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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.2.d.a 25.d 25.d $4$ $0.200$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
25.2.e.a 25.e 25.e $8$ $0.200$ 8.0.58140625.2 None \(-5\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)
25.3.c.a 25.c 5.c $4$ $0.681$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)
25.3.f.a 25.f 25.f $32$ $0.681$ None \(-10\) \(-10\) \(-10\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
25.4.a.a 25.a 1.a $1$ $1.475$ \(\Q\) None \(-1\) \(-7\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b 25.a 1.a $1$ $1.475$ \(\Q\) None \(1\) \(7\) \(0\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c 25.a 1.a $1$ $1.475$ \(\Q\) None \(4\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)
25.4.b.a 25.b 5.b $2$ $1.475$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-8q^{4}-8q^{6}-3iq^{7}+\cdots\)
25.4.b.b 25.b 5.b $2$ $1.475$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-7iq^{3}+7q^{4}+7q^{6}+6iq^{7}+\cdots\)
25.4.d.a 25.d 25.d $28$ $1.475$ None \(-1\) \(-7\) \(-20\) \(-16\) $\mathrm{SU}(2)[C_{5}]$
25.4.e.a 25.e 25.e $24$ $1.475$ None \(-5\) \(-5\) \(15\) \(0\) $\mathrm{SU}(2)[C_{10}]$
25.5.c.a 25.c 5.c $2$ $2.584$ \(\Q(\sqrt{-1}) \) None \(2\) \(12\) \(0\) \(52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+(6-6i)q^{3}-14iq^{4}+\cdots\)
25.5.c.b 25.c 5.c $4$ $2.584$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+3\beta _{1}q^{2}+7\beta _{3}q^{3}+11\beta _{2}q^{4}-63q^{6}+\cdots\)
25.5.c.c 25.c 5.c $4$ $2.584$ \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+42q^{6}+\cdots\)
25.5.f.a 25.f 25.f $72$ $2.584$ None \(-8\) \(2\) \(-50\) \(42\) $\mathrm{SU}(2)[C_{20}]$
25.6.a.a 25.a 1.a $1$ $4.010$ \(\Q\) None \(-2\) \(4\) \(0\) \(-192\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots\)
25.6.a.b 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{241}) \) None \(-5\) \(-20\) \(0\) \(-200\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
25.6.a.c 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{11}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots\)
25.6.a.d 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{241}) \) None \(5\) \(20\) \(0\) \(200\) $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots\)
25.6.b.a 25.b 5.b $2$ $4.010$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}+28q^{4}-8q^{6}+96iq^{7}+\cdots\)
25.6.b.b 25.b 5.b $4$ $4.010$ \(\Q(i, \sqrt{241})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
25.6.d.a 25.d 25.d $44$ $4.010$ None \(-7\) \(-1\) \(115\) \(-202\) $\mathrm{SU}(2)[C_{5}]$
25.6.e.a 25.e 25.e $48$ $4.010$ None \(-5\) \(-5\) \(-60\) \(0\) $\mathrm{SU}(2)[C_{10}]$
25.7.c.a 25.c 5.c $2$ $5.751$ \(\Q(\sqrt{-1}) \) None \(-6\) \(66\) \(0\) \(414\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-3-3i)q^{2}+(33-33i)q^{3}-46iq^{4}+\cdots\)
25.7.c.b 25.c 5.c $2$ $5.751$ \(\Q(\sqrt{-1}) \) None \(6\) \(-66\) \(0\) \(-414\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3+3i)q^{2}+(-33+33i)q^{3}-46iq^{4}+\cdots\)
25.7.c.c 25.c 5.c $4$ $5.751$ \(\Q(i, \sqrt{201})\) None \(10\) \(-30\) \(0\) \(-550\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-3\beta _{1}+\beta _{3})q^{2}+(-8-7\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.7.c.d 25.c 5.c $8$ $5.751$ 8.0.\(\cdots\).23 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+(4\beta _{4}+3\beta _{5})q^{3}+(22\beta _{1}+\cdots)q^{4}+\cdots\)
