{7}+(102+\cdots)q^{9}+\cdots\)
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