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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.18.a.a 1.a 1.a $1$ $1.832$ \(\Q\) None 1.18.a.a \(-528\) \(-4284\) \(-1025850\) \(3225992\) $+$ $\mathrm{SU}(2)$ \(q-528q^{2}-4284q^{3}+147712q^{4}+\cdots\)
1.20.a.a 1.a 1.a $1$ $2.288$ \(\Q\) None 1.20.a.a \(456\) \(50652\) \(-2377410\) \(-16917544\) $+$ $\mathrm{SU}(2)$ \(q+456q^{2}+50652q^{3}-316352q^{4}+\cdots\)
1.22.a.a 1.a 1.a $1$ $2.795$ \(\Q\) None 1.22.a.a \(-288\) \(-128844\) \(21640950\) \(-768078808\) $+$ $\mathrm{SU}(2)$ \(q-288q^{2}-128844q^{3}-2014208q^{4}+\cdots\)
1.24.a.a 1.a 1.a $2$ $3.352$ \(\Q(\sqrt{144169}) \) None 1.24.a.a \(1080\) \(339480\) \(73069020\) \(-1359184400\) $+$ $\mathrm{SU}(2)$ \(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)
2.18.a.a 2.a 1.a $1$ $3.664$ \(\Q\) None 2.18.a.a \(256\) \(6084\) \(1255110\) \(-22465912\) $-$ $\mathrm{SU}(2)$ \(q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots\)
1.26.a.a 1.a 1.a $1$ $3.960$ \(\Q\) None 1.26.a.a \(-48\) \(-195804\) \(-741989850\) \(39080597192\) $+$ $\mathrm{SU}(2)$ \(q-48q^{2}-195804q^{3}-33552128q^{4}+\cdots\)
2.20.a.a 2.a 1.a $1$ $4.576$ \(\Q\) None 2.20.a.a \(-512\) \(-13092\) \(6546750\) \(96674264\) $+$ $\mathrm{SU}(2)$ \(q-2^{9}q^{2}-13092q^{3}+2^{18}q^{4}+6546750q^{5}+\cdots\)
2.20.a.b 2.a 1.a $1$ $4.576$ \(\Q\) None 2.20.a.b \(512\) \(-53028\) \(-5556930\) \(-44496424\) $-$ $\mathrm{SU}(2)$ \(q+2^{9}q^{2}-53028q^{3}+2^{18}q^{4}-5556930q^{5}+\cdots\)
1.28.a.a 1.a 1.a $2$ $4.619$ \(\Q(\sqrt{18209}) \) None 1.28.a.a \(-8280\) \(-1286280\) \(5443587900\) \(-175391963600\) $+$ $\mathrm{SU}(2)$ \(q+(-4140-\beta )q^{2}+(-643140-192\beta )q^{3}+\cdots\)
3.17.b.a 3.b 3.b $4$ $4.870$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 3.17.b.a \(0\) \(-2052\) \(0\) \(-3141544\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)
1.30.a.a 1.a 1.a $2$ $5.328$ \(\Q(\sqrt{51349}) \) None 1.30.a.a \(8640\) \(-4967640\) \(-17477788500\) \(-30\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(4320-\beta )q^{2}+(-2483820+552\beta )q^{3}+\cdots\)
3.18.a.a 3.a 1.a $1$ $5.497$ \(\Q\) None 3.18.a.a \(204\) \(-6561\) \(-163554\) \(-20846560\) $+$ $\mathrm{SU}(2)$ \(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b 3.a 1.a $2$ $5.497$ \(\Q(\sqrt{14569}) \) None 3.18.a.b \(594\) \(13122\) \(382860\) \(24471568\) $-$ $\mathrm{SU}(2)$ \(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)
2.22.a.a 2.a 1.a $1$ $5.590$ \(\Q\) None 2.22.a.a \(-1024\) \(71604\) \(-28693770\) \(-853202392\) $+$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+71604q^{3}+2^{20}q^{4}-28693770q^{5}+\cdots\)
2.22.a.b 2.a 1.a $1$ $5.590$ \(\Q\) None 2.22.a.b \(1024\) \(59316\) \(4975350\) \(1427425832\) $-$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+59316q^{3}+2^{20}q^{4}+4975350q^{5}+\cdots\)
1.32.a.a 1.a 1.a $2$ $6.088$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 1.32.a.a \(39960\) \(17363160\) \(-19391218020\) \(30\!\cdots\!00\) $+$ $\mathrm{SU}(2)$ \(q+(19980-\beta )q^{2}+(8681580-432\beta )q^{3}+\cdots\)
