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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3267.1.b.a 3267.b 3.b $1$ $1.630$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}-q^{7}-q^{13}+q^{16}+2q^{19}+\cdots\)
3267.1.b.b 3267.b 3.b $1$ $1.630$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{4}+q^{7}+q^{13}+q^{16}-2q^{19}+\cdots\)
3267.1.b.c 3267.b 3.b $2$ $1.630$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{2}-q^{4}-\beta q^{5}-q^{7}+2q^{10}+\cdots\)
3267.1.b.d 3267.b 3.b $2$ $1.630$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{2}-q^{4}-\beta q^{5}+q^{7}-2q^{10}+\cdots\)
3267.1.b.e 3267.b 3.b $2$ $1.630$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}+q^{25}+\cdots\)
3267.1.c.a 3267.c 11.b $4$ $1.630$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\beta _{1}q^{7}-\beta _{3}q^{13}+q^{16}+(\beta _{1}+\cdots)q^{19}+\cdots\)
3267.1.h.a 3267.h 99.h $4$ $1.630$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+\cdots\)
3267.1.i.a 3267.i 9.d $2$ $1.630$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{16}+\cdots\)
3267.1.l.a 3267.l 11.d $16$ $1.630$ 16.0.\(\cdots\).7 \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{4}-\beta _{12}q^{7}+\beta _{3}q^{13}-\beta _{8}q^{16}+\cdots\)
3267.1.m.a 3267.m 33.h $4$ $1.630$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}q^{13}+\cdots\)
3267.1.m.b 3267.m 33.h $4$ $1.630$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{7}+\zeta_{10}q^{13}+\cdots\)
3267.1.m.c 3267.m 33.h $8$ $1.630$ 8.0.324000000.3 \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\beta _{3}q^{7}+\cdots\)
3267.1.m.d 3267.m 33.h $8$ $1.630$ 8.0.64000000.1 None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+\beta _{4}q^{7}+\cdots\)
3267.1.m.e 3267.m 33.h $8$ $1.630$ 8.0.64000000.1 None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots\)
3267.1.q.a 3267.q 27.f $6$ $1.630$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\zeta_{18}^{7}q^{3}+\zeta_{18}^{4}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots\)
3267.1.v.a 3267.v 99.n $8$ $1.630$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{30}^{11}q^{4}+(-\zeta_{30}^{7}-\zeta_{30}^{12})q^{5}+\cdots\)
3267.1.w.a 3267.w 99.o $8$ $1.630$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{30}^{13}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{11}q^{16}+\cdots\)
3267.1.w.b 3267.w 99.o $16$ $1.630$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{2}-\beta _{8}-\beta _{10}+\cdots)q^{5}+\cdots\)
3267.1.be.a 3267.be 297.v $24$ $1.630$ \(\Q(\zeta_{45})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q+\zeta_{90}^{11}q^{3}+\zeta_{90}^{14}q^{4}+(-\zeta_{90}^{3}+\cdots)q^{5}+\cdots\)
3267.1.bf.a 3267.bf 297.w $24$ $1.630$ \(\Q(\zeta_{45})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q+\zeta_{90}^{34}q^{3}-\zeta_{90}^{31}q^{4}+(\zeta_{90}^{32}+\cdots)q^{5}+\cdots\)
3267.2.a.a 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(-2\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{5}-q^{7}-4q^{10}+\cdots\)
3267.2.a.b 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(-1\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}+2q^{10}+\cdots\)
3267.2.a.c 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(-1\) \(0\) \(-2\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots\)
3267.2.a.d 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(-1\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
3267.2.a.e 3267.a 1.a $1$ $26.087$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-4q^{7}-7q^{13}+4q^{16}-7q^{19}+\cdots\)
3267.2.a.f 3267.a 1.a $1$ $26.087$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+q^{7}-5q^{13}+4q^{16}+7q^{19}+\cdots\)
3267.2.a.g 3267.a 1.a $1$ $26.087$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+4q^{7}+7q^{13}+4q^{16}+7q^{19}+\cdots\)
3267.2.a.h 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(1\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots\)
3267.2.a.i 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(1\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
3267.2.a.j 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(1\) \(0\) \(2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots\)
3267.2.a.k 3267.a 1.a $1$ $26.087$ \(\Q\) None None \(2\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-2q^{5}-q^{7}-4q^{10}+\cdots\)
3267.2.a.l 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
3267.2.a.m 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-\beta q^{7}+\beta q^{13}+4q^{16}+\beta q^{19}+\cdots\)
3267.2.a.n 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-2\beta q^{7}-\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
3267.2.a.o 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{7}-\beta q^{8}+\beta q^{13}+\cdots\)
3267.2.a.p 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{7}-\beta q^{8}-\beta q^{13}+\cdots\)
3267.2.a.q 3267.a 1.a $2$ $26.087$ \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
3267.2.a.r 3267.a 1.a $3$ $26.087$ 3.3.321.1 None None \(-1\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
3267.2.a.s 3267.a 1.a $3$ $26.087$ 3.3.321.1 None None \(-1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
3267.2.a.t 3267.a 1.a $3$ $26.087$ 3.3.564.1 None None \(-1\) \(0\) \(-2\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3267.2.a.u 3267.a 1.a $3$ $26.087$ 3.3.321.1 None None \(1\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
3267.2.a.v 3267.a 1.a $3$ $26.087$ 3.3.321.1 None None \(1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
3267.2.a.w 3267.a 1.a $3$ $26.087$ 3.3.564.1 None None \(1\) \(0\) \(2\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3267.2.a.x 3267.a 1.a $4$ $26.087$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
3267.2.a.y 3267.a 1.a $4$ $26.087$ \(\Q(\sqrt{2}, \sqrt{7})\) None None \(0\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3267.2.a.z 3267.a 1.a $4$ $26.087$ 4.4.29952.1 None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3267.2.a.ba 3267.a 1.a $4$ $26.087$ 4.4.29952.1 None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots\)
3267.2.a.bb 3267.a 1.a $4$ $26.087$ \(\Q(\sqrt{2}, \sqrt{7})\) None None \(0\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3267.2.a.bc 3267.a 1.a $6$ $26.087$ 6.6.19783872.1 None None \(0\) \(0\) \(-8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
3267.2.a.bd 3267.a 1.a $6$ $26.087$ 6.6.19783872.1 None None \(0\) \(0\) \(8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
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