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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.3.d.a 9.d 9.d $2$ $0.245$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
9.4.a.a 9.a 1.a $1$ $0.531$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) $+$ $N(\mathrm{U}(1))$ \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a 9.c 9.c $4$ $0.531$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
9.5.b.a 9.b 3.b $2$ $0.930$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a 9.d 9.d $6$ $0.930$ 6.0.39400128.1 None \(-3\) \(-3\) \(-12\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
9.6.a.a 9.a 1.a $1$ $1.443$ \(\Q\) None \(6\) \(0\) \(-6\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a 9.c 9.c $8$ $1.443$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(3\) \(-12\) \(78\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
9.7.b.a 9.b 3.b $2$ $2.070$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(1048\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)
9.7.d.a 9.d 9.d $10$ $2.070$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(24\) \(-219\) \(-121\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.8.a.a 9.a 1.a $1$ $2.811$ \(\Q\) None \(-6\) \(0\) \(-390\) \(-64\) $-$ $\mathrm{SU}(2)$ \(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
9.8.a.b 9.a 1.a $2$ $2.811$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(520\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\)
9.8.c.a 9.c 9.c $12$ $2.811$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-9\) \(24\) \(-180\) \(-84\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.9.b.a 9.b 3.b $2$ $3.666$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(3304\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
9.9.d.a 9.d 9.d $14$ $3.666$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-93\) \(438\) \(922\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
9.10.a.a 9.a 1.a $1$ $4.635$ \(\Q\) None \(-18\) \(0\) \(1530\) \(9128\) $-$ $\mathrm{SU}(2)$ \(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
9.10.a.b 9.a 1.a $1$ $4.635$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-12580\) $+$ $N(\mathrm{U}(1))$ \(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
9.10.a.c 9.a 1.a $1$ $4.635$ \(\Q\) None \(36\) \(0\) \(1314\) \(-4480\) $-$ $\mathrm{SU}(2)$ \(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
9.10.c.a 9.c 9.c $16$ $4.635$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(15\) \(-3\) \(453\) \(-343\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
9.11.b.a 9.b 3.b $4$ $5.718$ \(\Q(\sqrt{-2}, \sqrt{385})\) None \(0\) \(0\) \(0\) \(-44464\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
9.11.d.a 9.d 9.d $18$ $5.718$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(51\) \(4956\) \(-6120\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
9.12.a.a 9.a 1.a $1$ $6.915$ \(\Q\) None \(-78\) \(0\) \(5370\) \(-27760\) $-$ $\mathrm{SU}(2)$ \(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b 9.a 1.a $1$ $6.915$ \(\Q\) None \(24\) \(0\) \(-4830\) \(-16744\) $-$ $\mathrm{SU}(2)$ \(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c 9.a 1.a $2$ $6.915$ \(\Q(\sqrt{70}) \) None \(0\) \(0\) \(0\) \(116200\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a 9.c 9.c $20$ $6.915$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-33\) \(-12\) \(-7230\) \(8512\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9.13.b.a 9.b 3.b $2$ $8.226$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-223736\) $\mathrm{SU}(2)[C_{2}]$ \(q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots\)
