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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 11
4235.2.a.a \(1\) \(33.817\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
4235.2.a.b \(1\) \(33.817\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
4235.2.a.c \(1\) \(33.817\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}-2q^{9}-2q^{12}+\cdots\)
4235.2.a.d \(1\) \(33.817\) \(\Q\) None \(1\) \(-2\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
4235.2.a.e \(1\) \(33.817\) \(\Q\) None \(1\) \(-2\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}-q^{7}+\cdots\)
4235.2.a.f \(1\) \(33.817\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}-3q^{9}+\cdots\)
4235.2.a.g \(1\) \(33.817\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
4235.2.a.h \(2\) \(33.817\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
4235.2.a.i \(2\) \(33.817\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(2\) \(2\) \(-\) \(-\) \(+\) \(q-q^{2}+(1-\beta )q^{3}-q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4235.2.a.j \(2\) \(33.817\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+(1-2\beta )q^{2}+(-1+\beta )q^{3}+3q^{4}+\cdots\)
4235.2.a.k \(2\) \(33.817\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(q+(1-2\beta )q^{2}-\beta q^{3}+3q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
4235.2.a.l \(2\) \(33.817\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-q^{5}+(-3+\cdots)q^{6}+\cdots\)
4235.2.a.m \(2\) \(33.817\) \(\Q(\sqrt{17}) \) None \(1\) \(-1\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots\)
4235.2.a.n \(2\) \(33.817\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}-q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
4235.2.a.o \(3\) \(33.817\) 3.3.148.1 None \(-1\) \(0\) \(3\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
4235.2.a.p \(3\) \(33.817\) 3.3.148.1 None \(3\) \(-4\) \(-3\) \(-3\) \(+\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4235.2.a.q \(3\) \(33.817\) 3.3.148.1 None \(3\) \(-2\) \(-3\) \(3\) \(+\) \(-\) \(-\) \(q+(1+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4235.2.a.r \(4\) \(33.817\) 4.4.11348.1 None \(-2\) \(2\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{2}+(1+\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots\)
4235.2.a.s \(4\) \(33.817\) 4.4.6224.1 None \(-2\) \(4\) \(-4\) \(-4\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{3})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
4235.2.a.t \(4\) \(33.817\) 4.4.725.1 None \(-1\) \(-3\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
4235.2.a.u \(4\) \(33.817\) 4.4.15952.1 None \(0\) \(-2\) \(4\) \(4\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
4235.2.a.v \(4\) \(33.817\) 4.4.15952.1 None \(0\) \(-2\) \(4\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
4235.2.a.w \(4\) \(33.817\) 4.4.725.1 None \(1\) \(-3\) \(4\) \(4\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
4235.2.a.x \(4\) \(33.817\) 4.4.6224.1 None \(2\) \(4\) \(-4\) \(4\) \(+\) \(-\) \(+\) \(q+(1-\beta _{3})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
4235.2.a.y \(5\) \(33.817\) 5.5.173513.1 None \(-2\) \(-2\) \(-5\) \(5\) \(+\) \(-\) \(-\) \(q+\beta _{4}q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
4235.2.a.z \(5\) \(33.817\) 5.5.270017.1 None \(-2\) \(2\) \(5\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{4})q^{4}+q^{5}+\cdots\)
4235.2.a.ba \(5\) \(33.817\) 5.5.580017.1 None \(0\) \(-2\) \(-5\) \(-5\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{3}-\beta _{4})q^{4}-q^{5}+\cdots\)
4235.2.a.bb \(5\) \(33.817\) 5.5.580017.1 None \(0\) \(-2\) \(-5\) \(5\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{3}-\beta _{4})q^{4}-q^{5}+\cdots\)
4235.2.a.bc \(5\) \(33.817\) 5.5.288385.1 None \(0\) \(2\) \(5\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4235.2.a.bd \(5\) \(33.817\) 5.5.288385.1 None \(0\) \(2\) \(5\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4235.2.a.be \(5\) \(33.817\) 5.5.173513.1 None \(2\) \(-2\) \(-5\) \(-5\) \(+\) \(+\) \(-\) \(q-\beta _{4}q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
4235.2.a.bf \(5\) \(33.817\) 5.5.270017.1 None \(2\) \(2\) \(5\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{4})q^{4}+q^{5}+\cdots\)
4235.2.a.bg \(8\) \(33.817\) 8.8.\(\cdots\).1 None \(-2\) \(-3\) \(-8\) \(-8\) \(+\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
4235.2.a.bh \(8\) \(33.817\) 8.8.\(\cdots\).1 None \(2\) \(-3\) \(-8\) \(8\) \(+\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
4235.2.a.bi \(10\) \(33.817\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-4\) \(10\) \(10\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4235.2.a.bj \(10\) \(33.817\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(4\) \(-10\) \(-10\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4235.2.a.bk \(10\) \(33.817\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-4\) \(10\) \(-10\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4235.2.a.bl \(10\) \(33.817\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(4\) \(-10\) \(10\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4235.2.a.bm \(14\) \(33.817\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(5\) \(-14\) \(14\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
4235.2.a.bn \(14\) \(33.817\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(5\) \(-14\) \(-14\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
4235.2.a.bo \(18\) \(33.817\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(5\) \(18\) \(-18\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4235.2.a.bp \(18\) \(33.817\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(5\) \(18\) \(18\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
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