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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.1.p.a 72.p 72.p $2$ $0.036$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
72.2.a.a 72.a 1.a $1$ $0.575$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
72.2.d.a 72.d 8.b $2$ $0.575$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-2q^{4}+2\beta q^{5}+2q^{7}-2\beta q^{8}+\cdots\)
72.2.d.b 72.d 8.b $2$ $0.575$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2iq^{4}-2iq^{5}-2q^{7}+\cdots\)
72.2.f.a 72.f 24.f $4$ $0.575$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.2.i.a 72.i 9.c $2$ $0.575$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots\)
72.2.i.b 72.i 9.c $4$ $0.575$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
72.2.l.a 72.l 72.l $4$ $0.575$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
72.2.l.b 72.l 72.l $16$ $0.575$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
72.2.n.a 72.n 72.n $4$ $0.575$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
72.2.n.b 72.n 72.n $16$ $0.575$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)
72.3.b.a 72.b 8.d $1$ $1.962$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+8q^{8}-14q^{11}+2^{4}q^{16}+\cdots\)
72.3.b.b 72.b 8.d $4$ $1.962$ 4.0.4752.1 None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{1}-\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
72.3.b.c 72.b 8.d $4$ $1.962$ \(\Q(\sqrt{-6}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
72.3.e.a 72.e 3.b $2$ $1.962$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots\)
72.3.h.a 72.h 24.h $8$ $1.962$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
72.3.j.a 72.j 72.j $44$ $1.962$ None None \(-3\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
72.3.m.a 72.m 9.d $4$ $1.962$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-12\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
72.3.m.b 72.m 9.d $8$ $1.962$ 8.0.\(\cdots\).9 None None \(0\) \(10\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
72.3.p.a 72.p 72.p $4$ $1.962$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(4\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)
72.3.p.b 72.p 72.p $40$ $1.962$ None None \(-5\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
72.4.a.a 72.a 1.a $1$ $4.248$ \(\Q\) None None \(0\) \(0\) \(-16\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
72.4.a.b 72.a 1.a $1$ $4.248$ \(\Q\) None None \(0\) \(0\) \(-14\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\cdots\)
72.4.a.c 72.a 1.a $1$ $4.248$ \(\Q\) None None \(0\) \(0\) \(2\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\cdots\)
72.4.a.d 72.a 1.a $1$ $4.248$ \(\Q\) None None \(0\) \(0\) \(16\) \(-12\) $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)
72.4.d.a 72.d 8.b $2$ $4.248$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-68\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-8q^{4}-7\beta q^{5}-34q^{7}-8\beta q^{8}+\cdots\)
72.4.d.b 72.d 8.b $2$ $4.248$ \(\Q(\sqrt{-7}) \) None None \(2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{2}+(-6+2\beta )q^{4}+4\beta q^{5}+\cdots\)
72.4.d.c 72.d 8.b $4$ $4.248$ \(\Q(\sqrt{-10}, \sqrt{22})\) None None \(0\) \(0\) \(0\) \(40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(3+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
72.4.d.d 72.d 8.b $6$ $4.248$ 6.0.8248384.1 None None \(-2\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(3+\beta _{5})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.4.f.a 72.f 24.f $12$ $4.248$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.a 72.i 9.c $8$ $4.248$ 8.0.5206055409.1 None None \(0\) \(-3\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.b 72.i 9.c $10$ $4.248$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(4\) \(-5\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
72.4.l.a 72.l 72.l $4$ $4.248$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{1}q^{2}+(-5+\beta _{1}+5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
72.4.l.b 72.l 72.l $64$ $4.248$ None None \(-3\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
72.4.n.a 72.n 72.n $68$ $4.248$ None None \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
72.5.b.a 72.b 8.d $1$ $7.443$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+46q^{11}+\cdots\)
72.5.b.b 72.b 8.d $2$ $7.443$ \(\Q(\sqrt{-15}) \) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{2}+(-14+2\beta )q^{4}-8\beta q^{5}+\cdots\)
72.5.b.c 72.b 8.d $8$ $7.443$ 8.0.\(\cdots\).5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(3-\beta _{4})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
72.5.b.d 72.b 8.d $8$ $7.443$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots\)
72.5.e.a 72.e 3.b $2$ $7.443$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-120\) $\mathrm{SU}(2)[C_{2}]$ \(q+11\beta q^{5}-60q^{7}+44\beta q^{11}-176q^{13}+\cdots\)
72.5.e.b 72.e 3.b $2$ $7.443$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(72\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}+6^{2}q^{7}+116\beta q^{11}+304q^{13}+\cdots\)
72.5.h.a 72.h 24.h $16$ $7.443$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{4}+\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
72.5.j.a 72.j 72.j $92$ $7.443$ None None \(-3\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
72.5.m.a 72.m 9.d $24$ $7.443$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
72.5.p.a 72.p 72.p $4$ $7.443$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(-8\) \(14\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-4\beta _{2}q^{2}+(\beta _{1}+7\beta _{2}-\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
72.5.p.b 72.p 72.p $88$ $7.443$ None None \(7\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
72.6.a.a 72.a 1.a $1$ $11.548$ \(\Q\) None None \(0\) \(0\) \(-94\) \(144\) $-$ $\mathrm{SU}(2)$ \(q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots\)
72.6.a.b 72.a 1.a $1$ $11.548$ \(\Q\) None None \(0\) \(0\) \(-38\) \(120\) $+$ $\mathrm{SU}(2)$ \(q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots\)
72.6.a.c 72.a 1.a $1$ $11.548$ \(\Q\) None None \(0\) \(0\) \(-16\) \(12\) $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots\)
72.6.a.d 72.a 1.a $1$ $11.548$ \(\Q\) None None \(0\) \(0\) \(16\) \(12\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots\)
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