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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1215.1.d.a 1215.d 15.d $3$ $0.606$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
1215.1.d.b 1215.d 15.d $3$ $0.606$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
1215.1.h.a 1215.h 45.h $6$ $0.606$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
1215.1.h.b 1215.h 45.h $6$ $0.606$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
1215.2.a.a 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-2q^{11}+\cdots\)
1215.2.a.b 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(-1\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots\)
1215.2.a.c 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(-1\) \(0\) \(1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots\)
1215.2.a.d 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(-1\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots\)
1215.2.a.e 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-q^{7}+6q^{11}+2q^{13}+\cdots\)
1215.2.a.f 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-q^{7}-6q^{11}+2q^{13}+\cdots\)
1215.2.a.g 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(1\) \(0\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
1215.2.a.h 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(1\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots\)
1215.2.a.i 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(1\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots\)
1215.2.a.j 1215.a 1.a $1$ $9.702$ \(\Q\) None None \(2\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+2q^{11}+\cdots\)
1215.2.a.k 1215.a 1.a $2$ $9.702$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(-1+\beta )q^{7}+\cdots\)
1215.2.a.l 1215.a 1.a $2$ $9.702$ \(\Q(\sqrt{21}) \) None None \(-1\) \(0\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(3+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots\)
1215.2.a.m 1215.a 1.a $2$ $9.702$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots\)
1215.2.a.n 1215.a 1.a $2$ $9.702$ \(\Q(\sqrt{21}) \) None None \(1\) \(0\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3+\beta )q^{4}+q^{5}+(-1-\beta )q^{7}+\cdots\)
1215.2.a.o 1215.a 1.a $3$ $9.702$ 3.3.564.1 None None \(-1\) \(0\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
1215.2.a.p 1215.a 1.a $3$ $9.702$ \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
1215.2.a.q 1215.a 1.a $3$ $9.702$ \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
1215.2.a.r 1215.a 1.a $3$ $9.702$ 3.3.564.1 None None \(1\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
1215.2.a.s 1215.a 1.a $9$ $9.702$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(0\) \(-9\) \(9\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{8})q^{7}+\cdots\)
1215.2.a.t 1215.a 1.a $9$ $9.702$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(0\) \(9\) \(9\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{8})q^{7}+\cdots\)
1215.2.b.a 1215.b 5.b $12$ $9.702$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}+(-2+\beta _{7})q^{4}-\beta _{6}q^{5}+(-2\beta _{3}+\cdots)q^{8}+\cdots\)
1215.2.b.b 1215.b 5.b $12$ $9.702$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{1})q^{4}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots\)
1215.2.b.c 1215.b 5.b $12$ $9.702$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{3})q^{4}+(-\beta _{4}-\beta _{7}+\cdots)q^{5}+\cdots\)
1215.2.b.d 1215.b 5.b $12$ $9.702$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-1-\beta _{1})q^{4}-\beta _{4}q^{5}+(\beta _{9}+\cdots)q^{7}+\cdots\)
1215.2.b.e 1215.b 5.b $24$ $9.702$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1215.2.e.a 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1215.2.e.b 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1215.2.e.c 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1215.2.e.d 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
1215.2.e.e 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6+\cdots)q^{11}+\cdots\)
1215.2.e.f 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+\cdots)q^{11}+\cdots\)
1215.2.e.g 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1215.2.e.h 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1215.2.e.i 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
1215.2.e.j 1215.e 9.c $2$ $9.702$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots\)
1215.2.e.k 1215.e 9.c $4$ $9.702$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-1\) \(0\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}+(3\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\beta _{1}q^{5}+\cdots\)
1215.2.e.l 1215.e 9.c $4$ $9.702$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1215.2.e.m 1215.e 9.c $4$ $9.702$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(1\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(3\beta _{1}-\beta _{2}+\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots\)
1215.2.e.n 1215.e 9.c $4$ $9.702$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(1\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1215.2.e.o 1215.e 9.c $6$ $9.702$ 6.0.954288.1 None None \(-1\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
1215.2.e.p 1215.e 9.c $6$ $9.702$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
1215.2.e.q 1215.e 9.c $6$ $9.702$ \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
1215.2.e.r 1215.e 9.c $6$ $9.702$ 6.0.954288.1 None None \(1\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1215.2.e.s 1215.e 9.c $18$ $9.702$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(-9\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{6}+\beta _{12})q^{4}+\cdots\)
1215.2.e.t 1215.e 9.c $18$ $9.702$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(9\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{6}+\beta _{12})q^{4}+\cdots\)
1215.3.c.a 1215.c 3.b $2$ $33.106$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-q^{4}-\beta q^{5}-12q^{7}+3\beta q^{8}+\cdots\)
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