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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4056.2.a.a 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{9}+2q^{11}+4q^{15}+\cdots\)
4056.2.a.b 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(-3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
4056.2.a.c 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots\)
4056.2.a.d 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots\)
4056.2.a.e 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots\)
4056.2.a.f 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+2q^{11}-6q^{17}+\cdots\)
4056.2.a.g 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{15}+\cdots\)
4056.2.a.h 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots\)
4056.2.a.i 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{15}+\cdots\)
4056.2.a.j 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(-1\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
4056.2.a.k 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
4056.2.a.l 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots\)
4056.2.a.m 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{15}+2q^{17}+\cdots\)
4056.2.a.n 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
4056.2.a.o 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-6q^{11}+2q^{17}+4q^{23}+\cdots\)
4056.2.a.p 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
4056.2.a.q 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots\)
4056.2.a.r 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
4056.2.a.s 4056.a 1.a $1$ $32.387$ \(\Q\) None \(0\) \(1\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
4056.2.a.t 4056.a 1.a $2$ $32.387$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4056.2.a.u 4056.a 1.a $2$ $32.387$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
4056.2.a.v 4056.a 1.a $2$ $32.387$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4056.2.a.w 4056.a 1.a $2$ $32.387$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4056.2.a.x 4056.a 1.a $3$ $32.387$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4056.2.a.y 4056.a 1.a $3$ $32.387$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots\)
4056.2.a.z 4056.a 1.a $3$ $32.387$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4056.2.a.ba 4056.a 1.a $3$ $32.387$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
4056.2.a.bb 4056.a 1.a $3$ $32.387$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4056.2.a.bc 4056.a 1.a $3$ $32.387$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4056.2.a.bd 4056.a 1.a $4$ $32.387$ 4.4.25488.1 None \(0\) \(4\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
4056.2.a.be 4056.a 1.a $4$ $32.387$ 4.4.25488.1 None \(0\) \(4\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
4056.2.a.bf 4056.a 1.a $6$ $32.387$ 6.6.27700337.1 None \(0\) \(-6\) \(-1\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)
4056.2.a.bg 4056.a 1.a $6$ $32.387$ 6.6.27700337.1 None \(0\) \(-6\) \(1\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4056.2.a.bh 4056.a 1.a $6$ $32.387$ 6.6.27700337.1 None \(0\) \(6\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
4056.2.a.bi 4056.a 1.a $6$ $32.387$ 6.6.27700337.1 None \(0\) \(6\) \(1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
4056.2.c.a 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}-6iq^{11}+\cdots\)
4056.2.c.b 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+3iq^{5}+4iq^{7}+q^{9}-4iq^{11}+\cdots\)
4056.2.c.c 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+2iq^{7}+q^{9}-iq^{15}+\cdots\)
4056.2.c.d 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+q^{9}+iq^{11}-2iq^{15}+\cdots\)
4056.2.c.e 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+q^{9}+2iq^{11}-iq^{15}+\cdots\)
4056.2.c.f 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{7}+q^{9}+iq^{11}+6q^{17}+\cdots\)
4056.2.c.g 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+q^{9}+3iq^{11}-2q^{17}-4q^{23}+\cdots\)
4056.2.c.h 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}+q^{9}+iq^{15}-2q^{17}+\cdots\)
4056.2.c.i 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+3iq^{5}+q^{9}+3iq^{15}+q^{17}+\cdots\)
4056.2.c.j 4056.c 13.b $2$ $32.387$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}-2iq^{7}+q^{9}-iq^{11}+\cdots\)
4056.2.c.k 4056.c 13.b $4$ $32.387$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{12}^{2}q^{5}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
4056.2.c.l 4056.c 13.b $4$ $32.387$ \(\Q(i, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
4056.2.c.m 4056.c 13.b $6$ $32.387$ 6.0.44836416.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+q^{9}+\cdots\)
4056.2.c.n 4056.c 13.b $6$ $32.387$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(\beta _{3}+\beta _{5})q^{5}+(-2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
4056.2.c.o 4056.c 13.b $6$ $32.387$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
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