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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.3.c.a $1$ $0.327$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(2\) $-$ \(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
12.3.d.a $2$ $0.327$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(0\) $-$ \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
12.4.a.a $1$ $0.708$ \(\Q\) None \(0\) \(3\) \(-18\) \(8\) $+$ \(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
12.4.b.a $4$ $0.708$ \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
12.5.c.a $1$ $1.240$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(-94\) $-$ \(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
12.5.d.a $4$ $1.240$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(6\) \(0\) \(24\) \(0\) $-$ \(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)
12.6.b.a $8$ $1.925$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
12.7.c.a $2$ $2.761$ \(\Q(\sqrt{-5}) \) None \(0\) \(-6\) \(0\) \(484\) $-$ \(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)
12.7.d.a $6$ $2.761$ 6.0.50898483.1 None \(-10\) \(0\) \(-44\) \(0\) $-$ \(q+(-2-\beta _{1})q^{2}-\beta _{2}q^{3}+(3^{3}+2\beta _{1}+\cdots)q^{4}+\cdots\)
12.8.a.a $1$ $3.749$ \(\Q\) None \(0\) \(-27\) \(-378\) \(-832\) $-$ \(q-3^{3}q^{3}-378q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
12.8.a.b $1$ $3.749$ \(\Q\) None \(0\) \(27\) \(270\) \(1112\) $+$ \(q+3^{3}q^{3}+270q^{5}+1112q^{7}+3^{6}q^{9}+\cdots\)
12.8.b.a $4$ $3.749$ \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{3}q^{2}+(-3\beta _{2}+3\beta _{3})q^{3}+(88+4\beta _{1}+\cdots)q^{4}+\cdots\)
12.8.b.b $8$ $3.749$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-41+\beta _{2}+\cdots)q^{4}+\cdots\)
12.9.c.a $1$ $4.889$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(81\) \(0\) \(4034\) $-$ \(q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\)
12.9.c.b $2$ $4.889$ \(\Q(\sqrt{-110}) \) None \(0\) \(-102\) \(0\) \(-6188\) $-$ \(q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots\)
12.9.d.a $8$ $4.889$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(0\) \(-336\) \(0\) $-$ \(q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
12.10.a.a $1$ $6.180$ \(\Q\) None \(0\) \(-81\) \(990\) \(8576\) $-$ \(q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots\)
12.10.b.a $16$ $6.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots\)
12.11.c.a $1$ $7.624$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-243\) \(0\) \(22082\) $-$ \(q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\)
12.11.c.b $2$ $7.624$ \(\Q(\sqrt{-35}) \) None \(0\) \(234\) \(0\) \(-20636\) $-$ \(q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots\)
12.11.d.a $10$ $7.624$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(3116\) \(0\) $-$ \(q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots\)
12.12.a.a $1$ $9.220$ \(\Q\) None \(0\) \(-243\) \(9990\) \(-86128\) $-$ \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b $1$ $9.220$ \(\Q\) None \(0\) \(243\) \(2862\) \(9128\) $+$ \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)
12.12.b.a $20$ $9.220$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
12.13.c.a $4$ $10.968$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(300\) \(0\) \(15800\) $-$ \(q+(75+\beta _{1})q^{3}+(-3\beta _{1}+\beta _{2})q^{5}+(3950+\cdots)q^{7}+\cdots\)
12.13.d.a $12$ $10.968$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-90\) \(0\) \(-10296\) \(0\) $-$ \(q+(-8+\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-386+\cdots)q^{4}+\cdots\)
