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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.2.a.a 45.a 1.a $1$ $0.359$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+4q^{11}+\cdots\)
45.2.b.a 45.b 5.b $2$ $0.359$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots\)
45.2.e.a 45.e 9.c $2$ $0.359$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
45.2.e.b 45.e 9.c $6$ $0.359$ 6.0.954288.1 None \(-1\) \(1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots\)
45.2.f.a 45.f 15.e $4$ $0.359$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
45.2.j.a 45.j 45.j $8$ $0.359$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{5}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{3}q^{4}+\cdots\)
45.2.l.a 45.l 45.l $16$ $0.359$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-6\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{5}q^{2}+(-1+\beta _{9}-\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots\)
45.3.c.a 45.c 3.b $4$ $1.226$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(-3-2\beta _{3})q^{4}+\cdots\)
45.3.d.a 45.d 15.d $4$ $1.226$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+3q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
45.3.g.a 45.g 5.c $4$ $1.226$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots\)
45.3.g.b 45.g 5.c $4$ $1.226$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
45.3.h.a 45.h 45.h $20$ $1.226$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
45.3.i.a 45.i 9.d $16$ $1.226$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(-\beta _{7}+\beta _{11})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
45.3.k.a 45.k 45.k $40$ $1.226$ None \(-2\) \(-6\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
45.4.a.a 45.a 1.a $1$ $2.655$ \(\Q\) None \(-5\) \(0\) \(5\) \(-30\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+5q^{5}-30q^{7}-45q^{8}+\cdots\)
45.4.a.b 45.a 1.a $1$ $2.655$ \(\Q\) None \(-3\) \(0\) \(5\) \(20\) $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+20q^{7}+21q^{8}+\cdots\)
45.4.a.c 45.a 1.a $1$ $2.655$ \(\Q\) None \(-1\) \(0\) \(-5\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}-24q^{7}+15q^{8}+\cdots\)
45.4.a.d 45.a 1.a $1$ $2.655$ \(\Q\) None \(4\) \(0\) \(5\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}+5q^{5}+6q^{7}+20q^{10}+\cdots\)
45.4.a.e 45.a 1.a $1$ $2.655$ \(\Q\) None \(5\) \(0\) \(-5\) \(-30\) $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+17q^{4}-5q^{5}-30q^{7}+45q^{8}+\cdots\)
45.4.b.a 45.b 5.b $2$ $2.655$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+3q^{4}+5\beta q^{5}+11\beta q^{8}-5^{2}q^{10}+\cdots\)
45.4.b.b 45.b 5.b $4$ $2.655$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
45.4.e.a 45.e 9.c $4$ $2.655$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(1\) \(-6\) \(-10\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
45.4.e.b 45.e 9.c $6$ $2.655$ 6.0.15759792.1 None \(1\) \(9\) \(-15\) \(43\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}+(1+\beta _{2}-\beta _{5})q^{3}+\cdots\)
45.4.e.c 45.e 9.c $14$ $2.655$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(-5\) \(35\) \(-22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(\beta _{7}-\beta _{10})q^{3}+(-5+\cdots)q^{4}+\cdots\)
45.4.f.a 45.f 15.e $12$ $2.655$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}+(-6\beta _{1}+\beta _{5})q^{4}+(\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots\)
45.4.j.a 45.j 45.j $32$ $2.655$ None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
45.4.l.a 45.l 45.l $64$ $2.655$ None \(-6\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
45.5.c.a 45.c 3.b $4$ $4.652$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-48\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-7-2\beta _{3})q^{4}+5\beta _{2}q^{5}+\cdots\)
45.5.d.a 45.d 15.d $8$ $4.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(5+\beta _{2})q^{4}+(2\beta _{3}+\beta _{5})q^{5}+\cdots\)
45.5.g.a 45.g 5.c $2$ $4.652$ \(\Q(\sqrt{-1}) \) None \(-10\) \(0\) \(50\) \(80\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-5-5i)q^{2}+34iq^{4}+5^{2}q^{5}+\cdots\)
45.5.g.b 45.g 5.c $2$ $4.652$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-40\) \(-52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}-14iq^{4}+(-20-15i)q^{5}+\cdots\)
45.5.g.c 45.g 5.c $2$ $4.652$ \(\Q(\sqrt{-1}) \) None \(10\) \(0\) \(-50\) \(80\) $\mathrm{SU}(2)[C_{4}]$ \(q+(5+5i)q^{2}+34iq^{4}-5^{2}q^{5}+(40+\cdots)q^{7}+\cdots\)
45.5.g.d 45.g 5.c $4$ $4.652$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-11\beta _{2}q^{4}+(2\beta _{1}-11\beta _{3})q^{5}+\cdots\)
45.5.g.e 45.g 5.c $8$ $4.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(84\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(\beta _{1}-12\beta _{2}+\beta _{3}+\beta _{5})q^{4}+\cdots\)
45.5.h.a 45.h 45.h $44$ $4.652$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
45.5.i.a 45.i 9.d $32$ $4.652$ None \(0\) \(-8\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{6}]$
45.5.k.a 45.k 45.k $88$ $4.652$ None \(-2\) \(6\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
45.6.a.a 45.a 1.a $1$ $7.217$ \(\Q\) None \(-7\) \(0\) \(25\) \(12\) $+$ $\mathrm{SU}(2)$ \(q-7q^{2}+17q^{4}+5^{2}q^{5}+12q^{7}+105q^{8}+\cdots\)
45.6.a.b 45.a 1.a $1$ $7.217$ \(\Q\) None \(-2\) \(0\) \(-25\) \(192\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-28q^{4}-5^{2}q^{5}+192q^{7}+\cdots\)
45.6.a.c 45.a 1.a $1$ $7.217$ \(\Q\) None \(2\) \(0\) \(25\) \(-132\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-28q^{4}+5^{2}q^{5}-132q^{7}+\cdots\)
45.6.a.d 45.a 1.a $2$ $7.217$ \(\Q(\sqrt{145}) \) None \(-5\) \(0\) \(-50\) \(80\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+(8+5\beta )q^{4}-5^{2}q^{5}+\cdots\)
45.6.a.e 45.a 1.a $2$ $7.217$ \(\Q(\sqrt{409}) \) None \(1\) \(0\) \(-50\) \(-112\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(70+\beta )q^{4}-5^{2}q^{5}+(-2^{6}+\cdots)q^{7}+\cdots\)
45.6.a.f 45.a 1.a $2$ $7.217$ \(\Q(\sqrt{145}) \) None \(5\) \(0\) \(50\) \(80\) $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{2}+(13-5\beta )q^{4}+5^{2}q^{5}+\cdots\)
45.6.b.a 45.b 5.b $2$ $7.217$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots\)
45.6.b.b 45.b 5.b $2$ $7.217$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
45.6.b.c 45.b 5.b $4$ $7.217$ \(\Q(i, \sqrt{89})\) None \(0\) \(0\) \(-120\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots\)
45.6.b.d 45.b 5.b $4$ $7.217$ \(\Q(\sqrt{-5}, \sqrt{-14})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
45.6.e.a 45.e 9.c $18$ $7.217$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-4\) \(33\) \(225\) \(167\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{9})q^{3}+(-11+\cdots)q^{4}+\cdots\)
45.6.e.b 45.e 9.c $22$ $7.217$ None \(-4\) \(-11\) \(-275\) \(-225\) $\mathrm{SU}(2)[C_{3}]$
45.6.f.a 45.f 15.e $20$ $7.217$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(152\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{13}q^{2}+(-14\beta _{2}+\beta _{4})q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots\)
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