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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.2.a.a 114.a 1.a $1$ $0.910$ \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
114.2.a.b 114.a 1.a $1$ $0.910$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
114.2.a.c 114.a 1.a $1$ $0.910$ \(\Q\) None \(1\) \(1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
114.2.b.a 114.b 57.d $2$ $0.910$ \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
114.2.b.b 114.b 57.d $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.c 114.b 57.d $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
114.2.b.d 114.b 57.d $2$ $0.910$ \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)
114.2.e.a 114.e 19.c $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.e.b 114.e 19.c $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.a 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.b 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.c 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.d 114.h 57.f $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.h.e 114.h 57.f $4$ $0.910$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
114.2.h.f 114.h 57.f $4$ $0.910$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
114.2.i.a 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-9\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.b 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.c 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
114.2.i.d 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(9\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
114.2.l.a 114.l 57.j $18$ $0.910$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
114.2.l.b 114.l 57.j $18$ $0.910$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots\)
114.3.c.a 114.c 3.b $12$ $3.106$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{9}q^{3}-2q^{4}+\beta _{4}q^{5}+(1+\cdots)q^{6}+\cdots\)
114.3.d.a 114.d 19.b $8$ $3.106$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-2q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
114.3.f.a 114.f 19.d $8$ $3.106$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(-1-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots\)
114.3.f.b 114.f 19.d $8$ $3.106$ 8.0.\(\cdots\).10 None \(0\) \(12\) \(4\) \(-24\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(2-\beta _{4})q^{3}+(2-2\beta _{4})q^{4}+\cdots\)
114.3.g.a 114.g 57.h $24$ $3.106$ None \(0\) \(-2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$
114.3.j.a 114.j 19.f $12$ $3.106$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{11}q^{2}+(2\beta _{2}-\beta _{8})q^{3}-2\beta _{4}q^{4}+\cdots\)
114.3.j.b 114.j 19.f $24$ $3.106$ None \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$
114.3.k.a 114.k 57.l $84$ $3.106$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
114.4.a.a 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(-3\) \(-19\) \(9\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots\)
114.4.a.b 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(3\) \(-7\) \(-15\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots\)
114.4.a.c 114.a 1.a $1$ $6.726$ \(\Q\) None \(-2\) \(3\) \(12\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+12q^{5}-6q^{6}+\cdots\)
114.4.a.d 114.a 1.a $1$ $6.726$ \(\Q\) None \(2\) \(-3\) \(-11\) \(-15\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots\)
114.4.a.e 114.a 1.a $2$ $6.726$ \(\Q(\sqrt{17}) \) None \(4\) \(-6\) \(18\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots\)
114.4.a.f 114.a 1.a $2$ $6.726$ \(\Q(\sqrt{273}) \) None \(4\) \(6\) \(11\) \(9\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots\)
114.4.b.a 114.b 57.d $10$ $6.726$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-20\) \(5\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
114.4.b.b 114.b 57.d $10$ $6.726$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(20\) \(-5\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}-\beta _{3}q^{3}+4q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots\)
114.4.e.a 114.e 19.c $2$ $6.726$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-2\) \(-42\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
114.4.e.b 114.e 19.c $2$ $6.726$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(6\) \(38\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
114.4.e.c 114.e 19.c $4$ $6.726$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(-4\) \(-6\) \(-8\) \(36\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}-3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots\)
114.4.e.d 114.e 19.c $6$ $6.726$ 6.0.627014547.1 None \(-6\) \(9\) \(-10\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots\)
114.4.e.e 114.e 19.c $6$ $6.726$ 6.0.6967728.1 None \(6\) \(9\) \(-2\) \(-34\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{3})q^{2}+(3+3\beta _{3})q^{3}+4\beta _{3}q^{4}+\cdots\)
114.4.h.a 114.h 57.f $20$ $6.726$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(-4\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-2\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
114.4.h.b 114.h 57.f $20$ $6.726$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(1\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\beta _{1}q^{2}-\beta _{5}q^{3}+(-4-4\beta _{1})q^{4}+\cdots\)
114.4.i.a 114.i 19.e $12$ $6.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-15\) \(42\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-2\beta _{3}-2\beta _{8})q^{2}-3\beta _{3}q^{3}-4\beta _{5}q^{4}+\cdots\)
114.4.i.b 114.i 19.e $12$ $6.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-9\) \(12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(2\beta _{4}-2\beta _{7})q^{2}-3\beta _{4}q^{3}-4\beta _{8}q^{4}+\cdots\)
114.4.i.c 114.i 19.e $18$ $6.726$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(9\) \(-30\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-2\beta _{4}+2\beta _{6})q^{2}-3\beta _{4}q^{3}+(4\beta _{5}+\cdots)q^{4}+\cdots\)
114.4.i.d 114.i 19.e $18$ $6.726$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(15\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+2\beta _{5}q^{2}-3\beta _{6}q^{3}+4\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
114.4.l.a 114.l 57.j $60$ $6.726$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
114.4.l.b 114.l 57.j $60$ $6.726$ None \(0\) \(9\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
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