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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3864.1.v.a 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(-1\) \(-1\) \(-1\) \(-1\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
3864.1.v.b 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
3864.1.v.c 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(-1\) \(1\) \(-1\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
3864.1.v.d 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(-1\) \(1\) \(1\) \(1\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
3864.1.v.e 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(1\) \(-1\) \(-1\) \(1\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
3864.1.v.f 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(1\) \(-1\) \(1\) \(-1\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
3864.1.v.g 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(1\) \(1\) \(-1\) \(1\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
3864.1.v.h 3864.v 3864.v $1$ $1.928$ \(\Q\) \(\Q(\sqrt{-966}) \) None 3864.1.v.a \(1\) \(1\) \(1\) \(-1\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
3864.1.v.i 3864.v 3864.v $4$ $1.928$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None 3864.1.v.i \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)
3864.1.v.j 3864.v 3864.v $4$ $1.928$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None 3864.1.v.i \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)
3864.1.bx.a 3864.bx 3864.ax $2$ $1.928$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-138}) \) None 3864.1.bx.a \(-1\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots\)
3864.1.bx.b 3864.bx 3864.ax $2$ $1.928$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-138}) \) None 3864.1.bx.a \(-1\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots\)
3864.1.bx.c 3864.bx 3864.ax $2$ $1.928$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-138}) \) None 3864.1.bx.a \(1\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots\)
3864.1.bx.d 3864.bx 3864.ax $2$ $1.928$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-138}) \) None 3864.1.bx.a \(1\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots\)
3864.1.bx.e 3864.bx 3864.ax $4$ $1.928$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-138}) \) None 3864.1.bx.e \(-2\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3864.1.bx.f 3864.bx 3864.ax $4$ $1.928$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-138}) \) None 3864.1.bx.e \(2\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3864.1.cx.a 3864.cx 3864.bx $40$ $1.928$ \(\Q(\zeta_{88})\) \(\Q(\sqrt{-14}) \) None 3864.1.cx.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{88}^{42}q^{2}-\zeta_{88}^{23}q^{3}-\zeta_{88}^{40}q^{4}+\cdots\)
3864.1.cx.b 3864.cx 3864.bx $40$ $1.928$ \(\Q(\zeta_{88})\) \(\Q(\sqrt{-14}) \) None 3864.1.cx.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{88}^{6}q^{2}-\zeta_{88}^{11}q^{3}+\zeta_{88}^{12}q^{4}+\cdots\)
3864.1.dl.a 3864.dl 3864.cl $10$ $1.928$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-42}) \) None 3864.1.dl.a \(-1\) \(-1\) \(0\) \(-1\) \(q-\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)
3864.1.dl.b 3864.dl 3864.cl $10$ $1.928$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-42}) \) None 3864.1.dl.a \(-1\) \(1\) \(0\) \(1\) \(q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)
3864.1.dl.c 3864.dl 3864.cl $10$ $1.928$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-42}) \) None 3864.1.dl.a \(1\) \(-1\) \(0\) \(1\) \(q+\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)
3864.1.dl.d 3864.dl 3864.cl $10$ $1.928$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-42}) \) None 3864.1.dl.a \(1\) \(1\) \(0\) \(-1\) \(q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots\)
3864.2.a.a 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.a \(0\) \(-1\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{13}+3q^{15}+\cdots\)
3864.2.a.b 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.b \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
3864.2.a.c 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.c \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+q^{11}-6q^{13}+7q^{19}+\cdots\)
3864.2.a.d 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.d \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots\)
3864.2.a.e 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.e \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
3864.2.a.f 3864.a 1.a $1$ $30.854$ \(\Q\) None None 3864.2.a.f \(0\) \(1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots\)
3864.2.a.g 3864.a 1.a $2$ $30.854$ \(\Q(\sqrt{41}) \) None None 3864.2.a.g \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-\beta q^{11}+2q^{13}+\cdots\)
3864.2.a.h 3864.a 1.a $2$ $30.854$ \(\Q(\sqrt{29}) \) None None 3864.2.a.h \(0\) \(-2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+5q^{11}+(1+\cdots)q^{13}+\cdots\)
3864.2.a.i 3864.a 1.a $2$ $30.854$ \(\Q(\sqrt{33}) \) None None 3864.2.a.i \(0\) \(-2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
3864.2.a.j 3864.a 1.a $2$ $30.854$ \(\Q(\sqrt{5}) \) None None 3864.2.a.j \(0\) \(2\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-3+2\beta )q^{11}+\cdots\)
3864.2.a.k 3864.a 1.a $3$ $30.854$ 3.3.621.1 None None 3864.2.a.k \(0\) \(-3\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+q^{7}+q^{9}+\cdots\)
3864.2.a.l 3864.a 1.a $3$ $30.854$ 3.3.229.1 None None 3864.2.a.l \(0\) \(-3\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.m 3864.a 1.a $3$ $30.854$ 3.3.837.1 None None 3864.2.a.m \(0\) \(-3\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.n 3864.a 1.a $3$ $30.854$ 3.3.1229.1 None None 3864.2.a.n \(0\) \(-3\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.o 3864.a 1.a $3$ $30.854$ 3.3.733.1 None None 3864.2.a.o \(0\) \(3\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
3864.2.a.p 3864.a 1.a $3$ $30.854$ 3.3.229.1 None None 3864.2.a.p \(0\) \(3\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
3864.2.a.q 3864.a 1.a $3$ $30.854$ 3.3.229.1 None None 3864.2.a.q \(0\) \(3\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{2}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.r 3864.a 1.a $4$ $30.854$ 4.4.2225.1 None None 3864.2.a.r \(0\) \(-4\) \(-3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{3})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
3864.2.a.s 3864.a 1.a $4$ $30.854$ 4.4.75645.1 None None 3864.2.a.s \(0\) \(-4\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.t 3864.a 1.a $4$ $30.854$ 4.4.39605.1 None None 3864.2.a.t \(0\) \(4\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
3864.2.a.u 3864.a 1.a $4$ $30.854$ 4.4.256549.1 None None 3864.2.a.u \(0\) \(4\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
3864.2.a.v 3864.a 1.a $5$ $30.854$ 5.5.17679757.1 None None 3864.2.a.v \(0\) \(5\) \(-6\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3864.2.a.w 3864.a 1.a $6$ $30.854$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None 3864.2.a.w \(0\) \(-6\) \(2\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{3}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
3864.2.a.x 3864.a 1.a $6$ $30.854$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None 3864.2.a.x \(0\) \(6\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{5}q^{5}-q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)
3864.2.u.a 3864.u 161.c $4$ $30.854$ \(\Q(i, \sqrt{5})\) None None 3864.2.u.a \(0\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-2-\beta _{2})q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
3864.2.u.b 3864.u 161.c $4$ $30.854$ \(\Q(i, \sqrt{5})\) None None 3864.2.u.a \(0\) \(0\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(2+\beta _{2})q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3864.2.u.c 3864.u 161.c $8$ $30.854$ 8.0.2992527616.3 None None 3864.2.u.c \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}-q^{9}+\cdots\)
3864.2.u.d 3864.u 161.c $8$ $30.854$ 8.0.342102016.5 None None 3864.2.u.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{4}+\beta _{6})q^{7}+\cdots\)
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