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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
42.2.a.a 42.a 1.a $1$ $0.335$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
42.2.d.a 42.d 21.c $4$ $0.335$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
42.2.e.a 42.e 7.c $2$ $0.335$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
42.2.e.b 42.e 7.c $2$ $0.335$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)
42.2.f.a 42.f 21.g $4$ $0.335$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
42.3.b.a 42.b 3.b $4$ $1.144$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
42.3.c.a 42.c 7.b $4$ $1.144$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
42.3.g.a 42.g 7.d $4$ $1.144$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
42.3.h.a 42.h 21.h $4$ $1.144$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
42.3.h.b 42.h 21.h $8$ $1.144$ 8.0.4857532416.2 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
42.4.a.a 42.a 1.a $1$ $2.478$ \(\Q\) None \(2\) \(-3\) \(18\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+18q^{5}-6q^{6}+\cdots\)
42.4.a.b 42.a 1.a $1$ $2.478$ \(\Q\) None \(2\) \(3\) \(2\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+2q^{5}+6q^{6}+\cdots\)
42.4.d.a 42.d 21.c $8$ $2.478$ 8.0.\(\cdots\).13 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{5}q^{3}-4q^{4}+(2\beta _{5}-2\beta _{6}+\cdots)q^{5}+\cdots\)
42.4.e.a 42.e 7.c $2$ $2.478$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(6\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
42.4.e.b 42.e 7.c $2$ $2.478$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(15\) \(35\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
42.4.e.c 42.e 7.c $4$ $2.478$ \(\Q(\sqrt{-3}, \sqrt{1345})\) None \(-4\) \(-6\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(-3+3\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
42.4.f.a 42.f 21.g $16$ $2.478$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(80\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(4+4\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
42.5.b.a 42.b 3.b $8$ $4.342$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2-\beta _{3})q^{3}-8q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots\)
42.5.c.a 42.c 7.b $4$ $4.342$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+8q^{4}+(-4\beta _{2}+\cdots)q^{5}+\cdots\)
42.5.g.a 42.g 7.d $4$ $4.342$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(-66\) \(-70\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-6-3\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
42.5.g.b 42.g 7.d $8$ $4.342$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(36\) \(-42\) \(76\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(6+3\beta _{1})q^{3}+8\beta _{1}q^{4}+(-3+\cdots)q^{5}+\cdots\)
42.5.h.a 42.h 21.h $20$ $4.342$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(130\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{9})q^{2}-\beta _{10}q^{3}+(8+8\beta _{2}+\cdots)q^{4}+\cdots\)
42.6.a.a 42.a 1.a $1$ $6.736$ \(\Q\) None \(-4\) \(-9\) \(-54\) \(49\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-54q^{5}+6^{2}q^{6}+\cdots\)
42.6.a.b 42.a 1.a $1$ $6.736$ \(\Q\) None \(-4\) \(-9\) \(44\) \(-49\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+44q^{5}+6^{2}q^{6}+\cdots\)
42.6.a.c 42.a 1.a $1$ $6.736$ \(\Q\) None \(-4\) \(9\) \(-72\) \(49\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}-72q^{5}-6^{2}q^{6}+\cdots\)
42.6.a.d 42.a 1.a $1$ $6.736$ \(\Q\) None \(-4\) \(9\) \(26\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+26q^{5}-6^{2}q^{6}+\cdots\)
42.6.a.e 42.a 1.a $1$ $6.736$ \(\Q\) None \(4\) \(-9\) \(76\) \(-49\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots\)
42.6.a.f 42.a 1.a $1$ $6.736$ \(\Q\) None \(4\) \(9\) \(24\) \(49\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}+6^{2}q^{6}+\cdots\)
