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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.2.a.a 24.a 1.a $1$ $0.192$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a 24.d 8.b $2$ $0.192$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a 24.f 24.f $2$ $0.192$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
24.3.b.a 24.b 8.d $4$ $0.654$ 4.0.4752.1 None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
24.3.e.a 24.e 3.b $2$ $0.654$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
24.3.h.a 24.h 24.h $1$ $0.654$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b 24.h 24.h $1$ $0.654$ \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c 24.h 24.h $4$ $0.654$ \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
24.4.a.a 24.a 1.a $1$ $1.416$ \(\Q\) None \(0\) \(3\) \(14\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)
24.4.d.a 24.d 8.b $6$ $1.416$ 6.0.8248384.1 None \(2\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
24.4.f.a 24.f 24.f $2$ $1.416$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(10\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b 24.f 24.f $8$ $1.416$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
24.5.b.a 24.b 8.d $8$ $2.481$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.5.e.a 24.e 3.b $4$ $2.481$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(-4\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
24.5.h.a 24.h 24.h $1$ $2.481$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-4\) \(-9\) \(46\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.b 24.h 24.h $1$ $2.481$ \(\Q\) \(\Q(\sqrt{-6}) \) \(4\) \(9\) \(-46\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
24.5.h.c 24.h 24.h $12$ $2.481$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
24.6.a.a 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(-9\) \(-34\) \(-240\) $+$ $\mathrm{SU}(2)$ \(q-9q^{3}-34q^{5}-240q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.b 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(-9\) \(94\) \(144\) $-$ $\mathrm{SU}(2)$ \(q-9q^{3}+94q^{5}+12^{2}q^{7}+3^{4}q^{9}+\cdots\)
24.6.a.c 24.a 1.a $1$ $3.849$ \(\Q\) None \(0\) \(9\) \(38\) \(120\) $-$ $\mathrm{SU}(2)$ \(q+9q^{3}+38q^{5}+120q^{7}+3^{4}q^{9}+\cdots\)
24.6.d.a 24.d 8.b $10$ $3.849$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(0\) \(-196\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
24.6.f.a 24.f 24.f $2$ $3.849$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots\)
24.6.f.b 24.f 24.f $16$ $3.849$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(3+\beta _{2}+\cdots)q^{4}+\cdots\)
24.7.b.a 24.b 8.d $12$ $5.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
24.7.e.a 24.e 3.b $6$ $5.521$ 6.0.1173604352.2 None \(0\) \(-10\) \(0\) \(156\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3^{3}+\cdots)q^{7}+\cdots\)
24.7.h.a 24.h 24.h $1$ $5.521$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-8\) \(27\) \(-142\) \(470\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-142q^{5}+\cdots\)
24.7.h.b 24.h 24.h $1$ $5.521$ \(\Q\) \(\Q(\sqrt{-6}) \) \(8\) \(-27\) \(142\) \(470\) $\mathrm{U}(1)[D_{2}]$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+142q^{5}+\cdots\)
24.7.h.c 24.h 24.h $20$ $5.521$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-944\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-10+\beta _{3})q^{4}+\cdots\)
24.8.a.a 24.a 1.a $1$ $7.497$ \(\Q\) None \(0\) \(-27\) \(-26\) \(1056\) $+$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.b 24.a 1.a $1$ $7.497$ \(\Q\) None \(0\) \(27\) \(-530\) \(120\) $-$ $\mathrm{SU}(2)$ \(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.c 24.a 1.a $1$ $7.497$ \(\Q\) None \(0\) \(27\) \(110\) \(504\) $+$ $\mathrm{SU}(2)$ \(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\)
24.8.d.a 24.d 8.b $14$ $7.497$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(0\) \(1372\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)
24.8.f.a 24.f 24.f $2$ $7.497$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-86\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots\)
24.8.f.b 24.f 24.f $4$ $7.497$ \(\Q(\sqrt{6}, \sqrt{-26})\) None \(0\) \(-36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots\)
24.8.f.c 24.f 24.f $20$ $7.497$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(120\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots\)
24.9.b.a 24.b 8.d $16$ $9.777$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(26-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
24.9.e.a 24.e 3.b $8$ $9.777$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(56\) \(0\) \(1584\) $\mathrm{SU}(2)[C_{2}]$ \(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)
24.9.h.a 24.h 24.h $1$ $9.777$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-16\) \(-81\) \(-866\) \(-4798\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots\)
24.9.h.b 24.h 24.h $1$ $9.777$ \(\Q\) \(\Q(\sqrt{-6}) \) \(16\) \(81\) \(866\) \(-4798\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots\)
24.9.h.c 24.h 24.h $28$ $9.777$ None \(0\) \(0\) \(0\) \(9592\) $\mathrm{SU}(2)[C_{2}]$
24.10.a.a 24.a 1.a $1$ $12.361$ \(\Q\) None \(0\) \(-81\) \(830\) \(672\) $+$ $\mathrm{SU}(2)$ \(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b 24.a 1.a $1$ $12.361$ \(\Q\) None \(0\) \(81\) \(-794\) \(-5880\) $+$ $\mathrm{SU}(2)$ \(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c 24.a 1.a $1$ $12.361$ \(\Q\) None \(0\) \(81\) \(614\) \(2184\) $-$ $\mathrm{SU}(2)$ \(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d 24.a 1.a $2$ $12.361$ \(\Q(\sqrt{109}) \) None \(0\) \(-162\) \(-772\) \(-2880\) $-$ $\mathrm{SU}(2)$ \(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)
24.10.d.a 24.d 8.b $18$ $12.361$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(34\) \(0\) \(0\) \(-9604\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(29-2\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
24.10.f.a 24.f 24.f $2$ $12.361$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(190\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}\beta q^{2}+(95-73\beta )q^{3}-2^{9}q^{4}+\cdots\)
24.10.f.b 24.f 24.f $32$ $12.361$ None \(0\) \(-192\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
24.11.b.a 24.b 8.d $20$ $15.249$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-22\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+(-93-\beta _{1}+\cdots)q^{4}+\cdots\)
24.11.e.a 24.e 3.b $10$ $15.249$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-22\) \(0\) \(-5436\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-545+\cdots)q^{7}+\cdots\)
24.11.h.a 24.h 24.h $1$ $15.249$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-32\) \(243\) \(5282\) \(24950\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+5282q^{5}+\cdots\)
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