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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1323.1.b.a 1323.b 3.b $1$ $0.660$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-q^{13}+q^{16}+2q^{19}+q^{25}+\cdots\)
1323.1.b.b 1323.b 3.b $1$ $0.660$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{13}+q^{16}-2q^{19}+q^{25}+\cdots\)
1323.1.d.a 1323.d 7.b $2$ $0.660$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{16}+q^{25}+\cdots\)
1323.1.m.a 1323.m 7.d $2$ $0.660$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}-\zeta_{6}q^{16}+\cdots\)
1323.1.q.a 1323.q 21.h $2$ $0.660$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{4}+q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{19}+\cdots\)
1323.1.br.a 1323.br 147.n $12$ $0.660$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{42}^{13}q^{4}-\zeta_{42}^{3}q^{7}+(-\zeta_{42}-\zeta_{42}^{5}+\cdots)q^{13}+\cdots\)
1323.1.bv.a 1323.bv 49.h $12$ $0.660$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{42}^{10}q^{4}-\zeta_{42}^{12}q^{7}+(\zeta_{42}^{4}-\zeta_{42}^{20}+\cdots)q^{13}+\cdots\)
1323.2.a.a 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-2\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-2q^{11}+\cdots\)
1323.2.a.b 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-2\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots\)
1323.2.a.c 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-2\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-2q^{11}+\cdots\)
1323.2.a.d 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-1\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-4q^{5}+3q^{8}+4q^{10}+\cdots\)
1323.2.a.e 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-3q^{5}+3q^{8}+3q^{10}+\cdots\)
1323.2.a.f 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-1\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{5}+3q^{8}-3q^{10}+\cdots\)
1323.2.a.g 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(-1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots\)
1323.2.a.h 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(0\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}+6q^{11}+4q^{13}+4q^{16}+\cdots\)
1323.2.a.i 1323.a 1.a $1$ $10.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-5q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots\)
1323.2.a.j 1323.a 1.a $1$ $10.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-2q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots\)
1323.2.a.k 1323.a 1.a $1$ $10.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+2q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots\)
1323.2.a.l 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(0\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-6q^{11}+4q^{13}+4q^{16}+\cdots\)
1323.2.a.m 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(1\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
1323.2.a.n 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(1\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{5}-3q^{8}-3q^{10}+\cdots\)
1323.2.a.o 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(1\) \(0\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{5}-3q^{8}+3q^{10}+\cdots\)
1323.2.a.p 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
1323.2.a.q 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(2\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+2q^{11}+\cdots\)
1323.2.a.r 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(2\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+4q^{11}+\cdots\)
1323.2.a.s 1323.a 1.a $1$ $10.564$ \(\Q\) None None \(2\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}+6q^{10}+2q^{11}+\cdots\)
1323.2.a.t 1323.a 1.a $2$ $10.564$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots\)
1323.2.a.u 1323.a 1.a $2$ $10.564$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+4q^{4}-\beta q^{5}+2\beta q^{8}-6q^{10}+\cdots\)
1323.2.a.v 1323.a 1.a $2$ $10.564$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+4q^{4}+\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
1323.2.a.w 1323.a 1.a $2$ $10.564$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}+\beta q^{5}+3\beta q^{8}+7q^{10}+\cdots\)
1323.2.a.x 1323.a 1.a $3$ $10.564$ 3.3.321.1 None None \(-2\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1323.2.a.y 1323.a 1.a $3$ $10.564$ 3.3.321.1 None None \(-2\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1323.2.a.z 1323.a 1.a $3$ $10.564$ 3.3.321.1 None None \(2\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
1323.2.a.ba 1323.a 1.a $3$ $10.564$ 3.3.321.1 None None \(2\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
1323.2.a.bb 1323.a 1.a $4$ $10.564$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(0\) \(-8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2-\beta _{3})q^{5}+\cdots\)
1323.2.a.bc 1323.a 1.a $4$ $10.564$ 4.4.7168.1 None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\beta _{3}q^{8}+\cdots\)
1323.2.a.bd 1323.a 1.a $4$ $10.564$ 4.4.7168.1 None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+\beta _{3}q^{8}+\cdots\)
1323.2.a.be 1323.a 1.a $4$ $10.564$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(0\) \(8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(2+\beta _{3})q^{5}+\cdots\)
1323.2.c.a 1323.c 21.c $2$ $10.564$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}-4\zeta_{6}q^{13}+4q^{16}-3\zeta_{6}q^{19}+\cdots\)
1323.2.c.b 1323.c 21.c $4$ $10.564$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{8}-2\beta _{1}q^{11}+\cdots\)
1323.2.c.c 1323.c 21.c $4$ $10.564$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{5}+2\beta _{1}q^{8}+2\beta _{2}q^{10}+\cdots\)
1323.2.c.d 1323.c 21.c $12$ $10.564$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}+(-1-\beta _{6})q^{4}+\beta _{1}q^{5}+(-\beta _{8}+\cdots)q^{8}+\cdots\)
1323.2.c.e 1323.c 21.c $16$ $10.564$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
1323.2.c.f 1323.c 21.c $16$ $10.564$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-1+\beta _{13})q^{4}-\beta _{2}q^{5}+\cdots\)
1323.2.f.a 1323.f 9.c $2$ $10.564$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots\)
1323.2.f.b 1323.f 9.c $2$ $10.564$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+3q^{8}+\cdots\)
1323.2.f.c 1323.f 9.c $6$ $10.564$ 6.0.309123.1 None None \(-1\) \(0\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1323.2.f.d 1323.f 9.c $6$ $10.564$ \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
1323.2.f.e 1323.f 9.c $10$ $10.564$ 10.0.\(\cdots\).1 None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots\)
1323.2.f.f 1323.f 9.c $10$ $10.564$ 10.0.\(\cdots\).1 None None \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
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