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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.2.a.a 49.a 1.a $1$ $0.391$ \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\cdots\)
49.2.c.a 49.c 7.c $2$ $0.391$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)
49.2.e.a 49.e 49.e $6$ $0.391$ \(\Q(\zeta_{14})\) None \(-3\) \(-3\) \(6\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
49.2.e.b 49.e 49.e $12$ $0.391$ \(\Q(\zeta_{21})\) None \(-2\) \(0\) \(-7\) \(-7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots\)
49.2.g.a 49.g 49.g $48$ $0.391$ None \(-13\) \(-14\) \(-14\) \(-14\) $\mathrm{SU}(2)[C_{21}]$
49.3.b.a 49.b 7.b $4$ $1.335$ 4.0.2048.2 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)
49.3.d.a 49.d 7.d $2$ $1.335$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}-3q^{8}+\cdots\)
49.3.d.b 49.d 7.d $8$ $1.335$ 8.0.339738624.1 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+2\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
49.3.f.a 49.f 49.f $54$ $1.335$ None \(-5\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
49.3.h.a 49.h 49.h $96$ $1.335$ None \(-13\) \(-14\) \(-14\) \(-14\) $\mathrm{SU}(2)[C_{42}]$
49.4.a.a 49.a 1.a $1$ $2.891$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-5\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-5q^{2}+17q^{4}-45q^{8}-3^{3}q^{9}-68q^{11}+\cdots\)
49.4.a.b 49.a 1.a $1$ $2.891$ \(\Q\) None \(-1\) \(2\) \(-16\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
49.4.a.c 49.a 1.a $1$ $2.891$ \(\Q\) None \(2\) \(-7\) \(-7\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-7q^{3}-4q^{4}-7q^{5}-14q^{6}+\cdots\)
49.4.a.d 49.a 1.a $1$ $2.891$ \(\Q\) None \(2\) \(7\) \(7\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}-4q^{4}+7q^{5}+14q^{6}+\cdots\)
49.4.a.e 49.a 1.a $4$ $2.891$ \(\Q(\sqrt{2}, \sqrt{65})\) None \(2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(9+\beta _{1})q^{4}+\cdots\)
49.4.c.a 49.c 7.c $2$ $2.891$ \(\Q(\sqrt{-3}) \) None \(-2\) \(7\) \(7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(7-7\zeta_{6})q^{3}+(4-4\zeta_{6})q^{4}+\cdots\)
49.4.c.b 49.c 7.c $2$ $2.891$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(16\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.c 49.c 7.c $2$ $2.891$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.d 49.c 7.c $2$ $2.891$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-45q^{8}+\cdots\)
49.4.c.e 49.c 7.c $8$ $2.891$ 8.0.\(\cdots\).19 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots\)
49.4.e.a 49.e 49.e $78$ $2.891$ None \(-5\) \(-5\) \(-23\) \(0\) $\mathrm{SU}(2)[C_{7}]$
49.4.g.a 49.g 49.g $156$ $2.891$ None \(-13\) \(-7\) \(-7\) \(-42\) $\mathrm{SU}(2)[C_{21}]$
49.5.b.a 49.b 7.b $4$ $5.065$ \(\Q(\sqrt{-3}, \sqrt{22})\) None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{1})q^{2}+\beta _{2}q^{3}+(10+4\beta _{1})q^{4}+\cdots\)
49.5.b.b 49.b 7.b $8$ $5.065$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{2})q^{2}-\beta _{3}q^{3}+(8+\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)
49.5.d.a 49.d 7.d $2$ $5.065$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots\)
49.5.d.b 49.d 7.d $4$ $5.065$ \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(-6\) \(30\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(-2+\beta _{1}+\cdots)q^{3}+\cdots\)
49.5.d.c 49.d 7.d $16$ $5.065$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{2}+\beta _{12})q^{2}+\beta _{5}q^{3}+(5\beta _{2}+\cdots)q^{4}+\cdots\)
49.5.f.a 49.f 49.f $102$ $5.065$ None \(-5\) \(-7\) \(-7\) \(-56\) $\mathrm{SU}(2)[C_{14}]$
49.5.h.a 49.h 49.h $216$ $5.065$ None \(-13\) \(-20\) \(16\) \(-14\) $\mathrm{SU}(2)[C_{42}]$