3.19.b.a 3.b 3.b $1$ $6.162$ \(\Q\) \(\Q(\sqrt{-3}) \) 3.19.b.a \(0\) \(-19683\) \(0\) \(77549186\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b 3.b 3.b $4$ $6.162$ 4.0.601940665.1 None 3.19.b.b \(0\) \(15876\) \(0\) \(-95744152\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)
4.17.b.a 4.b 4.b $1$ $6.493$ \(\Q\) \(\Q(\sqrt{-1}) \) 4.17.b.a \(256\) \(0\) \(329666\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
4.17.b.b 4.b 4.b $6$ $6.493$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 4.17.b.b \(-164\) \(0\) \(-506740\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)
2.24.a.a 2.a 1.a $1$ $6.704$ \(\Q\) None 2.24.a.a \(-2048\) \(-505908\) \(-90135570\) \(6872255096\) $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots\)
3.20.a.a 3.a 1.a $1$ $6.865$ \(\Q\) None 3.20.a.a \(-1104\) \(19683\) \(3516270\) \(-195590584\) $-$ $\mathrm{SU}(2)$ \(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
3.20.a.b 3.a 1.a $2$ $6.865$ \(\Q(\sqrt{87481}) \) None 3.20.a.b \(702\) \(-39366\) \(6016140\) \(113892064\) $+$ $\mathrm{SU}(2)$ \(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)
4.18.a.a 4.a 1.a $2$ $7.329$ \(\Q(\sqrt{9361}) \) None 4.18.a.a \(0\) \(-5880\) \(604044\) \(25350160\) $-$ $\mathrm{SU}(2)$ \(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)
3.21.b.a 3.b 3.b $6$ $7.605$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 3.21.b.a \(0\) \(-4122\) \(0\) \(559607916\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)
2.26.a.a 2.a 1.a $1$ $7.920$ \(\Q\) None 2.26.a.a \(-4096\) \(97956\) \(341005350\) \(-40882637368\) $+$ $\mathrm{SU}(2)$ \(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\)
2.26.a.b 2.a 1.a $2$ $7.920$ \(\Q(\sqrt{106705}) \) None 2.26.a.b \(8192\) \(379848\) \(741953100\) \(-376536944\) $-$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\)
5.17.c.a 5.c 5.c $14$ $8.116$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 5.17.c.a \(-2\) \(7908\) \(192880\) \(-386452\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
4.19.b.a 4.b 4.b $8$ $8.215$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4.19.b.a \(84\) \(0\) \(860880\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)
3.22.a.a 3.a 1.a $1$ $8.384$ \(\Q\) None 3.22.a.a \(-2844\) \(-59049\) \(3109950\) \(363303920\) $+$ $\mathrm{SU}(2)$ \(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\)
3.22.a.b 3.a 1.a $1$ $8.384$ \(\Q\) None 3.22.a.b \(1728\) \(-59049\) \(-41512770\) \(538429808\) $+$ $\mathrm{SU}(2)$ \(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\)
3.22.a.c 3.a 1.a $2$ $8.384$ \(\Q(\sqrt{649}) \) None 3.22.a.c \(666\) \(118098\) \(996876\) \(679896112\) $-$ $\mathrm{SU}(2)$ \(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\)
4.20.a.a 4.a 1.a $1$ $9.153$ \(\Q\) None 4.20.a.a \(0\) \(-36\) \(-196290\) \(-35905576\) $-$ $\mathrm{SU}(2)$ \(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\)
