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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
37.2.a.a 37.a 1.a $1$ $0.295$ \(\Q\) None \(-2\) \(-3\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
37.2.a.b 37.a 1.a $1$ $0.295$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)
37.2.b.a 37.b 37.b $2$ $0.295$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-2q^{4}-iq^{5}-iq^{6}+\cdots\)
37.2.c.a 37.c 37.c $2$ $0.295$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
37.2.e.a 37.e 37.e $4$ $0.295$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
37.2.f.a 37.f 37.f $6$ $0.295$ \(\Q(\zeta_{18})\) None \(-6\) \(3\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}^{5})q^{2}+(\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
37.2.f.b 37.f 37.f $6$ $0.295$ \(\Q(\zeta_{18})\) None \(3\) \(-6\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
37.2.h.a 37.h 37.h $18$ $0.295$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-9\) \(-9\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\beta _{4}-\beta _{11})q^{2}+(-1-\beta _{12}+\beta _{16}+\cdots)q^{3}+\cdots\)
37.3.d.a 37.d 37.d $12$ $1.008$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}+\beta _{6})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
37.3.g.a 37.g 37.g $24$ $1.008$ None \(0\) \(-6\) \(-18\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
37.3.i.a 37.i 37.i $60$ $1.008$ None \(-12\) \(-12\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
37.4.a.a 37.a 1.a $4$ $2.183$ 4.4.21208.1 None \(-6\) \(-11\) \(-29\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{2}-\beta _{3})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
37.4.a.b 37.a 1.a $5$ $2.183$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4\) \(13\) \(11\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3-\beta _{2})q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
37.4.b.a 37.b 37.b $8$ $2.183$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-6\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-1-\beta _{3})q^{3}+(-4+\beta _{5}+\cdots)q^{4}+\cdots\)
37.4.c.a 37.c 37.c $18$ $2.183$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(1\) \(3\) \(-25\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-4+\beta _{1}+\cdots)q^{4}+\cdots\)
37.4.e.a 37.e 37.e $16$ $2.183$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-6\) \(-3\) \(18\) \(23\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(2-\beta _{3}-2\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
37.4.f.a 37.f 37.f $54$ $2.183$ None \(-9\) \(-12\) \(6\) \(96\) $\mathrm{SU}(2)[C_{9}]$
37.4.h.a 37.h 37.h $48$ $2.183$ None \(-3\) \(0\) \(-27\) \(-108\) $\mathrm{SU}(2)[C_{18}]$
37.5.d.a 37.d 37.d $22$ $3.825$ None \(4\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
37.5.g.a 37.g 37.g $44$ $3.825$ None \(-10\) \(-6\) \(98\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
37.5.i.a 37.i 37.i $144$ $3.825$ None \(-12\) \(-12\) \(-120\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
37.6.a.a 37.a 1.a $7$ $5.934$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(-47\) \(-64\) \(-293\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+\cdots\)
37.6.a.b 37.a 1.a $8$ $5.934$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(12\) \(25\) \(136\) \(99\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(3-\beta _{5})q^{3}+(20-2\beta _{1}+\cdots)q^{4}+\cdots\)
37.6.b.a 37.b 37.b $16$ $5.934$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-18\) \(0\) \(190\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-17+\beta _{2}+\cdots)q^{4}+\cdots\)
37.6.c.a 37.c 37.c $30$ $5.934$ None \(-4\) \(16\) \(-51\) \(50\) $\mathrm{SU}(2)[C_{3}]$
37.6.e.a 37.e 37.e $32$ $5.934$ None \(-6\) \(18\) \(144\) \(-52\) $\mathrm{SU}(2)[C_{6}]$
37.6.f.a 37.f 37.f $84$ $5.934$ None \(-9\) \(-3\) \(-30\) \(-213\) $\mathrm{SU}(2)[C_{9}]$
37.6.h.a 37.h 37.h $90$ $5.934$ None \(-3\) \(-9\) \(-153\) \(201\) $\mathrm{SU}(2)[C_{18}]$
37.7.d.a 37.d 37.d $36$ $8.512$ None \(-4\) \(0\) \(-256\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
37.7.g.a 37.g 37.g $72$ $8.512$ None \(-2\) \(-6\) \(52\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
37.7.i.a 37.i 37.i $216$ $8.512$ None \(-12\) \(-12\) \(186\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
37.8.a.a 37.a 1.a $10$ $11.558$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-24\) \(-95\) \(-624\) \(-501\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-10+\beta _{1}-\beta _{7}+\cdots)q^{3}+\cdots\)
37.8.a.b 37.a 1.a $11$ $11.558$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(16\) \(121\) \(376\) \(2243\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(11+\beta _{2})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots\)
37.8.b.a 37.b 37.b $20$ $11.558$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(78\) \(0\) \(-1746\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(4+\beta _{4})q^{3}+(-42+\beta _{2}+\cdots)q^{4}+\cdots\)
37.8.c.a 37.c 37.c $42$ $11.558$ None \(-16\) \(-68\) \(-337\) \(-158\) $\mathrm{SU}(2)[C_{3}]$
37.8.e.a 37.e 37.e $40$ $11.558$ None \(18\) \(-42\) \(-672\) \(156\) $\mathrm{SU}(2)[C_{6}]$
37.8.f.a 37.f 37.f $132$ $11.558$ None \(15\) \(33\) \(576\) \(-597\) $\mathrm{SU}(2)[C_{9}]$
37.8.h.a 37.h 37.h $126$ $11.558$ None \(-27\) \(-45\) \(663\) \(585\) $\mathrm{SU}(2)[C_{18}]$
37.9.d.a 37.d 37.d $50$ $15.073$ None \(4\) \(0\) \(124\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
37.9.g.a 37.g 37.g $100$ $15.073$ None \(-10\) \(-6\) \(-1642\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
37.9.i.a 37.i 37.i $288$ $15.073$ None \(-12\) \(-12\) \(1500\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
37.10.a.a 37.a 1.a $13$ $19.056$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-32\) \(-251\) \(-2159\) \(-12576\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-20+\beta _{1}-\beta _{5}+\cdots)q^{3}+\cdots\)
37.10.a.b 37.a 1.a $14$ $19.056$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(48\) \(397\) \(2841\) \(6632\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(28+\beta _{3})q^{3}+(248+5\beta _{1}+\cdots)q^{4}+\cdots\)
37.10.b.a 37.b 37.b $28$ $19.056$ None \(0\) \(-150\) \(0\) \(5940\) $\mathrm{SU}(2)[C_{2}]$
37.10.c.a 37.c 37.c $54$ $19.056$ None \(32\) \(73\) \(2729\) \(4231\) $\mathrm{SU}(2)[C_{3}]$
37.10.e.a 37.e 37.e $56$ $19.056$ None \(-54\) \(-75\) \(-186\) \(-4233\) $\mathrm{SU}(2)[C_{6}]$
37.10.f.a 37.f 37.f $162$ $19.056$ None \(-57\) \(-228\) \(-3420\) \(5808\) $\mathrm{SU}(2)[C_{9}]$
37.10.h.a 37.h 37.h $168$ $19.056$ None \(45\) \(216\) \(177\) \(-5820\) $\mathrm{SU}(2)[C_{18}]$
37.11.d.a 37.d 37.d $60$ $23.508$ None \(-12\) \(0\) \(11094\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
37.11.g.a 37.g 37.g $120$ $23.508$ None \(6\) \(-6\) \(2922\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
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