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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 43
1849.2.a.a \(1\) \(14.764\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
1849.2.a.b \(1\) \(14.764\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(+\) \(q-2q^{4}-3q^{9}-q^{11}+3q^{13}+4q^{16}+\cdots\)
1849.2.a.c \(1\) \(14.764\) \(\Q\) None \(1\) \(1\) \(-1\) \(3\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
1849.2.a.d \(1\) \(14.764\) \(\Q\) None \(2\) \(2\) \(4\) \(0\) \(-\) \(q+2q^{2}+2q^{3}+2q^{4}+4q^{5}+4q^{6}+\cdots\)
1849.2.a.e \(2\) \(14.764\) \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-2\) \(-4\) \(+\) \(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
1849.2.a.f \(2\) \(14.764\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) \(-\) \(q+\beta q^{2}-\beta q^{3}+(-2-\beta )q^{5}-2q^{6}+\cdots\)
1849.2.a.g \(2\) \(14.764\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{2}-\beta q^{3}+4q^{4}-\beta q^{5}-6q^{6}+\cdots\)
1849.2.a.h \(2\) \(14.764\) \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(2\) \(4\) \(-\) \(q+(1+\beta )q^{2}+(2-\beta )q^{3}+3\beta q^{4}+2\beta q^{5}+\cdots\)
1849.2.a.i \(3\) \(14.764\) \(\Q(\zeta_{14})^+\) None \(-2\) \(-5\) \(-6\) \(-8\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
1849.2.a.j \(3\) \(14.764\) \(\Q(\zeta_{14})^+\) None \(-1\) \(-1\) \(-2\) \(0\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1849.2.a.k \(3\) \(14.764\) \(\Q(\zeta_{14})^+\) None \(1\) \(1\) \(2\) \(0\) \(+\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1849.2.a.l \(3\) \(14.764\) \(\Q(\zeta_{14})^+\) None \(2\) \(5\) \(6\) \(8\) \(-\) \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
1849.2.a.m \(10\) \(14.764\) \(\Q(\zeta_{44})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1849.2.a.n \(18\) \(14.764\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-5\) \(-5\) \(-11\) \(-6\) \(+\) \(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
1849.2.a.o \(18\) \(14.764\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(5\) \(5\) \(11\) \(6\) \(-\) \(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
1849.2.a.p \(20\) \(14.764\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-5\) \(1\) \(3\) \(2\) \(-\) \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
1849.2.a.q \(20\) \(14.764\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{19})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots\)
1849.2.a.r \(20\) \(14.764\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(-1\) \(-3\) \(-2\) \(-\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
1849.4.a.a \(1\) \(109.095\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(+\) \(q-8q^{4}-3^{3}q^{9}+2^{5}q^{11}-90q^{13}+\cdots\)
1849.4.a.b \(4\) \(109.095\) 4.4.45868.1 None \(4\) \(11\) \(27\) \(20\) \(-\) \(q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
1849.4.a.c \(6\) \(109.095\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(-7\) \(-43\) \(-8\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
1849.4.a.d \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(5\) \(19\) \(51\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(2-\beta _{7}+\cdots)q^{5}+\cdots\)
1849.4.a.e \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{7}+\beta _{9})q^{4}+\cdots\)
1849.4.a.f \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-5\) \(-19\) \(-51\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1849.4.a.g \(30\) \(109.095\) None \(-6\) \(-2\) \(-27\) \(-48\) \(-\)
1849.4.a.h \(30\) \(109.095\) None \(6\) \(2\) \(27\) \(48\) \(+\)
1849.4.a.i \(50\) \(109.095\) None \(-10\) \(-2\) \(8\) \(-6\) \(-\)
1849.4.a.j \(50\) \(109.095\) None \(10\) \(2\) \(-8\) \(6\) \(-\)
1849.4.a.k \(60\) \(109.095\) None \(-15\) \(-37\) \(-51\) \(-54\) \(-\)
1849.4.a.l \(60\) \(109.095\) None \(15\) \(37\) \(51\) \(54\) \(+\)
1849.4.a.m \(110\) \(109.095\) None \(0\) \(0\) \(0\) \(0\) \(+\)


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