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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
43.2.a.a 43.a 1.a $1$ $0.343$ \(\Q\) None \(-2\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots\)
43.2.a.b 43.a 1.a $2$ $0.343$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
43.2.c.a 43.c 43.c $2$ $0.343$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
43.2.c.b 43.c 43.c $4$ $0.343$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-6\) \(3\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
43.2.e.a 43.e 43.e $6$ $0.343$ \(\Q(\zeta_{14})\) None \(-5\) \(2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
43.2.e.b 43.e 43.e $6$ $0.343$ \(\Q(\zeta_{14})\) None \(3\) \(-3\) \(2\) \(-16\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\zeta_{14}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(-1+\zeta_{14}+\cdots)q^{3}+\cdots\)
43.2.g.a 43.g 43.g $36$ $0.343$ None \(-10\) \(-16\) \(-17\) \(6\) $\mathrm{SU}(2)[C_{21}]$
43.3.b.a 43.b 43.b $1$ $1.172$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+9q^{9}-21q^{11}-17q^{13}+\cdots\)
43.3.b.b 43.b 43.b $6$ $1.172$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-2+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
43.3.d.a 43.d 43.d $12$ $1.172$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-3\) \(9\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
43.3.f.a 43.f 43.f $42$ $1.172$ None \(-7\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
43.3.h.a 43.h 43.h $72$ $1.172$ None \(-14\) \(-14\) \(-11\) \(-30\) $\mathrm{SU}(2)[C_{42}]$
43.4.a.a 43.a 1.a $4$ $2.537$ 4.4.45868.1 None \(-4\) \(-11\) \(-27\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-3+\beta _{2}-\beta _{3})q^{3}+\cdots\)
43.4.a.b 43.a 1.a $6$ $2.537$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(7\) \(43\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
43.4.c.a 43.c 43.c $20$ $2.537$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(-5\) \(-19\) \(-51\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)
43.4.e.a 43.e 43.e $60$ $2.537$ None \(-9\) \(-3\) \(-23\) \(96\) $\mathrm{SU}(2)[C_{7}]$
43.4.g.a 43.g 43.g $120$ $2.537$ None \(-12\) \(-9\) \(5\) \(-54\) $\mathrm{SU}(2)[C_{21}]$
43.5.b.a 43.b 43.b $1$ $4.445$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots\)
43.5.b.b 43.b 43.b $12$ $4.445$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
43.5.d.a 43.d 43.d $28$ $4.445$ None \(0\) \(6\) \(-3\) \(129\) $\mathrm{SU}(2)[C_{6}]$
43.5.f.a 43.f 43.f $78$ $4.445$ None \(-7\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
43.5.h.a 43.h 43.h $168$ $4.445$ None \(-14\) \(-20\) \(-11\) \(-150\) $\mathrm{SU}(2)[C_{42}]$
43.6.a.a 43.a 1.a $8$ $6.897$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-12\) \(-26\) \(-212\) \(-136\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
43.6.a.b 43.a 1.a $10$ $6.897$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(8\) \(28\) \(138\) \(60\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots\)
43.6.c.a 43.c 43.c $34$ $6.897$ None \(-14\) \(-14\) \(71\) \(225\) $\mathrm{SU}(2)[C_{3}]$
43.6.e.a 43.e 43.e $108$ $6.897$ None \(-3\) \(-9\) \(67\) \(-624\) $\mathrm{SU}(2)[C_{7}]$
43.6.g.a 43.g 43.g $204$ $6.897$ None \(0\) \(0\) \(-85\) \(454\) $\mathrm{SU}(2)[C_{21}]$
43.7.b.a 43.b 43.b $1$ $9.892$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{6}q^{4}+3^{6}q^{9}-1638q^{11}+3706q^{13}+\cdots\)
43.7.b.b 43.b 43.b $20$ $9.892$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-40+\beta _{2})q^{4}+\cdots\)
43.7.d.a 43.d 43.d $42$ $9.892$ None \(0\) \(-3\) \(-3\) \(-147\) $\mathrm{SU}(2)[C_{6}]$
43.7.f.a 43.f 43.f $126$ $9.892$ None \(-7\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
43.7.h.a 43.h 43.h $252$ $9.892$ None \(-14\) \(-11\) \(-11\) \(126\) $\mathrm{SU}(2)[C_{42}]$
43.8.a.a 43.a 1.a $11$ $13.433$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-24\) \(-68\) \(-752\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-6-\beta _{5})q^{3}+(54+\cdots)q^{4}+\cdots\)
43.8.a.b 43.a 1.a $13$ $13.433$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(16\) \(94\) \(998\) \(1360\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots\)
43.8.c.a 43.c 43.c $50$ $13.433$ None \(26\) \(-2\) \(-249\) \(-687\) $\mathrm{SU}(2)[C_{3}]$
43.8.e.a 43.e 43.e $144$ $13.433$ None \(1\) \(-33\) \(-253\) \(3440\) $\mathrm{SU}(2)[C_{7}]$
43.8.g.a 43.g 43.g $300$ $13.433$ None \(-40\) \(-12\) \(235\) \(-4122\) $\mathrm{SU}(2)[C_{21}]$
43.9.b.a 43.b 43.b $1$ $17.517$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots\)
43.9.b.b 43.b 43.b $28$ $17.517$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
43.9.d.a 43.d 43.d $56$ $17.517$ None \(0\) \(-84\) \(-3\) \(-5031\) $\mathrm{SU}(2)[C_{6}]$
43.9.f.a 43.f 43.f $174$ $17.517$ None \(-7\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
43.9.h.a 43.h 43.h $336$ $17.517$ None \(-14\) \(70\) \(-11\) \(5010\) $\mathrm{SU}(2)[C_{42}]$
43.10.a.a 43.a 1.a $15$ $22.147$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-32\) \(-317\) \(-4717\) \(-9680\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-21-\beta _{2})q^{3}+(6^{3}+\cdots)q^{4}+\cdots\)
43.10.a.b 43.a 1.a $17$ $22.147$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(48\) \(169\) \(4033\) \(-76\) $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{2}+(10-\beta _{3})q^{3}+(267-4\beta _{1}+\cdots)q^{4}+\cdots\)
43.10.c.a 43.c 43.c $64$ $22.147$ None \(-70\) \(307\) \(681\) \(957\) $\mathrm{SU}(2)[C_{3}]$
43.10.e.a 43.e 43.e $192$ $22.147$ None \(-23\) \(141\) \(677\) \(-23872\) $\mathrm{SU}(2)[C_{7}]$
43.10.g.a 43.g 43.g $384$ $22.147$ None \(56\) \(-321\) \(-695\) \(32650\) $\mathrm{SU}(2)[C_{21}]$
43.11.b.a 43.b 43.b $1$ $27.320$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{10}q^{4}+3^{10}q^{9}-18501q^{11}+\cdots\)
43.11.b.b 43.b 43.b $34$ $27.320$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
43.11.d.a 43.d 43.d $72$ $27.320$ None \(0\) \(-246\) \(-3\) \(31377\) $\mathrm{SU}(2)[C_{6}]$
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