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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 13 31
6045.2.a.a \(1\) \(48.270\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(-5\) \(+\) \(+\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-5q^{7}+\cdots\)
6045.2.a.b \(1\) \(48.270\) \(\Q\) None \(-2\) \(-1\) \(1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.c \(1\) \(48.270\) \(\Q\) None \(-2\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-3q^{7}+\cdots\)
6045.2.a.d \(1\) \(48.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.e \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{5}-5q^{7}+q^{9}+q^{11}+\cdots\)
6045.2.a.f \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
6045.2.a.g \(1\) \(48.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
6045.2.a.h \(1\) \(48.270\) \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
6045.2.a.i \(1\) \(48.270\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.j \(1\) \(48.270\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
6045.2.a.k \(1\) \(48.270\) \(\Q\) None \(2\) \(1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.l \(1\) \(48.270\) \(\Q\) None \(2\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
6045.2.a.m \(2\) \(48.270\) \(\Q(\sqrt{17}) \) None \(-4\) \(2\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
6045.2.a.n \(2\) \(48.270\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+(-1+2\beta )q^{7}+\cdots\)
6045.2.a.o \(2\) \(48.270\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots\)
6045.2.a.p \(2\) \(48.270\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}+(1+\beta )q^{7}+\cdots\)
6045.2.a.q \(3\) \(48.270\) 3.3.148.1 None \(0\) \(3\) \(-3\) \(7\) \(-\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
6045.2.a.r \(3\) \(48.270\) 3.3.316.1 None \(1\) \(3\) \(3\) \(8\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.s \(5\) \(48.270\) 5.5.230224.1 None \(0\) \(5\) \(5\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{2}+q^{3}+(1+\beta _{4})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
6045.2.a.t \(9\) \(48.270\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(9\) \(9\) \(-12\) \(-\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6045.2.a.u \(9\) \(48.270\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(9\) \(9\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
6045.2.a.v \(10\) \(48.270\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(-10\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.w \(11\) \(48.270\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(-11\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.x \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(-12\) \(3\) \(-\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.y \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(12\) \(-12\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.z \(12\) \(48.270\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-12\) \(-7\) \(+\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.ba \(13\) \(48.270\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(-13\) \(13\) \(-11\) \(+\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bb \(13\) \(48.270\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(13\) \(13\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bc \(14\) \(48.270\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-14\) \(-14\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bd \(14\) \(48.270\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(14\) \(5\) \(+\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.be \(15\) \(48.270\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(-15\) \(15\) \(-16\) \(+\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bf \(15\) \(48.270\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(15\) \(-15\) \(-5\) \(-\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bg \(16\) \(48.270\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-16\) \(-16\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
6045.2.a.bh \(17\) \(48.270\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-17\) \(17\) \(18\) \(+\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
6045.2.a.bi \(18\) \(48.270\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(4\) \(18\) \(18\) \(8\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
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