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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.a.a 637.a 1.a $1$ $5.086$ \(\Q\) None \(-2\) \(0\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-3q^{9}-6q^{10}+\cdots\)
637.2.a.b 637.a 1.a $1$ $5.086$ \(\Q\) None \(0\) \(2\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+3q^{5}+q^{9}-4q^{12}+\cdots\)
637.2.a.c 637.a 1.a $1$ $5.086$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.d 637.a 1.a $1$ $5.086$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}-3q^{9}-3q^{11}+\cdots\)
637.2.a.e 637.a 1.a $2$ $5.086$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.f 637.a 1.a $2$ $5.086$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+\cdots\)
637.2.a.g 637.a 1.a $2$ $5.086$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(-3-\beta )q^{5}+2q^{6}+\cdots\)
637.2.a.h 637.a 1.a $3$ $5.086$ 3.3.404.1 None \(-2\) \(-4\) \(-5\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
637.2.a.i 637.a 1.a $3$ $5.086$ 3.3.404.1 None \(-2\) \(4\) \(5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.a.j 637.a 1.a $3$ $5.086$ 3.3.316.1 None \(1\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
637.2.a.k 637.a 1.a $5$ $5.086$ 5.5.746052.1 None \(4\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.l 637.a 1.a $5$ $5.086$ 5.5.746052.1 None \(4\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.m 637.a 1.a $6$ $5.086$ 6.6.4507648.1 None \(0\) \(-8\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.a.n 637.a 1.a $6$ $5.086$ 6.6.4507648.1 None \(0\) \(8\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
637.2.c.a 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{3}-2q^{4}+iq^{5}-4iq^{6}+\cdots\)
637.2.c.b 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+\beta q^{5}-3q^{9}+\beta q^{13}+4q^{16}+\cdots\)
637.2.c.c 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+2q^{3}-2q^{4}-iq^{5}+4iq^{6}+\cdots\)
637.2.c.d 637.c 13.b $6$ $5.086$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.c.e 637.c 13.b $8$ $5.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.c.f 637.c 13.b $8$ $5.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.c.g 637.c 13.b $16$ $5.086$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.e.a 637.e 7.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
637.2.e.b 637.e 7.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.c 637.e 7.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.d 637.e 7.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
637.2.e.e 637.e 7.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
637.2.e.f 637.e 7.c $4$ $5.086$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.g 637.e 7.c $4$ $5.086$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.e.h 637.e 7.c $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.e.i 637.e 7.c $6$ $5.086$ 6.0.2696112.1 None \(-1\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
637.2.e.j 637.e 7.c $6$ $5.086$ 6.0.2696112.1 None \(-1\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
637.2.e.k 637.e 7.c $6$ $5.086$ 6.0.4406832.1 None \(2\) \(-4\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.l 637.e 7.c $6$ $5.086$ 6.0.4406832.1 None \(2\) \(4\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
637.2.e.m 637.e 7.c $10$ $5.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
637.2.e.n 637.e 7.c $12$ $5.086$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{11})q^{2}+(\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.e.o 637.e 7.c $12$ $5.086$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(8\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{8}+\cdots)q^{3}+\cdots\)
637.2.f.a 637.f 13.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.b 637.f 13.c $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.c 637.f 13.c $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+\cdots\)
637.2.f.d 637.f 13.c $4$ $5.086$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.f.e 637.f 13.c $4$ $5.086$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.f 637.f 13.c $4$ $5.086$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.g 637.f 13.c $8$ $5.086$ 8.0.\(\cdots\).7 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.f.h 637.f 13.c $8$ $5.086$ 8.0.\(\cdots\).6 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2}-\beta _{6})q^{2}+(-\beta _{3}+\beta _{7})q^{3}+\cdots\)
637.2.f.i 637.f 13.c $8$ $5.086$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(1\) \(14\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.j 637.f 13.c $12$ $5.086$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{11}q^{3}+\cdots\)
637.2.f.k 637.f 13.c $12$ $5.086$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+\beta _{11}q^{3}+\cdots\)
637.2.f.l 637.f 13.c $16$ $5.086$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4}+\beta _{10})q^{2}+(\beta _{8}-\beta _{15})q^{3}+\cdots\)
637.2.g.a 637.g 91.g $2$ $5.086$ \(\Q(\sqrt{-3}) \) None \(-1\) \(6\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+3q^{3}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
637.2.g.b 637.g 91.g $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-6\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+\cdots\)
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