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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
17.2.a.a 17.a 1.a $1$ $0.136$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a 17.d 17.d $4$ $0.136$ \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
17.3.e.a 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(16\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-24\) \(-16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
17.4.a.a 17.a 1.a $1$ $1.003$ \(\Q\) None \(-3\) \(-8\) \(6\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b 17.a 1.a $3$ $1.003$ 3.3.2636.1 None \(1\) \(4\) \(-8\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
17.4.b.a 17.b 17.b $4$ $1.003$ 4.0.4669632.2 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
17.4.c.a 17.c 17.c $8$ $1.003$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)
17.4.d.a 17.d 17.d $12$ $1.003$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(-4\) \(-20\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
17.5.e.a 17.e 17.e $40$ $1.757$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.6.a.a 17.a 1.a $1$ $2.727$ \(\Q\) None \(-6\) \(10\) \(-72\) \(-196\) $+$ $\mathrm{SU}(2)$ \(q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots\)
17.6.a.b 17.a 1.a $1$ $2.727$ \(\Q\) None \(1\) \(-18\) \(-16\) \(28\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots\)
17.6.a.c 17.a 1.a $4$ $2.727$ 4.4.5416116.1 None \(3\) \(28\) \(80\) \(284\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots\)
17.6.b.a 17.b 17.b $6$ $2.727$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(14+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
17.6.c.a 17.c 17.c $12$ $2.727$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-24\) \(-40\) \(-120\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3}-\beta _{8})q^{3}+\cdots\)
17.6.d.a 17.d 17.d $28$ $2.727$ None \(-4\) \(-4\) \(40\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.7.e.a 17.e 17.e $64$ $3.911$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.8.a.a 17.a 1.a $1$ $5.311$ \(\Q\) None \(-2\) \(18\) \(-10\) \(-902\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots\)
17.8.a.b 17.a 1.a $3$ $5.311$ 3.3.694349.1 None \(1\) \(-86\) \(-198\) \(-1558\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.a.c 17.a 1.a $6$ $5.311$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(-184\) \(2064\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.b.a 17.b 17.b $10$ $5.311$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-18\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{2})q^{2}+\beta _{1}q^{3}+(69-2\beta _{2}+\cdots)q^{4}+\cdots\)
17.8.c.a 17.c 17.c $20$ $5.311$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(24\) \(384\) \(392\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1-\beta _{6}+\beta _{8})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
17.8.d.a 17.d 17.d $36$ $5.311$ None \(-4\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.9.e.a 17.e 17.e $88$ $6.925$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.10.a.a 17.a 1.a $5$ $8.756$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(-236\) \(1480\) \(-13202\) $+$ $\mathrm{SU}(2)$ \(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
17.10.a.b 17.a 1.a $7$ $8.756$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(88\) \(1362\) \(9388\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)
17.10.b.a 17.b 17.b $12$ $8.756$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(30\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots\)
17.10.c.a 17.c 17.c $24$ $8.756$ None \(0\) \(144\) \(-1710\) \(3810\) $\mathrm{SU}(2)[C_{4}]$
17.10.d.a 17.d 17.d $52$ $8.756$ None \(-4\) \(-4\) \(-1140\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.11.e.a 17.e 17.e $112$ $10.801$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.12.a.a 17.a 1.a $6$ $13.062$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-9\) \(-476\) \(-12884\) \(-23436\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots\)
17.12.a.b 17.a 1.a $8$ $13.062$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(55\) \(496\) \(8592\) \(95288\) $+$ $\mathrm{SU}(2)$ \(q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots\)
17.12.b.a 17.b 17.b $16$ $13.062$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1271+\beta _{3})q^{4}+\cdots\)
17.12.c.a 17.c 17.c $32$ $13.062$ None \(0\) \(-528\) \(-15496\) \(-38368\) $\mathrm{SU}(2)[C_{4}]$
17.12.d.a 17.d 17.d $60$ $13.062$ None \(-4\) \(-4\) \(10120\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.13.e.a 17.e 17.e $136$ $15.538$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.14.a.a 17.a 1.a $8$ $18.229$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-65\) \(-1328\) \(15312\) \(-699576\) $+$ $\mathrm{SU}(2)$ \(q+(-8-\beta _{1})q^{2}+(-167+5\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
17.14.a.b 17.a 1.a $10$ $18.229$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(63\) \(1588\) \(-25820\) \(694532\) $-$ $\mathrm{SU}(2)$ \(q+(6+\beta _{1})q^{2}+(158+3\beta _{1}-\beta _{3})q^{3}+\cdots\)
17.14.b.a 17.b 17.b $18$ $18.229$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2710+\beta _{3})q^{4}+\cdots\)
17.14.c.a 17.c 17.c $36$ $18.229$ None \(0\) \(-264\) \(73220\) \(5040\) $\mathrm{SU}(2)[C_{4}]$
17.14.d.a 17.d 17.d $76$ $18.229$ None \(-4\) \(-4\) \(-62720\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.15.e.a 17.e 17.e $160$ $21.136$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.16.a.a 17.a 1.a $9$ $24.258$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-217\) \(-3656\) \(-222858\) \(-8750084\) $-$ $\mathrm{SU}(2)$ \(q+(-24-\beta _{1})q^{2}+(-406-4\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
17.16.a.b 17.a 1.a $11$ $24.258$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(39\) \(5092\) \(59416\) \(1250446\) $+$ $\mathrm{SU}(2)$ \(q+(4-\beta _{1})q^{2}+(462+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
17.16.b.a 17.b 17.b $22$ $24.258$ None \(-258\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
17.16.c.a 17.c 17.c $44$ $24.258$ None \(0\) \(5256\) \(-252126\) \(1854722\) $\mathrm{SU}(2)[C_{4}]$
17.16.d.a 17.d 17.d $84$ $24.258$ None \(-4\) \(-4\) \(311340\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
17.17.e.a 17.e 17.e $184$ $27.595$ None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
17.18.a.a 17.a 1.a $10$ $31.148$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(15\) \(-4760\) \(61880\) \(-19310368\) $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(-475-\beta _{1}+\beta _{3})q^{3}+\cdots\)
17.18.a.b 17.a 1.a $12$ $31.148$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(527\) \(21484\) \(1770512\) \(22379060\) $-$ $\mathrm{SU}(2)$ \(q+(44-\beta _{1})q^{2}+(1790+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
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