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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1040.1.l.a \(2\) \(0.519\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-65}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
1040.1.l.b \(2\) \(0.519\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-65}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{3}+q^{5}+q^{9}+\beta q^{11}-q^{13}+\cdots\)
1040.1.bf.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-iq^{9}-iq^{13}+(-1+i)q^{17}+\cdots\)
1040.1.cb.a \(4\) \(0.519\) \(\Q(\zeta_{8})\) None \(\Q(\sqrt{65}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1040.1.ce.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-iq^{9}+q^{13}+(1-i)q^{17}+q^{25}+\cdots\)
1040.1.cx.a \(2\) \(0.519\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+(1+\zeta_{6}+\cdots)q^{17}+\cdots\)
1040.1.cx.b \(2\) \(0.519\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots\)
1040.1.ea.a \(4\) \(0.519\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{5}-\zeta_{12}q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
1040.1.ez.a \(4\) \(0.519\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}-\zeta_{12}q^{13}+(-\zeta_{12}^{3}+\cdots)q^{17}+\cdots\)
1040.2.a.a \(1\) \(8.304\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(-2\) \(-\) \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
1040.2.a.b \(1\) \(8.304\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(4\) \(-\) \(q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
1040.2.a.c \(1\) \(8.304\) \(\Q\) None None \(0\) \(-2\) \(1\) \(0\) \(+\) \(q-2q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
1040.2.a.d \(1\) \(8.304\) \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) \(+\) \(q-q^{5}-3q^{9}+4q^{11}-q^{13}-6q^{17}+\cdots\)
1040.2.a.e \(1\) \(8.304\) \(\Q\) None None \(0\) \(0\) \(1\) \(0\) \(-\) \(q+q^{5}-3q^{9}+q^{13}+2q^{17}+8q^{19}+\cdots\)
1040.2.a.f \(1\) \(8.304\) \(\Q\) None None \(0\) \(2\) \(-1\) \(4\) \(-\) \(q+2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
1040.2.a.g \(1\) \(8.304\) \(\Q\) None None \(0\) \(2\) \(1\) \(4\) \(-\) \(q+2q^{3}+q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
1040.2.a.h \(2\) \(8.304\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(q+(-1+\beta )q^{3}-q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots\)
1040.2.a.i \(2\) \(8.304\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(q+(-1-\beta )q^{3}-q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
1040.2.a.j \(2\) \(8.304\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(-4\) \(+\) \(q+\beta q^{3}+q^{5}+(-2-2\beta )q^{7}-q^{9}+\cdots\)
1040.2.a.k \(2\) \(8.304\) \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(2\) \(-4\) \(-\) \(q+\beta q^{3}+q^{5}-2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots\)
1040.2.a.l \(2\) \(8.304\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
1040.2.a.m \(2\) \(8.304\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
1040.2.a.n \(2\) \(8.304\) \(\Q(\sqrt{2}) \) None None \(0\) \(4\) \(2\) \(4\) \(-\) \(q+(2+\beta )q^{3}+q^{5}+2q^{7}+(3+4\beta )q^{9}+\cdots\)
1040.2.a.o \(3\) \(8.304\) 3.3.564.1 None None \(0\) \(-2\) \(3\) \(2\) \(-\) \(q+(-1-\beta _{2})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
1040.2.d.a \(2\) \(8.304\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}-4iq^{7}+3q^{9}+2q^{11}+\cdots\)
1040.2.d.b \(6\) \(8.304\) 6.0.3534400.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
1040.2.d.c \(6\) \(8.304\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1040.2.d.d \(6\) \(8.304\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.d.e \(6\) \(8.304\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1040.2.d.f \(10\) \(8.304\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots\)
1040.2.f.a \(2\) \(8.304\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-i)q^{5}-q^{9}+iq^{11}+\cdots\)
1040.2.f.b \(2\) \(8.304\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+i)q^{5}-q^{9}-iq^{11}+(-3+\cdots)q^{13}+\cdots\)
1040.2.f.c \(4\) \(8.304\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(2\) \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1040.2.f.d \(4\) \(8.304\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(-2\) \(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
1040.2.f.e \(8\) \(8.304\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+\cdots\)
1040.2.f.f \(10\) \(8.304\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-3\) \(-2\) \(q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.f.g \(10\) \(8.304\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(3\) \(2\) \(q-\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.k.a \(2\) \(8.304\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) \(q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots\)
1040.2.k.b \(6\) \(8.304\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
1040.2.k.c \(6\) \(8.304\) 6.0.9144576.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
1040.2.k.d \(6\) \(8.304\) 6.0.5089536.1 None None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.k.e \(8\) \(8.304\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
1040.2.q.a \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-2\) \(3\) \(q+(-3+3\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.b \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(2\) \(3\) \(q+(-3+3\zeta_{6})q^{3}+q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.c \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-2\) \(-1\) \(q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1040.2.q.d \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-3\) \(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.e \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-3\) \(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.f \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(5\) \(q+(-1+\zeta_{6})q^{3}-q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.g \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(-3\) \(q+(-1+\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.h \(2\) \(8.304\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(-3\) \(q+q^{5}-3\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots\)
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