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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3.6.a.a 3.a 1.a $1$ $0.481$ \(\Q\) None \(-6\) \(9\) \(6\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
3.7.b.a 3.b 3.b $1$ $0.690$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-27\) \(0\) \(-286\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
3.8.a.a 3.a 1.a $1$ $0.937$ \(\Q\) None \(6\) \(-27\) \(390\) \(-64\) $+$ $\mathrm{SU}(2)$ \(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
3.9.b.a 3.b 3.b $2$ $1.222$ \(\Q(\sqrt{-14}) \) None \(0\) \(90\) \(0\) \(-3500\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)
3.10.a.a 3.a 1.a $1$ $1.545$ \(\Q\) None \(-36\) \(-81\) \(-1314\) \(-4480\) $+$ $\mathrm{SU}(2)$ \(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b 3.a 1.a $1$ $1.545$ \(\Q\) None \(18\) \(81\) \(-1530\) \(9128\) $-$ $\mathrm{SU}(2)$ \(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
3.11.b.a 3.b 3.b $2$ $1.906$ \(\Q(\sqrt{-5}) \) None \(0\) \(-54\) \(0\) \(34468\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots\)
3.12.a.a 3.a 1.a $1$ $2.305$ \(\Q\) None \(78\) \(-243\) \(-5370\) \(-27760\) $+$ $\mathrm{SU}(2)$ \(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
3.13.b.a 3.b 3.b $1$ $2.742$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(729\) \(0\) \(-153502\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots\)
3.13.b.b 3.b 3.b $2$ $2.742$ \(\Q(\sqrt{-26}) \) None \(0\) \(-1350\) \(0\) \(80500\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots\)
3.14.a.a 3.a 1.a $1$ $3.217$ \(\Q\) None \(-12\) \(-729\) \(-30210\) \(235088\) $+$ $\mathrm{SU}(2)$ \(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b 3.a 1.a $2$ $3.217$ \(\Q(\sqrt{1969}) \) None \(-54\) \(1458\) \(40716\) \(-21008\) $-$ $\mathrm{SU}(2)$ \(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)
3.15.b.a 3.b 3.b $4$ $3.730$ 4.0.1929141760.2 None \(0\) \(2196\) \(0\) \(825608\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots\)
3.16.a.a 3.a 1.a $1$ $4.281$ \(\Q\) None \(-234\) \(-2187\) \(280710\) \(-1373344\) $+$ $\mathrm{SU}(2)$ \(q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots\)
3.16.a.b 3.a 1.a $1$ $4.281$ \(\Q\) None \(-72\) \(2187\) \(-221490\) \(-2149000\) $-$ $\mathrm{SU}(2)$ \(q-72q^{2}+3^{7}q^{3}-27584q^{4}-221490q^{5}+\cdots\)
3.17.b.a 3.b 3.b $4$ $4.870$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(-2052\) \(0\) \(-3141544\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)
3.18.a.a 3.a 1.a $1$ $5.497$ \(\Q\) None \(204\) \(-6561\) \(-163554\) \(-20846560\) $+$ $\mathrm{SU}(2)$ \(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b 3.a 1.a $2$ $5.497$ \(\Q(\sqrt{14569}) \) None \(594\) \(13122\) \(382860\) \(24471568\) $-$ $\mathrm{SU}(2)$ \(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)
3.19.b.a 3.b 3.b $1$ $6.162$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-19683\) \(0\) \(77549186\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b 3.b 3.b $4$ $6.162$ 4.0.601940665.1 None \(0\) \(15876\) \(0\) \(-95744152\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)
3.20.a.a 3.a 1.a $1$ $6.865$ \(\Q\) None \(-1104\) \(19683\) \(3516270\) \(-195590584\) $-$ $\mathrm{SU}(2)$ \(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
3.20.a.b 3.a 1.a $2$ $6.865$ \(\Q(\sqrt{87481}) \) None \(702\) \(-39366\) \(6016140\) \(113892064\) $+$ $\mathrm{SU}(2)$ \(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)
3.21.b.a 3.b 3.b $6$ $7.605$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-4122\) \(0\) \(559607916\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.22.a.a 3.a 1.a $1$ $8.384$ \(\Q\) None \(-2844\) \(-59049\) \(3109950\) \(363303920\) $+$ $\mathrm{SU}(2)$ \(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\)
3.22.a.b 3.a 1.a $1$ $8.384$ \(\Q\) None \(1728\) \(-59049\) \(-41512770\) \(538429808\) $+$ $\mathrm{SU}(2)$ \(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\)
3.22.a.c 3.a 1.a $2$ $8.384$ \(\Q(\sqrt{649}) \) None \(666\) \(118098\) \(996876\) \(679896112\) $-$ $\mathrm{SU}(2)$ \(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\)
3.23.b.a 3.b 3.b $6$ $9.201$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(86670\) \(0\) \(-3447063060\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.24.a.a 3.a 1.a $1$ $10.056$ \(\Q\) None \(1128\) \(177147\) \(-48863730\) \(-1723688680\) $-$ $\mathrm{SU}(2)$ \(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b 3.a 1.a $2$ $10.056$ \(\Q(\sqrt{530401}) \) None \(-1242\) \(-354294\) \(-46808820\) \(-211963904\) $+$ $\mathrm{SU}(2)$ \(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)