42.6.d.a 42.d 21.c $12$ $6.736$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-252\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-2^{4}q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
42.6.e.a 42.e 7.c $2$ $6.736$ \(\Q(\sqrt{-3}) \) None \(-4\) \(-9\) \(6\) \(119\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots\)
42.6.e.b 42.e 7.c $2$ $6.736$ \(\Q(\sqrt{-3}) \) None \(4\) \(9\) \(-86\) \(49\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}+9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots\)
42.6.e.c 42.e 7.c $4$ $6.736$ \(\Q(\sqrt{-3}, \sqrt{9601})\) None \(-8\) \(18\) \(53\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{2}q^{2}+(9-9\beta _{2})q^{3}+(-2^{4}+2^{4}\beta _{2}+\cdots)q^{4}+\cdots\)
42.6.e.d 42.e 7.c $4$ $6.736$ \(\Q(\sqrt{-3}, \sqrt{505})\) None \(8\) \(-18\) \(-17\) \(-408\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1})q^{2}-9\beta _{1}q^{3}-2^{4}\beta _{1}q^{4}+\cdots\)
42.6.f.a 42.f 21.g $28$ $6.736$ None \(0\) \(0\) \(0\) \(-154\) $\mathrm{SU}(2)[C_{6}]$
42.7.b.a 42.b 3.b $12$ $9.662$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-84\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-7+\beta _{1})q^{3}-2^{5}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
42.7.c.a 42.c 7.b $8$ $9.662$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(-212\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+2^{5}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
42.7.g.a 42.g 7.d $8$ $9.662$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-108\) \(462\) \(580\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(-18+9\beta _{1})q^{3}-2^{5}\beta _{1}q^{4}+\cdots\)
42.7.g.b 42.g 7.d $8$ $9.662$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(108\) \(210\) \(-608\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(9+9\beta _{1})q^{3}+(-2^{5}+2^{5}\beta _{1}+\cdots)q^{4}+\cdots\)
42.7.h.a 42.h 21.h $32$ $9.662$ None \(0\) \(0\) \(0\) \(-1684\) $\mathrm{SU}(2)[C_{6}]$
42.8.a.a 42.a 1.a $1$ $13.120$ \(\Q\) None \(-8\) \(-27\) \(-410\) \(-343\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-410q^{5}+\cdots\)
42.8.a.b 42.a 1.a $1$ $13.120$ \(\Q\) None \(-8\) \(-27\) \(-18\) \(343\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-18q^{5}+6^{3}q^{6}+\cdots\)
42.8.a.c 42.a 1.a $1$ $13.120$ \(\Q\) None \(-8\) \(27\) \(-122\) \(-343\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}-122q^{5}+\cdots\)
42.8.a.d 42.a 1.a $1$ $13.120$ \(\Q\) None \(-8\) \(27\) \(270\) \(343\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+270q^{5}+\cdots\)
42.8.a.e 42.a 1.a $1$ $13.120$ \(\Q\) None \(8\) \(-27\) \(30\) \(343\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+30q^{5}-6^{3}q^{6}+\cdots\)
42.8.a.f 42.a 1.a $1$ $13.120$ \(\Q\) None \(8\) \(27\) \(470\) \(-343\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+470q^{5}+\cdots\)
42.8.d.a 42.d 21.c $20$ $13.120$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(892\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{3}q^{3}-2^{6}q^{4}+\beta _{1}q^{5}+\cdots\)
42.8.e.a 42.e 7.c $2$ $13.120$ \(\Q(\sqrt{-3}) \) None \(8\) \(-27\) \(-165\) \(-343\) $\mathrm{SU}(2)[C_{3}]$ \(q+(8-8\zeta_{6})q^{2}-3^{3}\zeta_{6}q^{3}-2^{6}\zeta_{6}q^{4}+\cdots\)
42.8.e.b 42.e 7.c $2$ $13.120$ \(\Q(\sqrt{-3}) \) None \(8\) \(-27\) \(290\) \(1477\) $\mathrm{SU}(2)[C_{3}]$ \(q+(8-8\zeta_{6})q^{2}-3^{3}\zeta_{6}q^{3}-2^{6}\zeta_{6}q^{4}+\cdots\)
42.8.e.c 42.e 7.c $4$ $13.120$ \(\Q(\sqrt{-3}, \sqrt{2881})\) None \(-16\) \(54\) \(-309\) \(868\) $\mathrm{SU}(2)[C_{3}]$ \(q-8\beta _{1}q^{2}+(3^{3}-3^{3}\beta _{1})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
42.8.e.d 42.e 7.c $6$ $13.120$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-24\) \(-81\) \(70\) \(-895\) $\mathrm{SU}(2)[C_{3}]$ \(q-8\beta _{1}q^{2}+(-3^{3}+3^{3}\beta _{1})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
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