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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.2.a.a 32.a 1.a $1$ $0.256$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)
32.2.g.a 32.g 32.g $4$ $0.256$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b 32.g 32.g $8$ $0.256$ 8.0.18939904.2 None \(-4\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
32.3.c.a 32.c 4.b $2$ $0.872$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{5}-2iq^{7}-7q^{9}-iq^{11}+\cdots\)
32.3.d.a 32.d 8.d $1$ $0.872$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{3}-5q^{9}-14q^{11}+2q^{17}+34q^{19}+\cdots\)
32.3.h.a 32.h 32.h $28$ $0.872$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.4.a.a 32.a 1.a $1$ $1.888$ \(\Q\) None \(0\) \(-8\) \(-10\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q-8q^{3}-10q^{5}-2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
32.4.a.b 32.a 1.a $1$ $1.888$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(22\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+22q^{5}-3^{3}q^{9}-18q^{13}-94q^{17}+\cdots\)
32.4.a.c 32.a 1.a $1$ $1.888$ \(\Q\) None \(0\) \(8\) \(-10\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+8q^{3}-10q^{5}+2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)
32.4.b.a 32.b 8.b $2$ $1.888$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}-2\beta q^{5}+8q^{7}-q^{9}+3\beta q^{11}+\cdots\)
32.4.g.a 32.g 32.g $44$ $1.888$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.5.c.a 32.c 4.b $2$ $3.308$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-76\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-38q^{5}+2iq^{7}-63q^{9}+\cdots\)
32.5.c.b 32.c 4.b $2$ $3.308$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(52\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+26q^{5}+22iq^{7}+65q^{9}+\cdots\)
32.5.d.a 32.d 8.d $1$ $3.308$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+14q^{3}+115q^{9}+46q^{11}-574q^{17}+\cdots\)
32.5.d.b 32.d 8.d $2$ $3.308$ \(\Q(\sqrt{-15}) \) None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-6q^{3}-\beta q^{5}-2\beta q^{7}-45q^{9}+26q^{11}+\cdots\)
32.5.h.a 32.h 32.h $60$ $3.308$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.6.a.a 32.a 1.a $1$ $5.132$ \(\Q\) None \(0\) \(-8\) \(14\) \(-208\) $+$ $\mathrm{SU}(2)$ \(q-8q^{3}+14q^{5}-208q^{7}-179q^{9}+\cdots\)
32.6.a.b 32.a 1.a $1$ $5.132$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-82\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots\)
32.6.a.c 32.a 1.a $1$ $5.132$ \(\Q\) None \(0\) \(8\) \(14\) \(208\) $-$ $\mathrm{SU}(2)$ \(q+8q^{3}+14q^{5}+208q^{7}-179q^{9}+\cdots\)
32.6.a.d 32.a 1.a $2$ $5.132$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(92\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+46q^{5}-6\beta q^{7}+525q^{9}+\cdots\)
32.6.b.a 32.b 8.b $4$ $5.132$ 4.0.218489.1 None \(0\) \(0\) \(0\) \(-96\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-24-\beta _{3})q^{7}+\cdots\)
32.6.g.a 32.g 32.g $76$ $5.132$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.7.c.a 32.c 4.b $2$ $7.362$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(100\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+50q^{5}+46iq^{7}+713q^{9}+\cdots\)
32.7.c.b 32.c 4.b $4$ $7.362$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-56\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-14-\beta _{3})q^{5}+(2\beta _{1}-5\beta _{2}+\cdots)q^{7}+\cdots\)
32.7.d.a 32.d 8.d $1$ $7.362$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(-46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-46q^{3}+1387q^{9}+2338q^{11}-1726q^{17}+\cdots\)
32.7.d.b 32.d 8.d $4$ $7.362$ 4.0.3803625.2 None \(0\) \(48\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(12-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
