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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1550.2.a.a 1550.a 1.a $1$ $12.377$ \(\Q\) None 310.2.a.b \(-1\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
1550.2.a.b 1550.a 1.a $1$ $12.377$ \(\Q\) None 1550.2.a.b \(-1\) \(0\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-5q^{7}-q^{8}-3q^{9}+5q^{11}+\cdots\)
1550.2.a.c 1550.a 1.a $1$ $12.377$ \(\Q\) None 62.2.a.a \(-1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{13}+q^{16}+\cdots\)
1550.2.a.d 1550.a 1.a $1$ $12.377$ \(\Q\) None 1550.2.a.d \(-1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
1550.2.a.e 1550.a 1.a $1$ $12.377$ \(\Q\) None 310.2.a.a \(-1\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+4q^{7}-q^{8}+\cdots\)
1550.2.a.f 1550.a 1.a $1$ $12.377$ \(\Q\) None 1550.2.a.d \(1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
1550.2.a.g 1550.a 1.a $1$ $12.377$ \(\Q\) None 1550.2.a.b \(1\) \(0\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+5q^{7}+q^{8}-3q^{9}+5q^{11}+\cdots\)
1550.2.a.h 1550.a 1.a $2$ $12.377$ \(\Q(\sqrt{3}) \) None 62.2.a.b \(2\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1550.2.a.i 1550.a 1.a $2$ $12.377$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(2\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+2q^{7}+q^{8}+\cdots\)
1550.2.a.j 1550.a 1.a $2$ $12.377$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(2\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1550.2.a.k 1550.a 1.a $3$ $12.377$ 3.3.148.1 None 310.2.a.e \(-3\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
1550.2.a.l 1550.a 1.a $3$ $12.377$ 3.3.564.1 None 1550.2.a.l \(-3\) \(-2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
1550.2.a.m 1550.a 1.a $3$ $12.377$ 3.3.564.1 None 1550.2.a.l \(3\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
1550.2.a.n 1550.a 1.a $4$ $12.377$ 4.4.11344.1 None 310.2.b.b \(-4\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
1550.2.a.o 1550.a 1.a $4$ $12.377$ 4.4.6224.1 None 310.2.b.a \(-4\) \(4\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots\)
1550.2.a.p 1550.a 1.a $4$ $12.377$ 4.4.6224.1 None 310.2.b.a \(4\) \(-4\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots\)
1550.2.a.q 1550.a 1.a $4$ $12.377$ 4.4.11344.1 None 310.2.b.b \(4\) \(2\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
1550.2.a.r 1550.a 1.a $5$ $12.377$ 5.5.12203472.1 None 1550.2.a.r \(-5\) \(-1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1550.2.a.s 1550.a 1.a $5$ $12.377$ 5.5.12203472.1 None 1550.2.a.r \(5\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1-\beta _{4})q^{7}+\cdots\)
1550.2.b.a 1550.b 5.b $2$ $12.377$ \(\Q(\sqrt{-1}) \) None 310.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-4iq^{7}+\cdots\)
1550.2.b.b 1550.b 5.b $2$ $12.377$ \(\Q(\sqrt{-1}) \) None 1550.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
1550.2.b.c 1550.b 5.b $2$ $12.377$ \(\Q(\sqrt{-1}) \) None 62.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2iq^{13}+\cdots\)
1550.2.b.d 1550.b 5.b $2$ $12.377$ \(\Q(\sqrt{-1}) \) None 1550.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-5iq^{7}+iq^{8}+3q^{9}+\cdots\)
1550.2.b.e 1550.b 5.b $2$ $12.377$ \(\Q(\sqrt{-1}) \) None 310.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
1550.2.b.f 1550.b 5.b $4$ $12.377$ \(\Q(\zeta_{12})\) None 62.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1550.2.b.g 1550.b 5.b $4$ $12.377$ \(\Q(i, \sqrt{6})\) None 310.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
1550.2.b.h 1550.b 5.b $4$ $12.377$ \(\Q(\zeta_{12})\) None 310.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1550.2.b.i 1550.b 5.b $6$ $12.377$ 6.0.5089536.1 None 1550.2.a.l \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{4})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
1550.2.b.j 1550.b 5.b $6$ $12.377$ 6.0.350464.1 None 310.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
1550.2.b.k 1550.b 5.b $10$ $12.377$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 1550.2.a.r \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1550.2.e.a 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.a \(-2\) \(-2\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-2+2\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{6}+\cdots\)
1550.2.e.b 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.b \(-2\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1+\zeta_{6})q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots\)
1550.2.e.c 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.c \(-2\) \(2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(2-2\zeta_{6})q^{3}+q^{4}+(-2+2\zeta_{6})q^{6}+\cdots\)
1550.2.e.d 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 62.2.c.b \(-2\) \(3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(3-3\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{6}+\cdots\)
1550.2.e.e 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.c \(2\) \(-2\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-2+2\zeta_{6})q^{3}+q^{4}+(-2+\cdots)q^{6}+\cdots\)
1550.2.e.f 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.b \(2\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(1-\zeta_{6})q^{7}+q^{8}+3\zeta_{6}q^{9}+\cdots\)
1550.2.e.g 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 62.2.c.a \(2\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{6}+\cdots\)
1550.2.e.h 1550.e 31.c $2$ $12.377$ \(\Q(\sqrt{-3}) \) None 1550.2.e.a \(2\) \(2\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(2-2\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{6}+\cdots\)
1550.2.e.i 1550.e 31.c $4$ $12.377$ \(\Q(\sqrt{-3}, \sqrt{13})\) None 1550.2.e.i \(-4\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(2-2\beta _{1}+\cdots)q^{7}+\cdots\)
1550.2.e.j 1550.e 31.c $4$ $12.377$ \(\Q(\sqrt{-3}, \sqrt{13})\) None 1550.2.e.i \(4\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots\)
1550.2.e.k 1550.e 31.c $6$ $12.377$ 6.0.771147.1 None 310.2.e.d \(-6\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
1550.2.e.l 1550.e 31.c $6$ $12.377$ 6.0.309123.1 None 310.2.e.c \(-6\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{1}+\beta _{5})q^{3}+q^{4}+(\beta _{1}-\beta _{5})q^{6}+\cdots\)
1550.2.e.m 1550.e 31.c $6$ $12.377$ 6.0.49572675.1 None 310.2.e.b \(6\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1550.2.e.n 1550.e 31.c $6$ $12.377$ 6.0.309123.1 None 310.2.e.a \(6\) \(1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1550.2.e.o 1550.e 31.c $10$ $12.377$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 1550.2.e.o \(-10\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
1550.2.e.p 1550.e 31.c $10$ $12.377$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 1550.2.e.o \(10\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1550.2.e.q 1550.e 31.c $16$ $12.377$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 310.2.k.a \(-16\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
1550.2.e.r 1550.e 31.c $16$ $12.377$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 310.2.k.a \(16\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{13}q^{7}+\cdots\)
1550.2.f.a 1550.f 155.f $16$ $12.377$ 16.0.\(\cdots\).7 None 1550.2.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}-\beta _{11}q^{3}+\beta _{10}q^{4}+\beta _{12}q^{6}+\cdots\)
1550.2.f.b 1550.f 155.f $32$ $12.377$ None 310.2.f.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
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