12.14.a.a $1$ $12.868$ \(\Q\) None \(0\) \(-729\) \(-14850\) \(-62896\) $-$ \(q-3^{6}q^{3}-14850q^{5}-62896q^{7}+\cdots\)
12.14.a.b $1$ $12.868$ \(\Q\) None \(0\) \(729\) \(-24570\) \(-173704\) $+$ \(q+3^{6}q^{3}-24570q^{5}-173704q^{7}+\cdots\)
12.14.b.a $24$ $12.868$ None \(0\) \(0\) \(0\) \(0\) $-$
12.15.c.a $1$ $14.919$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-2187\) \(0\) \(-1389022\) $-$ \(q-3^{7}q^{3}-1389022q^{7}+3^{14}q^{9}+\cdots\)
12.15.c.b $4$ $14.919$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(2148\) \(0\) \(1709288\) $-$ \(q+(537-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(427322+\cdots)q^{7}+\cdots\)
12.15.d.a $14$ $14.919$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(182\) \(0\) \(-16124\) \(0\) $-$ \(q+(13-\beta _{1})q^{2}+\beta _{2}q^{3}+(665-13\beta _{1}+\cdots)q^{4}+\cdots\)
12.16.a.a $1$ $17.123$ \(\Q\) None \(0\) \(-2187\) \(45702\) \(1217888\) $-$ \(q-3^{7}q^{3}+45702q^{5}+1217888q^{7}+\cdots\)
12.16.a.b $2$ $17.123$ \(\Q(\sqrt{8017}) \) None \(0\) \(4374\) \(69660\) \(2491504\) $+$ \(q+3^{7}q^{3}+(34830-\beta )q^{5}+(1245752+\cdots)q^{7}+\cdots\)
12.16.b.a $28$ $17.123$ None \(0\) \(0\) \(0\) \(0\) $-$
12.17.c.a $1$ $19.479$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(6561\) \(0\) \(4743554\) $-$ \(q+3^{8}q^{3}+4743554q^{7}+3^{16}q^{9}+\cdots\)
12.17.c.b $4$ $19.479$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(-12420\) \(0\) \(-1050280\) $-$ \(q+(-3105-\beta _{1})q^{3}+(-8\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
12.17.d.a $16$ $19.479$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-186\) \(0\) \(354144\) \(0\) $-$ \(q+(-12-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(8542+\cdots)q^{4}+\cdots\)
12.18.a.a $1$ $21.987$ \(\Q\) None \(0\) \(-6561\) \(-1608930\) \(-9417184\) $-$ \(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
12.18.a.b $1$ $21.987$ \(\Q\) None \(0\) \(6561\) \(130950\) \(-14846776\) $+$ \(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)
12.18.b.a $32$ $21.987$ None \(0\) \(0\) \(0\) \(0\) $-$
12.19.c.a $6$ $24.646$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(23934\) \(0\) \(11024364\) $-$ \(q+(3989-\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
12.19.d.a $18$ $24.646$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-170\) \(0\) \(-1721764\) \(0\) $-$ \(q+(-9-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-24281+\cdots)q^{4}+\cdots\)
12.20.a.a $2$ $27.458$ \(\Q(\sqrt{193153}) \) None \(0\) \(-39366\) \(624780\) \(4667104\) $-$ \(q-3^{9}q^{3}+(312390-\beta )q^{5}+(2333552+\cdots)q^{7}+\cdots\)
12.20.a.b $2$ $27.458$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(39366\) \(-3267108\) \(-27023984\) $+$ \(q+3^{9}q^{3}+(-1633554-\beta )q^{5}+(-13511992+\cdots)q^{7}+\cdots\)
12.20.b.a $36$ $27.458$ None \(0\) \(0\) \(0\) \(0\) $-$
12.21.c.a $1$ $30.422$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(59049\) \(0\) \(-77335774\) $-$ \(q+3^{10}q^{3}-77335774q^{7}+3^{20}q^{9}+\cdots\)
12.21.c.b $6$ $30.422$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-84378\) \(0\) \(-145040532\) $-$ \(q+(-14063+\beta _{1})q^{3}+(3^{3}\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
12.21.d.a $20$ $30.422$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1254\) \(0\) \(1476984\) \(0\) $-$ \(q+(63-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
12.22.a.a $1$ $33.537$ \(\Q\) None \(0\) \(59049\) \(-11268090\) \(281914136\) $+$ \(q+3^{10}q^{3}-11268090q^{5}+281914136q^{7}+\cdots\)
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