32.7.h.a 32.h 32.h $92$ $7.362$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.8.a.a 32.a 1.a $1$ $9.996$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-58\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-58q^{5}-3^{7}q^{9}-8898q^{13}-40094q^{17}+\cdots\)
32.8.a.b 32.a 1.a $2$ $9.996$ \(\Q(\sqrt{10}) \) None \(0\) \(-16\) \(-180\) \(1248\) $+$ $\mathrm{SU}(2)$ \(q+(-8+\beta )q^{3}+(-90+8\beta )q^{5}+(624+\cdots)q^{7}+\cdots\)
32.8.a.c 32.a 1.a $2$ $9.996$ \(\Q(\sqrt{15}) \) None \(0\) \(0\) \(140\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+70q^{5}+18\beta q^{7}+1653q^{9}+\cdots\)
32.8.a.d 32.a 1.a $2$ $9.996$ \(\Q(\sqrt{10}) \) None \(0\) \(16\) \(-180\) \(-1248\) $-$ $\mathrm{SU}(2)$ \(q+(8+\beta )q^{3}+(-90-8\beta )q^{5}+(-624+\cdots)q^{7}+\cdots\)
32.8.b.a 32.b 8.b $6$ $9.996$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(688\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(115+\beta _{1}+\cdots)q^{7}+\cdots\)
32.8.g.a 32.g 32.g $108$ $9.996$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.9.c.a 32.c 4.b $4$ $13.036$ \(\Q(i, \sqrt{39})\) None \(0\) \(0\) \(-728\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(-182+\beta _{2})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots\)
32.9.c.b 32.c 4.b $4$ $13.036$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(1064\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(266+3\beta _{2})q^{5}+(-7\beta _{1}+\cdots)q^{7}+\cdots\)
32.9.d.a 32.d 8.d $1$ $13.036$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(-34\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-34q^{3}-5405q^{9}+27166q^{11}+\cdots\)
32.9.d.b 32.d 8.d $6$ $13.036$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(6+\beta _{1})q^{3}-\beta _{2}q^{5}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
32.9.h.a 32.h 32.h $124$ $13.036$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.10.a.a 32.a 1.a $1$ $16.481$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2398\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+2398q^{5}-3^{9}q^{9}+112806q^{13}+\cdots\)
32.10.a.b 32.a 1.a $2$ $16.481$ \(\Q(\sqrt{106}) \) None \(0\) \(-176\) \(1404\) \(-2784\) $+$ $\mathrm{SU}(2)$ \(q+(-88+\beta )q^{3}+(702-8\beta )q^{5}+(-1392+\cdots)q^{7}+\cdots\)
32.10.a.c 32.a 1.a $2$ $16.481$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4420\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2210q^{5}-42\beta q^{7}+26397q^{9}+\cdots\)
32.10.a.d 32.a 1.a $2$ $16.481$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-68\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-34q^{5}-86\beta q^{7}-3555q^{9}+\cdots\)
32.10.a.e 32.a 1.a $2$ $16.481$ \(\Q(\sqrt{106}) \) None \(0\) \(176\) \(1404\) \(2784\) $-$ $\mathrm{SU}(2)$ \(q+(88+\beta )q^{3}+(702+8\beta )q^{5}+(1392+\cdots)q^{7}+\cdots\)
32.10.b.a 32.b 8.b $8$ $16.481$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(-4800\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-600-\beta _{3}+\cdots)q^{7}+\cdots\)
32.10.g.a 32.g 32.g $140$ $16.481$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
32.11.c.a 32.c 4.b $4$ $20.331$ \(\Q(i, \sqrt{30})\) None \(0\) \(0\) \(-1400\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}+(-350-\beta _{3})q^{5}+\cdots\)
32.11.c.b 32.c 4.b $6$ $20.331$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-1716\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-286+\beta _{2})q^{5}+(58\beta _{1}+\cdots)q^{7}+\cdots\)
32.11.d.a 32.d 8.d $1$ $20.331$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(482\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+482q^{3}+173275q^{9}+97426q^{11}+\cdots\)
32.11.d.b 32.d 8.d $8$ $20.331$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-480\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-60+\beta _{1})q^{3}+\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
32.11.h.a 32.h 32.h $156$ $20.331$ None \(-4\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
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