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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3762.2.a.a 3762.a 1.a $1$ $30.040$ \(\Q\) None 3762.2.a.a \(-1\) \(0\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
3762.2.a.b 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.k \(-1\) \(0\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+2q^{7}-q^{8}+3q^{10}+\cdots\)
3762.2.a.c 3762.a 1.a $1$ $30.040$ \(\Q\) None 418.2.a.b \(-1\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots\)
3762.2.a.d 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.j \(-1\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
3762.2.a.e 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.h \(-1\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
3762.2.a.f 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.i \(-1\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-4q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.a.g 3762.a 1.a $1$ $30.040$ \(\Q\) None 418.2.a.a \(-1\) \(0\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.a.h 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.g \(-1\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
3762.2.a.i 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.f \(-1\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
3762.2.a.j 3762.a 1.a $1$ $30.040$ \(\Q\) None 418.2.a.c \(-1\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.a.k 3762.a 1.a $1$ $30.040$ \(\Q\) None 3762.2.a.k \(-1\) \(0\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-q^{11}+\cdots\)
3762.2.a.l 3762.a 1.a $1$ $30.040$ \(\Q\) None 3762.2.a.k \(1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots\)
3762.2.a.m 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.c \(1\) \(0\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots\)
3762.2.a.n 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.b \(1\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{11}-4q^{14}+\cdots\)
3762.2.a.o 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.e \(1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}+q^{11}-4q^{13}+\cdots\)
3762.2.a.p 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.d \(1\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
3762.2.a.q 3762.a 1.a $1$ $30.040$ \(\Q\) None 3762.2.a.a \(1\) \(0\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots\)
3762.2.a.r 3762.a 1.a $1$ $30.040$ \(\Q\) None 1254.2.a.a \(1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}-q^{11}+\cdots\)
3762.2.a.s 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{21}) \) None 418.2.a.f \(-2\) \(0\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
3762.2.a.t 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{5}) \) None 1254.2.a.o \(-2\) \(0\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+(3-\beta )q^{7}+\cdots\)
3762.2.a.u 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{3}) \) None 3762.2.a.u \(-2\) \(0\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-3-\beta )q^{7}-q^{8}-q^{11}+\cdots\)
3762.2.a.v 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{5}) \) None 1254.2.a.n \(-2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+2q^{7}-q^{8}+\cdots\)
3762.2.a.w 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{6}) \) None 3762.2.a.w \(-2\) \(0\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-\beta q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.a.x 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{6}) \) None 3762.2.a.w \(2\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+\beta q^{7}+q^{8}-2q^{10}+\cdots\)
3762.2.a.y 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{17}) \) None 418.2.a.e \(2\) \(0\) \(-4\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
3762.2.a.z 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{33}) \) None 1254.2.a.l \(2\) \(0\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{5}-2q^{7}+q^{8}+\cdots\)
3762.2.a.ba 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{3}) \) None 3762.2.a.u \(2\) \(0\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-3+\beta )q^{7}+q^{8}+q^{11}+\cdots\)
3762.2.a.bb 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{13}) \) None 418.2.a.d \(2\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(-1+\beta )q^{7}+q^{8}+\cdots\)
3762.2.a.bc 3762.a 1.a $2$ $30.040$ \(\Q(\sqrt{33}) \) None 1254.2.a.m \(2\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)
3762.2.a.bd 3762.a 1.a $3$ $30.040$ 3.3.469.1 None 418.2.a.h \(-3\) \(0\) \(-5\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots\)
3762.2.a.be 3762.a 1.a $3$ $30.040$ 3.3.229.1 None 1254.2.a.q \(-3\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3762.2.a.bf 3762.a 1.a $3$ $30.040$ \(\Q(\zeta_{14})^+\) None 1254.2.a.p \(3\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
3762.2.a.bg 3762.a 1.a $3$ $30.040$ 3.3.621.1 None 418.2.a.g \(3\) \(0\) \(3\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3762.2.a.bh 3762.a 1.a $4$ $30.040$ 4.4.23377.1 None 1254.2.a.r \(4\) \(0\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
3762.2.a.bi 3762.a 1.a $5$ $30.040$ 5.5.7578576.1 None 3762.2.a.bi \(-5\) \(0\) \(-3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
3762.2.a.bj 3762.a 1.a $5$ $30.040$ 5.5.7318736.1 None 3762.2.a.bj \(-5\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}-q^{8}+\cdots\)
3762.2.a.bk 3762.a 1.a $5$ $30.040$ 5.5.7318736.1 None 3762.2.a.bj \(5\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{4}q^{5}+(1-\beta _{3})q^{7}+q^{8}+\cdots\)
3762.2.a.bl 3762.a 1.a $5$ $30.040$ 5.5.7578576.1 None 3762.2.a.bi \(5\) \(0\) \(3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
3762.2.b.a 3762.b 33.d $36$ $30.040$ None 3762.2.b.a \(-36\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3762.2.b.b 3762.b 33.d $36$ $30.040$ None 3762.2.b.a \(36\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3762.2.d.a 3762.d 57.d $36$ $30.040$ None 3762.2.d.a \(-36\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
3762.2.d.b 3762.d 57.d $36$ $30.040$ None 3762.2.d.a \(36\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
3762.2.g.a 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-2}) \) None 3762.2.g.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-q^{8}+(-3+\beta )q^{11}+4q^{13}+\cdots\)
3762.2.g.b 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-2}) \) None 3762.2.g.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-q^{8}+(3+\beta )q^{11}-4q^{13}+\cdots\)
3762.2.g.c 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-10}) \) None 418.2.b.a \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+2q^{5}-\beta q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.g.d 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-2}) \) None 3762.2.g.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+q^{8}+(-3+\beta )q^{11}-4q^{13}+\cdots\)
3762.2.g.e 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-2}) \) None 3762.2.g.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+q^{8}+(3+\beta )q^{11}+4q^{13}+\cdots\)
3762.2.g.f 3762.g 209.d $2$ $30.040$ \(\Q(\sqrt{-10}) \) None 418.2.b.a \(2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+2q^{5}-\beta q^{7}+q^{8}+2q^{10}+\cdots\)
3762.2.g.g 3762.g 209.d $8$ $30.040$ 8.0.\(\cdots\).1 None 418.2.b.c \(-8\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-\beta _{2}q^{5}+(\beta _{3}+\beta _{5})q^{7}+\cdots\)
3762.2.g.h 3762.g 209.d $8$ $30.040$ 8.0.\(\cdots\).1 None 418.2.b.c \(8\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(-\beta _{3}-\beta _{5})q^{7}+\cdots\)
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