3.25.b.a 3.b 3.b $1$ $10.949$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(531441\) \(0\) \(-4119710398\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b 3.b 3.b $6$ $10.949$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-616842\) \(0\) \(1988064876\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.26.a.a 3.a 1.a $2$ $11.880$ \(\Q(\sqrt{1287001}) \) None \(-324\) \(-1062882\) \(570861756\) \(-29687385728\) $+$ $\mathrm{SU}(2)$ \(q+(-162-\beta )q^{2}-3^{12}q^{3}+(12803848+\cdots)q^{4}+\cdots\)
3.26.a.b 3.a 1.a $3$ $11.880$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-3678\) \(1594323\) \(-163152750\) \(-9622572744\) $-$ $\mathrm{SU}(2)$ \(q+(-1226+\beta _{1})q^{2}+3^{12}q^{3}+(30249196+\cdots)q^{4}+\cdots\)
3.27.b.a 3.b 3.b $8$ $12.849$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-1261080\) \(0\) \(-83723264240\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-157635-5\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.28.a.a 3.a 1.a $2$ $13.856$ \(\Q(\sqrt{6469}) \) None \(3168\) \(3188646\) \(-4906065060\) \(-151657089584\) $-$ $\mathrm{SU}(2)$ \(q+(1584-\beta )q^{2}+3^{13}q^{3}+(2432512+\cdots)q^{4}+\cdots\)
3.28.a.b 3.a 1.a $2$ $13.856$ \(\Q(\sqrt{30001}) \) None \(21582\) \(-3188646\) \(-1771946100\) \(369665199904\) $+$ $\mathrm{SU}(2)$ \(q+(10791-\beta )q^{2}-3^{13}q^{3}+(101301922+\cdots)q^{4}+\cdots\)
3.29.b.a 3.b 3.b $8$ $14.901$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(6092280\) \(0\) \(401156726320\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(761535-18\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.30.a.a 3.a 1.a $2$ $15.983$ \(\Q(\sqrt{77089}) \) None \(-45036\) \(-9565938\) \(187613820\) \(26\!\cdots\!48\) $+$ $\mathrm{SU}(2)$ \(q+(-22518-\beta )q^{2}-3^{14}q^{3}+(106174408+\cdots)q^{4}+\cdots\)
3.30.a.b 3.a 1.a $3$ $15.983$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(11370\) \(14348907\) \(35492909586\) \(723913582632\) $-$ $\mathrm{SU}(2)$ \(q+(3790-\beta _{1})q^{2}+3^{14}q^{3}+(701653900+\cdots)q^{4}+\cdots\)
3.31.b.a 3.b 3.b $1$ $17.104$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-14348907\) \(0\) \(-79\!\cdots\!86\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{15}q^{3}+2^{30}q^{4}-7945347009886q^{7}+\cdots\)
3.31.b.b 3.b 3.b $8$ $17.104$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(5373000\) \(0\) \(11\!\cdots\!80\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(671625-17\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.32.a.a 3.a 1.a $2$ $18.263$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-39528\) \(28697814\) \(-7930517220\) \(-10\!\cdots\!76\) $-$ $\mathrm{SU}(2)$ \(q+(-19764-\beta )q^{2}+3^{15}q^{3}+(-100683488+\cdots)q^{4}+\cdots\)
3.32.a.b 3.a 1.a $3$ $18.263$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-7626\) \(-43046721\) \(50622172050\) \(-25\!\cdots\!08\) $+$ $\mathrm{SU}(2)$ \(q+(-2542+\beta _{1})q^{2}-3^{15}q^{3}+(1406276044+\cdots)q^{4}+\cdots\)
3.33.b.a 3.b 3.b $10$ $19.460$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-21387150\) \(0\) \(-55\!\cdots\!40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.34.a.a 3.a 1.a $3$ $20.695$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(41202\) \(129140163\) \(51261823890\) \(76\!\cdots\!56\) $-$ $\mathrm{SU}(2)$ \(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b 3.a 1.a $3$ $20.695$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(136620\) \(-129140163\) \(-260488036134\) \(10\!\cdots\!32\) $+$ $\mathrm{SU}(2)$ \(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
3.35.b.a 3.b 3.b $10$ $21.968$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(119369106\) \(0\) \(-12\!\cdots\!72\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.36.a.a 3.a 1.a $2$ $23.279$ \(\Q(\sqrt{2196841}) \) None \(-60912\) \(258280326\) \(-13\!\cdots\!40\) \(-12\!\cdots\!44\) $-$ $\mathrm{SU}(2)$ \(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b 3.a 1.a $3$ $23.279$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-87330\) \(-387420489\) \(27\!\cdots\!10\) \(48\!\cdots\!64\) $+$ $\mathrm{SU}(2)$ \(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
3.37.b.a 3.b 3.b $1$ $24.627$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(387420489\) \(0\) \(27\!\cdots\!98\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
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