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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 11
3850.2.a.a 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.b 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.c 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.d 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.e 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.f 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.g 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.h 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.i 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.j 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.k 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.l 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.m 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.n 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.o 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.p 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.q 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.r 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.s 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.t 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.u 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.v 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.w 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.x 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.y 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.z 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.ba 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bb 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bc 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{33}) \) None \(-2\) \(-4\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bd 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
3850.2.a.be 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bf 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bg 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bh 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bi 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bj 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bk 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bl 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bm 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bn 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bo 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bp 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bq 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.br 3850.a 1.a $3$ $30.742$ 3.3.940.1 None \(-3\) \(-3\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bs 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bt 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
3850.2.a.bu 3850.a 1.a $3$ $30.742$ 3.3.892.1 None \(3\) \(0\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
3850.2.a.bv 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(3\) \(2\) \(0\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bw 3850.a 1.a $3$ $30.742$ 3.3.940.1 None \(3\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bx 3850.a 1.a $4$ $30.742$ 4.4.10304.1 None \(-4\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+q^{7}+\cdots\)
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