5.18.a.a 5.a 1.a $2$ $9.161$ \(\Q(\sqrt{39}) \) None 5.18.a.a \(680\) \(-10980\) \(-781250\) \(-22820700\) $+$ $\mathrm{SU}(2)$ \(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
5.18.a.b 5.a 1.a $3$ $9.161$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 5.18.a.b \(118\) \(15944\) \(1171875\) \(2139308\) $-$ $\mathrm{SU}(2)$ \(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)
5.18.b.a 5.b 5.b $8$ $9.161$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 5.18.b.a \(0\) \(0\) \(379200\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)
3.23.b.a 3.b 3.b $6$ $9.201$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 3.23.b.a \(0\) \(86670\) \(0\) \(-3447063060\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)
2.28.a.a 2.a 1.a $1$ $9.237$ \(\Q\) None 2.28.a.a \(-8192\) \(3984828\) \(-2851889250\) \(368721063704\) $+$ $\mathrm{SU}(2)$ \(q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots\)
2.28.a.b 2.a 1.a $1$ $9.237$ \(\Q\) None 2.28.a.b \(8192\) \(-1016388\) \(-3341197410\) \(-51021361384\) $-$ $\mathrm{SU}(2)$ \(q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots\)
6.17.b.a 6.b 3.b $6$ $9.739$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 6.17.b.a \(0\) \(6006\) \(0\) \(-167892\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots\)
3.24.a.a 3.a 1.a $1$ $10.056$ \(\Q\) None 3.24.a.a \(1128\) \(177147\) \(-48863730\) \(-1723688680\) $-$ $\mathrm{SU}(2)$ \(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b 3.a 1.a $2$ $10.056$ \(\Q(\sqrt{530401}) \) None 3.24.a.b \(-1242\) \(-354294\) \(-46808820\) \(-211963904\) $+$ $\mathrm{SU}(2)$ \(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)
4.21.b.a 4.b 4.b $1$ $10.141$ \(\Q\) \(\Q(\sqrt{-1}) \) 4.21.b.a \(-1024\) \(0\) \(-19306574\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
4.21.b.b 4.b 4.b $8$ $10.141$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4.21.b.b \(396\) \(0\) \(18568080\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)
5.19.c.a 5.c 5.c $16$ $10.269$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 5.19.c.a \(510\) \(-20130\) \(3145170\) \(78767350\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots\)
2.30.a.a 2.a 1.a $1$ $10.656$ \(\Q\) None 2.30.a.a \(-16384\) \(-2792556\) \(6651856470\) \(14\!\cdots\!48\) $+$ $\mathrm{SU}(2)$ \(q-2^{14}q^{2}-2792556q^{3}+2^{28}q^{4}+\cdots\)
2.30.a.b 2.a 1.a $1$ $10.656$ \(\Q\) None 2.30.a.b \(16384\) \(4782996\) \(6065841750\) \(904018883432\) $-$ $\mathrm{SU}(2)$ \(q+2^{14}q^{2}+4782996q^{3}+2^{28}q^{4}+\cdots\)
3.25.b.a 3.b 3.b $1$ $10.949$ \(\Q\) \(\Q(\sqrt{-3}) \) 3.25.b.a \(0\) \(531441\) \(0\) \(-4119710398\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b 3.b 3.b $6$ $10.949$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 3.25.b.b \(0\) \(-616842\) \(0\) \(1988064876\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
6.18.a.a 6.a 1.a $1$ $10.993$ \(\Q\) None 6.18.a.a \(-256\) \(-6561\) \(645150\) \(3974432\) $+$ $\mathrm{SU}(2)$ \(q-2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}+645150q^{5}+\cdots\)
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