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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2023.1.c.a \(1\) \(1.010\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}-q^{7}+q^{8}+q^{9}-2q^{11}+q^{14}+\cdots\)
2023.1.c.b \(1\) \(1.010\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}+q^{9}+2q^{11}-q^{14}+\cdots\)
2023.1.c.c \(3\) \(1.010\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
2023.1.c.d \(3\) \(1.010\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
2023.1.c.e \(4\) \(1.010\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-119}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
2023.1.d.a \(2\) \(1.010\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-iq^{7}-q^{8}-q^{9}-iq^{11}-iq^{14}+\cdots\)
2023.1.d.b \(6\) \(1.010\) 6.0.419904.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{7}+\cdots\)
2023.1.f.a \(4\) \(1.010\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
2023.1.f.b \(8\) \(1.010\) 8.0.40960000.1 \(\Q(\sqrt{-119}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
2023.1.f.c \(12\) \(1.010\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+(-1+\beta _{6})q^{4}-\beta _{10}q^{7}+\cdots\)
2023.1.l.a \(8\) \(1.010\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{2}-\zeta_{16}q^{7}-\zeta_{16}^{6}q^{8}+\zeta_{16}^{6}q^{9}+\cdots\)
2023.1.l.b \(16\) \(1.010\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-119}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{12}q^{2}-\beta _{1}q^{3}-\beta _{8}q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots\)
2023.1.l.c \(24\) \(1.010\) 24.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{21}q^{2}+(-\beta _{11}+\beta _{13}-\beta _{15})q^{4}+\cdots\)
2023.2.a.a \(1\) \(16.154\) \(\Q\) None None \(-1\) \(-3\) \(-4\) \(1\) \(-\) \(q-q^{2}-3q^{3}-q^{4}-4q^{5}+3q^{6}+q^{7}+\cdots\)
2023.2.a.b \(1\) \(16.154\) \(\Q\) None None \(-1\) \(3\) \(4\) \(-1\) \(-\) \(q-q^{2}+3q^{3}-q^{4}+4q^{5}-3q^{6}-q^{7}+\cdots\)
2023.2.a.c \(3\) \(16.154\) 3.3.148.1 None None \(-1\) \(-1\) \(-2\) \(-3\) \(+\) \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.d \(3\) \(16.154\) 3.3.148.1 None None \(-1\) \(1\) \(2\) \(3\) \(+\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.e \(4\) \(16.154\) 4.4.9301.1 None None \(-1\) \(-2\) \(-2\) \(-4\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.f \(4\) \(16.154\) 4.4.2225.1 None None \(3\) \(-2\) \(-4\) \(-4\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.g \(4\) \(16.154\) 4.4.2225.1 None None \(3\) \(2\) \(4\) \(4\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.h \(5\) \(16.154\) 5.5.240133.1 None None \(2\) \(0\) \(-4\) \(-5\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.i \(5\) \(16.154\) 5.5.240133.1 None None \(2\) \(0\) \(4\) \(5\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.j \(5\) \(16.154\) 5.5.453749.1 None None \(2\) \(2\) \(0\) \(5\) \(-\) \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots\)
2023.2.a.k \(9\) \(16.154\) 9.9.\(\cdots\).1 None None \(-6\) \(0\) \(0\) \(9\) \(+\) \(q+(-1-\beta _{5})q^{2}-\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
2023.2.a.l \(9\) \(16.154\) 9.9.\(\cdots\).1 None None \(-6\) \(0\) \(0\) \(-9\) \(+\) \(q+(-1-\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
2023.2.a.m \(10\) \(16.154\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-4\) \(-8\) \(-10\) \(+\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots\)
2023.2.a.n \(10\) \(16.154\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(4\) \(8\) \(10\) \(-\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots\)
2023.2.a.o \(15\) \(16.154\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(6\) \(0\) \(0\) \(15\) \(-\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{13})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.p \(15\) \(16.154\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(6\) \(0\) \(0\) \(-15\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{13})q^{3}+(1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2023.2.a.q \(16\) \(16.154\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(-8\) \(-16\) \(16\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2023.2.a.r \(16\) \(16.154\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(8\) \(16\) \(-16\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2023.4.a.a \(1\) \(119.361\) \(\Q\) None None \(-1\) \(2\) \(-16\) \(7\) \(-\) \(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
2023.4.a.b \(1\) \(119.361\) \(\Q\) None None \(-1\) \(6\) \(20\) \(7\) \(-\) \(q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots\)
2023.4.a.c \(1\) \(119.361\) \(\Q\) None None \(3\) \(-1\) \(6\) \(-7\) \(+\) \(q+3q^{2}-q^{3}+q^{4}+6q^{5}-3q^{6}-7q^{7}+\cdots\)
2023.4.a.d \(1\) \(119.361\) \(\Q\) None None \(3\) \(1\) \(-6\) \(7\) \(+\) \(q+3q^{2}+q^{3}+q^{4}-6q^{5}+3q^{6}+7q^{7}+\cdots\)
2023.4.a.e \(3\) \(119.361\) 3.3.2429.1 None None \(-1\) \(-5\) \(19\) \(21\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
2023.4.a.f \(4\) \(119.361\) 4.4.68557.1 None None \(-2\) \(7\) \(9\) \(-28\) \(+\) \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
2023.4.a.g \(7\) \(119.361\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(4\) \(-5\) \(-35\) \(49\) \(-\) \(q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
2023.4.a.h \(9\) \(119.361\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(2\) \(-11\) \(3\) \(-63\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
2023.4.a.i \(11\) \(119.361\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-7\) \(-2\) \(2\) \(-77\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.j \(11\) \(119.361\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-7\) \(2\) \(-2\) \(77\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.k \(12\) \(119.361\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(-3\) \(12\) \(84\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.l \(12\) \(119.361\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(3\) \(-12\) \(-84\) \(+\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.m \(13\) \(119.361\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(-14\) \(-20\) \(91\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.n \(13\) \(119.361\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(14\) \(20\) \(-91\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.o \(26\) \(119.361\) None None \(-8\) \(-12\) \(-40\) \(182\) \(-\)
2023.4.a.p \(26\) \(119.361\) None None \(-8\) \(12\) \(40\) \(-182\) \(+\)
2023.4.a.q \(33\) \(119.361\) None None \(-12\) \(0\) \(0\) \(-231\) \(-\)
2023.4.a.r \(33\) \(119.361\) None None \(-12\) \(0\) \(0\) \(231\) \(-\)
2023.4.a.s \(39\) \(119.361\) None None \(12\) \(0\) \(0\) \(273\) \(+\)
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