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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5220.2.a.a 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.f \(0\) \(0\) \(-1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-5q^{7}-5q^{11}-5q^{13}-7q^{17}+\cdots\)
5220.2.a.b 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.g \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
5220.2.a.c 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.b \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{11}-2q^{13}+4q^{17}+\cdots\)
5220.2.a.d 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.d \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+q^{11}-2q^{17}-2q^{19}+\cdots\)
5220.2.a.e 5220.a 1.a $1$ $41.682$ \(\Q\) None 580.2.a.b \(0\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}-6q^{13}+4q^{17}+\cdots\)
5220.2.a.f 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.f \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots\)
5220.2.a.g 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.h \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}+2q^{13}+4q^{19}+\cdots\)
5220.2.a.h 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.c \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+4q^{11}+2q^{13}+8q^{17}+\cdots\)
5220.2.a.i 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.d \(0\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-3q^{11}+3q^{13}-q^{17}+\cdots\)
5220.2.a.j 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.j \(0\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+q^{11}-5q^{13}+3q^{17}+\cdots\)
5220.2.a.k 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.d \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-q^{11}+2q^{17}-2q^{19}+\cdots\)
5220.2.a.l 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.e \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots\)
5220.2.a.m 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.f \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots\)
5220.2.a.n 5220.a 1.a $1$ $41.682$ \(\Q\) None 580.2.a.a \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}-2q^{13}-2q^{19}+8q^{23}+\cdots\)
5220.2.a.o 5220.a 1.a $1$ $41.682$ \(\Q\) None 1740.2.a.a \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+6q^{11}+6q^{13}-4q^{17}+2q^{19}+\cdots\)
5220.2.a.p 5220.a 1.a $1$ $41.682$ \(\Q\) None 5220.2.a.j \(0\) \(0\) \(1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-q^{11}-5q^{13}-3q^{17}+\cdots\)
5220.2.a.q 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{17}) \) None 1740.2.a.k \(0\) \(0\) \(-2\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2-\beta )q^{7}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
5220.2.a.r 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{57}) \) None 1740.2.a.n \(0\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+(2-\beta )q^{11}+2q^{13}+\cdots\)
5220.2.a.s 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{33}) \) None 1740.2.a.i \(0\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(-2-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
5220.2.a.t 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{33}) \) None 1740.2.a.l \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+(-2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
5220.2.a.u 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{17}) \) None 1740.2.a.m \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2\beta q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots\)
5220.2.a.v 5220.a 1.a $2$ $41.682$ \(\Q(\sqrt{17}) \) None 1740.2.a.j \(0\) \(0\) \(2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
5220.2.a.w 5220.a 1.a $3$ $41.682$ 3.3.148.1 None 580.2.a.d \(0\) \(0\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1-\beta _{2})q^{7}+(-1+\beta _{2})q^{11}+\cdots\)
5220.2.a.x 5220.a 1.a $3$ $41.682$ 3.3.564.1 None 580.2.a.c \(0\) \(0\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta _{2})q^{7}+(-3-\beta _{2})q^{11}+\cdots\)
5220.2.a.y 5220.a 1.a $7$ $41.682$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 5220.2.a.y \(0\) \(0\) \(-7\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta _{2}q^{7}-\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots\)
5220.2.a.z 5220.a 1.a $7$ $41.682$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 5220.2.a.y \(0\) \(0\) \(7\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta _{2}q^{7}+\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots\)
5220.2.b.a 5220.b 145.d $4$ $41.682$ \(\Q(\sqrt{-5}, \sqrt{-29})\) \(\Q(\sqrt{-435}) \) 5220.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{11}+(-3\beta _{1}+\cdots)q^{23}+\cdots\)