25.7.f.a 25.f 25.f $112$ $5.751$ None \(0\) \(-40\) \(60\) \(-560\) $\mathrm{SU}(2)[C_{20}]$
25.8.a.a 25.a 1.a $1$ $7.810$ \(\Q\) None \(14\) \(48\) \(0\) \(1644\) $+$ $\mathrm{SU}(2)$ \(q+14q^{2}+48q^{3}+68q^{4}+672q^{6}+\cdots\)
25.8.a.b 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{19}) \) None \(-20\) \(-20\) \(0\) \(100\) $+$ $\mathrm{SU}(2)$ \(q+(-10+\beta )q^{2}+(-10-8\beta )q^{3}+(48+\cdots)q^{4}+\cdots\)
25.8.a.c 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{649}) \) None \(-15\) \(-40\) \(0\) \(600\) $-$ $\mathrm{SU}(2)$ \(q+(-7-\beta )q^{2}+(-19-2\beta )q^{3}+(83+\cdots)q^{4}+\cdots\)
25.8.a.d 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{29}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3\beta q^{3}-12q^{4}-348q^{6}+\cdots\)
25.8.a.e 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{649}) \) None \(15\) \(40\) \(0\) \(-600\) $+$ $\mathrm{SU}(2)$ \(q+(8-\beta )q^{2}+(21-2\beta )q^{3}+(98-15\beta )q^{4}+\cdots\)
25.8.b.a 25.b 5.b $2$ $7.810$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+7iq^{2}-24iq^{3}-68q^{4}+672q^{6}+\cdots\)
25.8.b.b 25.b 5.b $4$ $7.810$ \(\Q(i, \sqrt{649})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+2\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2})q^{3}+\cdots\)
25.8.b.c 25.b 5.b $4$ $7.810$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+8\beta _{3})q^{3}+(-48+\cdots)q^{4}+\cdots\)
25.8.d.a 25.d 25.d $68$ $7.810$ None \(-11\) \(23\) \(475\) \(1734\) $\mathrm{SU}(2)[C_{5}]$
25.8.e.a 25.e 25.e $64$ $7.810$ None \(-5\) \(-5\) \(-510\) \(0\) $\mathrm{SU}(2)[C_{10}]$
25.9.c.a 25.c 5.c $4$ $10.184$ \(\Q(i, \sqrt{141})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots\)
25.9.c.b 25.c 5.c $6$ $10.184$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2\) \(72\) \(0\) \(2352\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\)
25.9.c.c 25.c 5.c $12$ $10.184$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots\)
25.9.f.a 25.f 25.f $152$ $10.184$ None \(-8\) \(62\) \(-230\) \(2342\) $\mathrm{SU}(2)[C_{20}]$
25.10.a.a 25.a 1.a $1$ $12.876$ \(\Q\) None \(8\) \(114\) \(0\) \(-4242\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+114q^{3}-448q^{4}+912q^{6}+\cdots\)
25.10.a.b 25.a 1.a $2$ $12.876$ \(\Q(\sqrt{1009}) \) None \(10\) \(-260\) \(0\) \(-1700\) $+$ $\mathrm{SU}(2)$ \(q+(5-\beta )q^{2}+(-130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
25.10.a.c 25.a 1.a $3$ $12.876$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-33\) \(-89\) \(0\) \(-5258\) $+$ $\mathrm{SU}(2)$ \(q+(-11-\beta _{1})q^{2}+(-30-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
25.10.a.d 25.a 1.a $3$ $12.876$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(33\) \(89\) \(0\) \(5258\) $-$ $\mathrm{SU}(2)$ \(q+(11+\beta _{1})q^{2}+(30+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
25.10.a.e 25.a 1.a $4$ $12.876$ 4.4.49740556.1 None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(342-\beta _{3})q^{4}+\cdots\)
25.10.b.a 25.b 5.b $2$ $12.876$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{2}-57iq^{3}+448q^{4}+912q^{6}+\cdots\)
25.10.b.b 25.b 5.b $4$ $12.876$ \(\Q(i, \sqrt{1009})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}+14\beta _{2}+\cdots)q^{3}+\cdots\)
25.10.b.c 25.b 5.b $6$ $12.876$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-2\beta _{2}-\beta _{4})q^{3}+(-114+\cdots)q^{4}+\cdots\)
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