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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 19
7581.2.a.a \(1\) \(60.535\) \(\Q\) None \(-1\) \(1\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.b \(1\) \(60.535\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
7581.2.a.c \(1\) \(60.535\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.d \(1\) \(60.535\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.e \(1\) \(60.535\) \(\Q\) None \(1\) \(-1\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.f \(1\) \(60.535\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots\)
7581.2.a.g \(2\) \(60.535\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7581.2.a.h \(2\) \(60.535\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-4\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots\)
7581.2.a.i \(2\) \(60.535\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-4\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots\)
7581.2.a.j \(2\) \(60.535\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(3\) \(-2\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}+(2-\beta )q^{5}-q^{6}+\cdots\)
7581.2.a.k \(3\) \(60.535\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
7581.2.a.l \(3\) \(60.535\) 3.3.404.1 None \(-1\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(q-\beta _{2}q^{2}-q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.m \(3\) \(60.535\) 3.3.148.1 None \(-1\) \(3\) \(2\) \(3\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.n \(3\) \(60.535\) 3.3.148.1 None \(-1\) \(3\) \(4\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.o \(3\) \(60.535\) 3.3.148.1 None \(1\) \(-3\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.p \(3\) \(60.535\) \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}+(2\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots\)
7581.2.a.q \(4\) \(60.535\) 4.4.6224.1 None \(-2\) \(-4\) \(6\) \(-4\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
7581.2.a.r \(4\) \(60.535\) 4.4.1957.1 None \(-1\) \(-4\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.s \(4\) \(60.535\) 4.4.12197.1 None \(-1\) \(-4\) \(-2\) \(4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.t \(4\) \(60.535\) 4.4.1957.1 None \(1\) \(4\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.u \(4\) \(60.535\) 4.4.12197.1 None \(1\) \(4\) \(-2\) \(4\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.v \(4\) \(60.535\) 4.4.6224.1 None \(2\) \(4\) \(6\) \(-4\) \(-\) \(+\) \(+\) \(q+(1-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
7581.2.a.w \(5\) \(60.535\) 5.5.368464.1 None \(-3\) \(5\) \(4\) \(5\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
7581.2.a.x \(5\) \(60.535\) 5.5.1240016.1 None \(-1\) \(-5\) \(-2\) \(5\) \(+\) \(-\) \(-\) \(q-\beta _{3}q^{2}-q^{3}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots\)
7581.2.a.y \(6\) \(60.535\) 6.6.5953625.1 None \(-3\) \(6\) \(2\) \(-6\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{3})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7581.2.a.z \(6\) \(60.535\) 6.6.8512625.1 None \(-2\) \(-6\) \(-5\) \(-6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.ba \(6\) \(60.535\) 6.6.343395288.1 None \(-1\) \(-6\) \(0\) \(-6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
7581.2.a.bb \(6\) \(60.535\) 6.6.130040728.1 None \(-1\) \(-6\) \(4\) \(6\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
7581.2.a.bc \(6\) \(60.535\) 6.6.343395288.1 None \(1\) \(6\) \(0\) \(-6\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
7581.2.a.bd \(6\) \(60.535\) 6.6.130040728.1 None \(1\) \(6\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
7581.2.a.be \(6\) \(60.535\) 6.6.8512625.1 None \(2\) \(6\) \(-5\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.bf \(6\) \(60.535\) 6.6.5953625.1 None \(3\) \(-6\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(q+(1+\beta _{3})q^{2}-q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
7581.2.a.bg \(9\) \(60.535\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(-9\) \(0\) \(-9\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots\)
7581.2.a.bh \(9\) \(60.535\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(9\) \(0\) \(-9\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots\)
7581.2.a.bi \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(-2\) \(12\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
7581.2.a.bj \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-12\) \(-2\) \(12\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bk \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-12\) \(-2\) \(12\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
7581.2.a.bl \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-12\) \(12\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bm \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(-12\) \(12\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bn \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(12\) \(-2\) \(12\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
7581.2.a.bo \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(12\) \(-2\) \(12\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bp \(12\) \(60.535\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-12\) \(-2\) \(12\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
7581.2.a.bq \(18\) \(60.535\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-18\) \(0\) \(-18\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
7581.2.a.br \(18\) \(60.535\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-18\) \(12\) \(18\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots\)
7581.2.a.bs \(18\) \(60.535\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(0\) \(-18\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
7581.2.a.bt \(18\) \(60.535\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(12\) \(18\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots\)
7581.2.a.bu \(20\) \(60.535\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-20\) \(-2\) \(-20\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
7581.2.a.bv \(20\) \(60.535\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(4\) \(20\) \(-2\) \(-20\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
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