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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.2.a.a 74.a 1.a $2$ $0.591$ \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
74.2.a.b 74.a 1.a $2$ $0.591$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
74.2.b.a 74.b 37.b $4$ $0.591$ \(\Q(i, \sqrt{21})\) None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
74.2.c.a 74.c 37.c $2$ $0.591$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
74.2.c.b 74.c 37.c $2$ $0.591$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
74.2.c.c 74.c 37.c $6$ $0.591$ 6.0.4406832.1 None \(-3\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots\)
74.2.e.a 74.e 37.e $4$ $0.591$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
74.2.e.b 74.e 37.e $4$ $0.591$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(6\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
74.2.f.a 74.f 37.f $6$ $0.591$ \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(3\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
74.2.f.b 74.f 37.f $12$ $0.591$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)
74.2.h.a 74.h 37.h $12$ $0.591$ \(\Q(\zeta_{36})\) None \(0\) \(6\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{18}]$ \(q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots\)
74.3.d.a 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-12\) \(10\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-6+6i)q^{5}+\cdots\)
74.3.d.b 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+4iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.c 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}-3iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.d 74.d 37.d $4$ $2.016$ \(\Q(i, \sqrt{65})\) None \(-4\) \(0\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}-2\beta _{1}q^{4}+\cdots\)
74.3.g.a 74.g 37.g $8$ $2.016$ 8.0.303595776.1 None \(4\) \(0\) \(12\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(2\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
74.3.g.b 74.g 37.g $12$ $2.016$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{4}-\beta _{7})q^{2}-\beta _{3}q^{3}+2\beta _{6}q^{4}+(1+\cdots)q^{5}+\cdots\)
74.3.i.a 74.i 37.i $36$ $2.016$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{36}]$
74.3.i.b 74.i 37.i $48$ $2.016$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
74.4.a.a 74.a 1.a $1$ $4.366$ \(\Q\) None \(-2\) \(-5\) \(12\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}+4q^{4}+12q^{5}+10q^{6}+\cdots\)
74.4.a.b 74.a 1.a $1$ $4.366$ \(\Q\) None \(2\) \(-5\) \(-14\) \(-19\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-5q^{3}+4q^{4}-14q^{5}-10q^{6}+\cdots\)
74.4.a.c 74.a 1.a $3$ $4.366$ 3.3.15629.1 None \(-6\) \(4\) \(7\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots\)
74.4.a.d 74.a 1.a $4$ $4.366$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(21\) \(23\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(5+\beta _{2}+\cdots)q^{5}+\cdots\)
74.4.b.a 74.b 37.b $10$ $4.366$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(14\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(1-\beta _{2})q^{3}-4q^{4}+(2\beta _{5}+\cdots)q^{5}+\cdots\)
74.4.c.a 74.c 37.c $8$ $4.366$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-5\) \(-10\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-4\beta _{2}q^{4}+\cdots\)
74.4.c.b 74.c 37.c $10$ $4.366$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(-5\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)
74.4.e.a 74.e 37.e $20$ $4.366$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-2\) \(-18\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{2}+\beta _{14}q^{3}+4\beta _{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
74.4.f.a 74.f 37.f $24$ $4.366$ None \(0\) \(6\) \(-9\) \(-75\) $\mathrm{SU}(2)[C_{9}]$
74.4.f.b 74.f 37.f $30$ $4.366$ None \(0\) \(6\) \(-6\) \(-75\) $\mathrm{SU}(2)[C_{9}]$
74.4.h.a 74.h 37.h $60$ $4.366$ None \(0\) \(-12\) \(18\) \(150\) $\mathrm{SU}(2)[C_{18}]$
74.5.d.a 74.d 37.d $14$ $7.649$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-28\) \(0\) \(-12\) \(48\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}-8\beta _{5}q^{4}+\cdots\)
74.5.d.b 74.d 37.d $14$ $7.649$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(28\) \(0\) \(36\) \(-48\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+8\beta _{5}q^{4}+\cdots\)
74.5.g.a 74.g 37.g $28$ $7.649$ None \(-28\) \(0\) \(42\) \(48\) $\mathrm{SU}(2)[C_{12}]$
74.5.g.b 74.g 37.g $28$ $7.649$ None \(28\) \(0\) \(-102\) \(-48\) $\mathrm{SU}(2)[C_{12}]$
74.5.i.a 74.i 37.i $72$ $7.649$ None \(0\) \(0\) \(-78\) \(0\) $\mathrm{SU}(2)[C_{36}]$
74.5.i.b 74.i 37.i $72$ $7.649$ None \(0\) \(0\) \(114\) \(0\) $\mathrm{SU}(2)[C_{36}]$
74.6.a.a 74.a 1.a $1$ $11.868$ \(\Q\) None \(4\) \(-15\) \(4\) \(15\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-15q^{3}+2^{4}q^{4}+4q^{5}-60q^{6}+\cdots\)
74.6.a.b 74.a 1.a $1$ $11.868$ \(\Q\) None \(4\) \(7\) \(-84\) \(-139\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+7q^{3}+2^{4}q^{4}-84q^{5}+28q^{6}+\cdots\)
74.6.a.c 74.a 1.a $3$ $11.868$ 3.3.324233.1 None \(-12\) \(-8\) \(-42\) \(84\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3+\beta _{1}-\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
74.6.a.d 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(19\) \(-67\) \(182\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(4+\beta _{2})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots\)
74.6.a.e 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(19\) \(95\) \(170\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(4-\beta _{1})q^{3}+2^{4}q^{4}+(19+\beta _{2}+\cdots)q^{5}+\cdots\)
74.6.b.a 74.b 37.b $14$ $11.868$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(14\) \(0\) \(-312\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{2}+(1+\beta _{2})q^{3}-2^{4}q^{4}+(\beta _{9}+\cdots)q^{5}+\cdots\)
74.6.c.a 74.c 37.c $14$ $11.868$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-28\) \(-8\) \(57\) \(188\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots\)
74.6.c.b 74.c 37.c $16$ $11.868$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(-8\) \(70\) \(-32\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4+4\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2^{4}\beta _{3}q^{4}+\cdots\)
74.6.e.a 74.e 37.e $28$ $11.868$ None \(0\) \(-20\) \(-90\) \(-156\) $\mathrm{SU}(2)[C_{6}]$
74.6.f.a 74.f 37.f $48$ $11.868$ None \(0\) \(-3\) \(-72\) \(114\) $\mathrm{SU}(2)[C_{9}]$
74.6.f.b 74.f 37.f $54$ $11.868$ None \(0\) \(-3\) \(39\) \(114\) $\mathrm{SU}(2)[C_{9}]$
74.6.h.a 74.h 37.h $96$ $11.868$ None \(0\) \(6\) \(90\) \(-228\) $\mathrm{SU}(2)[C_{18}]$
74.7.d.a 74.d 37.d $18$ $17.024$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(72\) \(0\) \(294\) \(-104\) $\mathrm{SU}(2)[C_{4}]$ \(q+(4-4\beta _{6})q^{2}+(\beta _{1}-4\beta _{6})q^{3}-2^{5}\beta _{6}q^{4}+\cdots\)
74.7.d.b 74.d 37.d $20$ $17.024$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-80\) \(0\) \(60\) \(104\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-4-4\beta _{6})q^{2}+(-\beta _{1}+3\beta _{6})q^{3}+\cdots\)
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