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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 11
4851.2.a.a 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.b 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.c 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.d 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.e 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.f 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.g 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots\)
4851.2.a.h 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{5}-q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.i 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{5}+q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.j 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.k 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.l 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{5}-q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.m 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{5}+q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.n 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.o 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.p 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
4851.2.a.q 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
4851.2.a.r 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{11}-5q^{13}-4q^{16}+\cdots\)
4851.2.a.s 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{11}+5q^{13}-4q^{16}+\cdots\)
4851.2.a.t 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots\)
4851.2.a.u 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.v 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.w 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
4851.2.a.x 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.y 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}-2q^{5}-\beta q^{8}+2\beta q^{10}+\cdots\)
4851.2.a.z 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.ba 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{21}) \) None \(1\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3+\beta )q^{4}+3q^{5}+(5+2\beta )q^{8}+\cdots\)
4851.2.a.bb 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bc 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bd 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.be 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.bf 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+(1+4\beta )q^{8}+\cdots\)
4851.2.a.bg 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bh 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
4851.2.a.bi 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(-2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bj 4851.a 1.a $3$ $38.735$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2-\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bk 4851.a 1.a $3$ $38.735$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2+\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bl 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4851.2.a.bm 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bn 4851.a 1.a $3$ $38.735$ 3.3.257.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bo 4851.a 1.a $3$ $38.735$ 3.3.257.1 None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bp 4851.a 1.a $3$ $38.735$ 3.3.837.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bq 4851.a 1.a $4$ $38.735$ 4.4.725.1 None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.br 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bs 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bt 4851.a 1.a $4$ $38.735$ 4.4.11344.1 None \(-2\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bu 4851.a 1.a $4$ $38.735$ 4.4.11344.1 None \(-2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bv 4851.a 1.a $4$ $38.735$ 4.4.9248.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bw 4851.a 1.a $4$ $38.735$ 4.4.725.1 None \(2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bx 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(2\) \(0\) \(-8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
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