9.13.b.b 9.b 3.b $2$ $8.226$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(232456\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots\)
9.13.d.a 9.d 9.d $22$ $8.226$ None \(-3\) \(618\) \(-15987\) \(34319\) $\mathrm{SU}(2)[C_{6}]$
9.14.a.a 9.a 1.a $1$ $9.651$ \(\Q\) None \(12\) \(0\) \(30210\) \(235088\) $-$ $\mathrm{SU}(2)$ \(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
9.14.a.b 9.a 1.a $2$ $9.651$ \(\Q(\sqrt{55}) \) None \(0\) \(0\) \(0\) \(-266600\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
9.14.a.c 9.a 1.a $2$ $9.651$ \(\Q(\sqrt{1969}) \) None \(54\) \(0\) \(-40716\) \(-21008\) $-$ $\mathrm{SU}(2)$ \(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)
9.14.c.a 9.c 9.c $24$ $9.651$ None \(63\) \(-732\) \(52128\) \(-93912\) $\mathrm{SU}(2)[C_{3}]$
9.15.b.a 9.b 3.b $4$ $11.190$ \(\Q(\sqrt{-2}, \sqrt{3745})\) None \(0\) \(0\) \(0\) \(-1065904\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots\)
9.15.d.a 9.d 9.d $26$ $11.190$ None \(-3\) \(-2199\) \(-107994\) \(-146330\) $\mathrm{SU}(2)[C_{6}]$
9.16.a.a 9.a 1.a $1$ $12.842$ \(\Q\) None \(-216\) \(0\) \(-52110\) \(2822456\) $-$ $\mathrm{SU}(2)$ \(q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots\)
9.16.a.b 9.a 1.a $1$ $12.842$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1244900\) $+$ $N(\mathrm{U}(1))$ \(q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots\)
9.16.a.c 9.a 1.a $1$ $12.842$ \(\Q\) None \(72\) \(0\) \(221490\) \(-2149000\) $-$ $\mathrm{SU}(2)$ \(q+72q^{2}-27584q^{4}+221490q^{5}+\cdots\)
9.16.a.d 9.a 1.a $1$ $12.842$ \(\Q\) None \(234\) \(0\) \(-280710\) \(-1373344\) $-$ $\mathrm{SU}(2)$ \(q+234q^{2}+21988q^{4}-280710q^{5}+\cdots\)
9.16.a.e 9.a 1.a $2$ $12.842$ \(\Q(\sqrt{370}) \) None \(0\) \(0\) \(0\) \(-5182520\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots\)
9.16.c.a 9.c 9.c $28$ $12.842$ None \(-129\) \(3345\) \(-152655\) \(803705\) $\mathrm{SU}(2)[C_{3}]$
9.17.b.a 9.b 3.b $6$ $14.609$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(5400696\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots\)
9.17.d.a 9.d 9.d $30$ $14.609$ None \(-3\) \(2049\) \(507588\) \(220596\) $\mathrm{SU}(2)[C_{6}]$
9.18.a.a 9.a 1.a $1$ $16.490$ \(\Q\) None \(-204\) \(0\) \(163554\) \(-20846560\) $-$ $\mathrm{SU}(2)$ \(q-204q^{2}-89456q^{4}+163554q^{5}+\cdots\)
9.18.a.b 9.a 1.a $1$ $16.490$ \(\Q\) None \(528\) \(0\) \(1025850\) \(3225992\) $-$ $\mathrm{SU}(2)$ \(q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots\)
9.18.a.c 9.a 1.a $2$ $16.490$ \(\Q(\sqrt{14569}) \) None \(-594\) \(0\) \(-382860\) \(24471568\) $-$ $\mathrm{SU}(2)$ \(q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots\)
9.18.a.d 9.a 1.a $2$ $16.490$ \(\Q(\sqrt{910}) \) None \(0\) \(0\) \(0\) \(-392840\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots\)
9.18.c.a 9.c 9.c $32$ $16.490$ None \(255\) \(-2280\) \(255678\) \(-5846540\) $\mathrm{SU}(2)[C_{3}]$
9.19.b.a 9.b 3.b $6$ $18.485$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(19180488\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)
9.19.d.a 9.d 9.d $34$ $18.485$ None \(-3\) \(3804\) \(2192181\) \(4302359\) $\mathrm{SU}(2)[C_{6}]$
9.20.a.a 9.a 1.a $1$ $20.594$ \(\Q\) None \(-456\) \(0\) \(2377410\) \(-16917544\) $-$ $\mathrm{SU}(2)$ \(q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots\)
9.20.a.b 9.a 1.a $1$ $20.594$ \(\Q\) None \(1104\) \(0\) \(-3516270\) \(-195590584\) $-$ $\mathrm{SU}(2)$ \(q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots\)
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