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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1859.1.c.a \(3\) \(0.928\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
1859.1.c.b \(3\) \(0.928\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
1859.1.c.c \(4\) \(0.928\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots\)
1859.1.d.a \(6\) \(0.928\) 6.0.153664.1 \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{2}+\beta _{4})q^{3}-q^{4}-\beta _{1}q^{5}+\cdots\)
1859.1.i.a \(4\) \(0.928\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.1.i.b \(4\) \(0.928\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(1\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.1.i.c \(12\) \(0.928\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{5})q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1859.1.k.a \(6\) \(0.928\) 6.0.64827.1 \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.b \(6\) \(0.928\) 6.0.64827.1 \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.c \(8\) \(0.928\) 8.0.12960000.1 \(\Q(\sqrt{-143}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(1-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
1859.2.a.a \(1\) \(14.844\) \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) \(-\) \(q-q^{3}-2q^{4}+q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\)
1859.2.a.b \(1\) \(14.844\) \(\Q\) None None \(2\) \(-1\) \(-1\) \(2\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots\)
1859.2.a.c \(2\) \(14.844\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-6\) \(-\) \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
1859.2.a.d \(2\) \(14.844\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(6\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
1859.2.a.e \(3\) \(14.844\) 3.3.756.1 None None \(-3\) \(0\) \(-3\) \(0\) \(+\) \(q-q^{2}+\beta _{1}q^{3}-q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1859.2.a.f \(3\) \(14.844\) 3.3.361.1 None None \(-1\) \(1\) \(-1\) \(5\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.2.a.g \(3\) \(14.844\) 3.3.361.1 None None \(1\) \(1\) \(1\) \(-5\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
1859.2.a.h \(3\) \(14.844\) 3.3.756.1 None None \(3\) \(0\) \(3\) \(0\) \(-\) \(q+q^{2}+\beta _{1}q^{3}-q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
1859.2.a.i \(4\) \(14.844\) 4.4.1957.1 None None \(-3\) \(0\) \(0\) \(-6\) \(+\) \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.2.a.j \(6\) \(14.844\) 6.6.84512328.1 None None \(-1\) \(-2\) \(-4\) \(-4\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1859.2.a.k \(6\) \(14.844\) 6.6.28561300.1 None None \(0\) \(1\) \(-6\) \(-3\) \(+\) \(q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1859.2.a.l \(6\) \(14.844\) 6.6.28561300.1 None None \(0\) \(1\) \(6\) \(3\) \(-\) \(q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1859.2.a.m \(6\) \(14.844\) 6.6.194616205.1 None None \(0\) \(3\) \(-1\) \(-4\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1859.2.a.n \(6\) \(14.844\) 6.6.84512328.1 None None \(1\) \(-2\) \(4\) \(4\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1859.2.a.o \(8\) \(14.844\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(0\) \(-8\) \(-14\) \(+\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.p \(8\) \(14.844\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(2\) \(0\) \(8\) \(14\) \(-\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.q \(9\) \(14.844\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-5\) \(-4\) \(1\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.r \(9\) \(14.844\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-5\) \(4\) \(-1\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.s \(21\) \(14.844\) None None \(0\) \(6\) \(-7\) \(-1\) \(-\)
1859.2.a.t \(21\) \(14.844\) None None \(0\) \(6\) \(7\) \(1\) \(-\)
1859.4.a.a \(2\) \(109.685\) \(\Q(\sqrt{3}) \) None None \(-2\) \(-2\) \(-2\) \(-20\) \(-\) \(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
1859.4.a.b \(4\) \(109.685\) 4.4.297133.1 None None \(0\) \(-4\) \(6\) \(17\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
1859.4.a.c \(6\) \(109.685\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(6\) \(-6\) \(8\) \(53\) \(+\) \(q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.d \(9\) \(109.685\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(8\) \(-30\) \(-25\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1859.4.a.e \(11\) \(109.685\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-6\) \(6\) \(4\) \(-45\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.f \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(-4\) \(-6\) \(-16\) \(6\) \(-\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.g \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(-6\) \(-24\) \(-62\) \(-\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.h \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(-6\) \(24\) \(62\) \(+\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
1859.4.a.i \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(4\) \(-6\) \(16\) \(-6\) \(+\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
1859.4.a.j \(18\) \(109.685\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-2\) \(0\) \(-20\) \(-28\) \(-\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.k \(18\) \(109.685\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(20\) \(28\) \(+\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)
1859.4.a.l \(36\) \(109.685\) None None \(-4\) \(12\) \(-40\) \(-56\) \(-\)
1859.4.a.m \(36\) \(109.685\) None None \(4\) \(12\) \(40\) \(56\) \(+\)
1859.4.a.n \(39\) \(109.685\) None None \(0\) \(-23\) \(-23\) \(4\) \(-\)
1859.4.a.o \(39\) \(109.685\) None None \(0\) \(-23\) \(23\) \(-4\) \(-\)
1859.4.a.p \(51\) \(109.685\) None None \(0\) \(21\) \(-41\) \(-4\) \(+\)
1859.4.a.q \(51\) \(109.685\) None None \(0\) \(21\) \(41\) \(4\) \(+\)
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