5220.2.b.b 5220.b 145.d $4$ $41.682$ \(\Q(\sqrt{-5}, \sqrt{-29})\) \(\Q(\sqrt{-435}) \) 5220.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{11}+(3\beta _{1}+\beta _{2}+\cdots)q^{23}+\cdots\)
5220.2.b.c 5220.b 145.d $14$ $41.682$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 1740.2.b.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{9}q^{7}-\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots\)
5220.2.b.d 5220.b 145.d $14$ $41.682$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 1740.2.b.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{9}q^{7}+\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots\)
5220.2.b.e 5220.b 145.d $16$ $41.682$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 580.2.f.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{5}+\beta _{10}q^{7}+\beta _{8}q^{11}+\beta _{4}q^{13}+\cdots\)
5220.2.b.f 5220.b 145.d $24$ $41.682$ None 5220.2.b.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
5220.2.g.a 5220.g 5.b $2$ $41.682$ \(\Q(\sqrt{-1}) \) None 1740.2.g.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}+2iq^{7}-5q^{11}+4iq^{17}+\cdots\)
5220.2.g.b 5220.g 5.b $2$ $41.682$ \(\Q(\sqrt{-1}) \) None 1740.2.g.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-i)q^{5}+2iq^{7}+q^{11}-4iq^{13}+\cdots\)
5220.2.g.c 5220.g 5.b $4$ $41.682$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 580.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
5220.2.g.d 5220.g 5.b $10$ $41.682$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 580.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{5}+(\beta _{1}-\beta _{8}-\beta _{9})q^{7}+(\beta _{2}-\beta _{7}+\cdots)q^{11}+\cdots\)
5220.2.g.e 5220.g 5.b $12$ $41.682$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1740.2.g.d \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{5}-\beta _{5}q^{7}+(-\beta _{8}+\beta _{9}+\beta _{10}+\cdots)q^{11}+\cdots\)
5220.2.g.f 5220.g 5.b $12$ $41.682$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1740.2.g.c \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}-\beta _{8}q^{7}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
5220.2.g.g 5220.g 5.b $14$ $41.682$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 5220.2.g.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}-\beta _{12}q^{13}+\cdots\)
5220.2.g.h 5220.g 5.b $14$ $41.682$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 5220.2.g.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{5}+\beta _{4}q^{7}-\beta _{6}q^{11}-\beta _{12}q^{13}+\cdots\)
5220.2.l.a 5220.l 29.b $2$ $41.682$ \(\Q(\sqrt{-1}) \) None 1740.2.l.a \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+q^{7}-3iq^{11}+7q^{13}-7iq^{17}+\cdots\)
5220.2.l.b 5220.l 29.b $2$ $41.682$ \(\Q(\sqrt{-1}) \) None 1740.2.l.b \(0\) \(0\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+4q^{7}+3iq^{11}-2iq^{17}+2iq^{19}+\cdots\)
5220.2.l.c 5220.l 29.b $2$ $41.682$ \(\Q(\sqrt{-7}) \) None 580.2.d.a \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}-2q^{7}-\beta q^{11}-2q^{13}+\beta q^{19}+\cdots\)
5220.2.l.d 5220.l 29.b $4$ $41.682$ \(\Q(\sqrt{-2}, \sqrt{11})\) None 580.2.d.c \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+(-1+\beta _{3})q^{7}-\beta _{1}q^{11}+(-2\beta _{1}+\cdots)q^{17}+\cdots\)
5220.2.l.e 5220.l 29.b $4$ $41.682$ \(\Q(\sqrt{-5}, \sqrt{-13})\) None 5220.2.l.e \(0\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+(1-\beta _{3})q^{7}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
5220.2.l.f 5220.l 29.b $4$ $41.682$ \(\Q(\sqrt{-5}, \sqrt{-13})\) None 5220.2.l.e \(0\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}+(1-\beta _{3})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
5220.2.l.g 5220.l 29.b $4$ $41.682$ 4.0.7168.1 None 580.2.d.b \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}+(2+\beta _{3})q^{7}-\beta _{2}q^{11}+4\beta _{3}q^{13}+\cdots\)
5220.2.l.h 5220.l 29.b $6$ $41.682$ 6.0.399424.1 None 1740.2.l.c \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+(-1-\beta _{2})q^{7}+(-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)
5220.2.l.i 5220.l 29.b $6$ $41.682$ 6.0.16516096.2 None 5220.2.l.i \(0\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{4})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
5220.2.l.j 5220.l 29.b $6$ $41.682$ 6.0.16516096.2 None 5220.2.l.i \(0\) \(0\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{4})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
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