49.6.a.a 49.a 1.a $1$ $7.859$ \(\Q\) None \(-10\) \(14\) \(56\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-10q^{2}+14q^{3}+68q^{4}+56q^{5}+\cdots\)
49.6.a.b 49.a 1.a $1$ $7.859$ \(\Q\) \(\Q(\sqrt{-7}) \) \(11\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+11q^{2}+89q^{4}+627q^{8}-3^{5}q^{9}+\cdots\)
49.6.a.c 49.a 1.a $2$ $7.859$ \(\Q(\sqrt{39}) \) None \(-4\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta q^{3}-28q^{4}+3\beta q^{5}-2\beta q^{6}+\cdots\)
49.6.a.d 49.a 1.a $2$ $7.859$ \(\Q(\sqrt{37}) \) None \(2\) \(-8\) \(-38\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(6+2\beta )q^{4}+\cdots\)
49.6.a.e 49.a 1.a $2$ $7.859$ \(\Q(\sqrt{37}) \) None \(2\) \(8\) \(38\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(4+\beta )q^{3}+(6+2\beta )q^{4}+\cdots\)
49.6.a.f 49.a 1.a $2$ $7.859$ \(\Q(\sqrt{57}) \) None \(9\) \(6\) \(18\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(5-\beta )q^{2}+(6-6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
49.6.a.g 49.a 1.a $4$ $7.859$ \(\Q(\sqrt{2}, \sqrt{113})\) None \(-10\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(2\beta _{2}-\beta _{3})q^{3}-5\beta _{1}q^{4}+\cdots\)
49.6.c.a 49.c 7.c $2$ $7.859$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(-11\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-11\zeta_{6}q^{2}+(-89+89\zeta_{6})q^{4}+627q^{8}+\cdots\)
49.6.c.b 49.c 7.c $2$ $7.859$ \(\Q(\sqrt{-3}) \) None \(10\) \(-14\) \(-56\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+10\zeta_{6}q^{2}+(-14+14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots\)
49.6.c.c 49.c 7.c $2$ $7.859$ \(\Q(\sqrt{-3}) \) None \(10\) \(14\) \(56\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+10\zeta_{6}q^{2}+(14-14\zeta_{6})q^{3}+(-68+\cdots)q^{4}+\cdots\)
49.6.c.d 49.c 7.c $4$ $7.859$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-9\) \(-6\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(-6-6\beta _{1}+\cdots)q^{3}+\cdots\)
49.6.c.e 49.c 7.c $4$ $7.859$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-9\) \(6\) \(18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(5\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(6+6\beta _{1}-6\beta _{3})q^{3}+\cdots\)
49.6.c.f 49.c 7.c $4$ $7.859$ \(\Q(\sqrt{-3}, \sqrt{37})\) None \(-2\) \(-8\) \(-38\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(-4+4\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
49.6.c.g 49.c 7.c $4$ $7.859$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{1})q^{2}+\beta _{2}q^{3}+28\beta _{1}q^{4}+\cdots\)
49.6.c.h 49.c 7.c $8$ $7.859$ 8.0.\(\cdots\).19 None \(10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-2\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{3}+\cdots\)
49.6.e.a 49.e 49.e $138$ $7.859$ None \(-5\) \(13\) \(67\) \(-56\) $\mathrm{SU}(2)[C_{7}]$
49.6.g.a 49.g 49.g $264$ $7.859$ None \(-13\) \(-22\) \(-52\) \(154\) $\mathrm{SU}(2)[C_{21}]$
49.7.b.a 49.b 7.b $2$ $11.273$ \(\Q(\sqrt{-3}) \) None \(-24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-12q^{2}-\zeta_{6}q^{3}+80q^{4}-15\zeta_{6}q^{5}+\cdots\)
49.7.b.b 49.b 7.b $4$ $11.273$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(4+\beta _{1})q^{2}+(6\beta _{2}-\beta _{3})q^{3}+(-30+\cdots)q^{4}+\cdots\)
49.7.b.c 49.b 7.b $12$ $11.273$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{1})q^{2}+\beta _{3}q^{3}+(47-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
49.7.d.a 49.d 7.d $2$ $11.273$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(-9\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-9\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-423q^{8}+\cdots\)
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