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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3969.1.b.a \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(2\beta _{1}-\beta _{3})q^{8}+\cdots\)
3969.1.j.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-\zeta_{6}q^{13}+q^{16}+\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots\)
3969.1.j.b \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}+(-\beta _{1}+\beta _{3})q^{11}-q^{16}+\cdots\)
3969.1.j.c \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{11})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
3969.1.k.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}+q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{16}+q^{25}+\zeta_{6}q^{37}+\cdots\)
3969.1.k.c \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(1+\zeta_{6})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.d \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}-q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.k.e \(4\) \(1.981\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.l.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.l.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-q^{8}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots\)
3969.1.m.c \(4\) \(1.981\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.n.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{13}-\zeta_{6}q^{16}-\zeta_{6}^{2}q^{19}+\cdots\)
3969.1.n.b \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{11}+\cdots\)
3969.1.n.c \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.q.a \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.r.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}-q^{19}+\cdots\)
3969.1.r.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+q^{19}+\cdots\)
3969.1.r.c \(4\) \(1.981\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
3969.1.r.d \(8\) \(1.981\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
3969.1.t.a \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{8}-\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.b \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+(-1-\zeta_{6})q^{13}+q^{16}+\zeta_{6}^{2}q^{25}+\cdots\)
3969.1.t.c \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{16}+\zeta_{6}^{2}q^{25}-\zeta_{6}^{2}q^{37}+\cdots\)
3969.1.t.d \(2\) \(1.981\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{8}+\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots\)
3969.1.t.e \(4\) \(1.981\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{5})q^{2}+(1+\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
3969.1.br.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{18}q^{4}-\zeta_{42}^{2}q^{7}+(-\zeta_{42}^{3}+\cdots)q^{13}+\cdots\)
3969.1.bt.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+(\zeta_{42}^{8}-\zeta_{42}^{17}+\cdots)q^{13}+\cdots\)
3969.1.bx.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{42}q^{4}+\zeta_{42}^{4}q^{7}+(-\zeta_{42}^{9}-\zeta_{42}^{13}+\cdots)q^{13}+\cdots\)
3969.1.bz.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{16}q^{4}-\zeta_{42}^{8}q^{7}+(-\zeta_{42}^{4}+\cdots)q^{13}+\cdots\)
3969.1.ca.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{10}q^{4}+\zeta_{42}^{19}q^{7}+(\zeta_{42}^{4}-\zeta_{42}^{6}+\cdots)q^{13}+\cdots\)
3969.1.cb.a \(12\) \(1.981\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{42}^{18}q^{4}+\zeta_{42}^{16}q^{7}+(-\zeta_{42}+\cdots)q^{13}+\cdots\)
3969.2.a.a \(1\) \(31.693\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-5q^{11}+\cdots\)
3969.2.a.b \(1\) \(31.693\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(0\) \(-\) \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-2q^{11}+\cdots\)
3969.2.a.c \(1\) \(31.693\) \(\Q\) None None \(-1\) \(0\) \(1\) \(0\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-5q^{11}+\cdots\)
3969.2.a.d \(1\) \(31.693\) \(\Q\) None None \(1\) \(0\) \(-1\) \(0\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+5q^{11}+\cdots\)
3969.2.a.e \(1\) \(31.693\) \(\Q\) None None \(1\) \(0\) \(1\) \(0\) \(-\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots\)
3969.2.a.f \(1\) \(31.693\) \(\Q\) None None \(1\) \(0\) \(1\) \(0\) \(-\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+5q^{11}+\cdots\)
3969.2.a.g \(2\) \(31.693\) \(\Q(\sqrt{15}) \) None None \(-2\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots\)
3969.2.a.h \(2\) \(31.693\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots\)
3969.2.a.i \(2\) \(31.693\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots\)
3969.2.a.j \(2\) \(31.693\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}+(1+\cdots)q^{11}+\cdots\)
3969.2.a.k \(2\) \(31.693\) \(\Q(\sqrt{15}) \) None None \(2\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+\beta q^{10}+\cdots\)
3969.2.a.l \(3\) \(31.693\) \(\Q(\zeta_{18})^+\) None None \(-3\) \(0\) \(3\) \(0\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
3969.2.a.m \(3\) \(31.693\) 3.3.321.1 None None \(-1\) \(0\) \(5\) \(0\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots\)
3969.2.a.n \(3\) \(31.693\) 3.3.621.1 None None \(0\) \(0\) \(-3\) \(0\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3969.2.a.o \(3\) \(31.693\) 3.3.621.1 None None \(0\) \(0\) \(3\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3969.2.a.p \(3\) \(31.693\) 3.3.321.1 None None \(1\) \(0\) \(-5\) \(0\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
3969.2.a.q \(3\) \(31.693\) \(\Q(\zeta_{18})^+\) None None \(3\) \(0\) \(-3\) \(0\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
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