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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4001.2.a.a \(149\) \(31.948\) None \(-6\) \(-28\) \(-19\) \(-47\) \(+\)
4001.2.a.b \(184\) \(31.948\) None \(3\) \(28\) \(15\) \(49\) \(-\)
4002.2.a.a \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
4002.2.a.b \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
4002.2.a.c \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(1\) \(4\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
4002.2.a.d \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
4002.2.a.e \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.f \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.g \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.h \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
4002.2.a.i \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(-2\) \(2\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
4002.2.a.j \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(1\) \(-4\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
4002.2.a.k \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4002.2.a.l \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4002.2.a.m \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-3\) \(-4\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.n \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.o \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-1\) \(-3\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
4002.2.a.p \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4002.2.a.q \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4002.2.a.r \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(3\) \(1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
4002.2.a.s \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(3\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
4002.2.a.t \(2\) \(31.956\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots\)
4002.2.a.u \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(1\) \(1\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots\)
4002.2.a.v \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4002.2.a.w \(2\) \(31.956\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(6\) \(6\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
4002.2.a.x \(2\) \(31.956\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(8\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots\)
4002.2.a.y \(3\) \(31.956\) 3.3.1772.1 None \(-3\) \(-3\) \(-1\) \(6\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
4002.2.a.z \(3\) \(31.956\) 3.3.316.1 None \(3\) \(-3\) \(0\) \(-2\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.ba \(4\) \(31.956\) 4.4.16448.2 None \(-4\) \(-4\) \(2\) \(6\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
4002.2.a.bb \(4\) \(31.956\) 4.4.23252.1 None \(-4\) \(4\) \(-3\) \(-2\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}-q^{6}+\cdots\)
4002.2.a.bc \(4\) \(31.956\) 4.4.11324.1 None \(4\) \(4\) \(-4\) \(-4\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4002.2.a.bd \(4\) \(31.956\) 4.4.19796.1 None \(4\) \(4\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.be \(5\) \(31.956\) 5.5.2389280.1 None \(-5\) \(-5\) \(1\) \(-4\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{4}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bf \(6\) \(31.956\) 6.6.61157024.1 None \(-6\) \(6\) \(3\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.bg \(7\) \(31.956\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-5\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bh \(7\) \(31.956\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(1\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)
4002.2.a.bi \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(-3\) \(-6\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bj \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(1\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{2}q^{7}+\cdots\)
4002.2.a.bk \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(2\) \(5\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
4003.2.a.a \(2\) \(31.964\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots\)
4003.2.a.b \(152\) \(31.964\) None \(-22\) \(-18\) \(-59\) \(-19\) \(+\)
4003.2.a.c \(179\) \(31.964\) None \(22\) \(16\) \(61\) \(21\) \(-\)
4004.2.a.a \(1\) \(31.972\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(-\) \(q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
4004.2.a.b \(1\) \(31.972\) \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) \(+\) \(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
4004.2.a.c \(1\) \(31.972\) \(\Q\) None \(0\) \(2\) \(4\) \(1\) \(-\) \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
4004.2.a.d \(4\) \(31.972\) 4.4.3981.1 None \(0\) \(-3\) \(-1\) \(4\) \(+\) \(q+(-1-\beta _{2})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
4004.2.a.e \(4\) \(31.972\) \(\Q(\zeta_{15})^+\) None \(0\) \(1\) \(1\) \(-4\) \(+\) \(q+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4004.2.a.f \(5\) \(31.972\) 5.5.463341.1 None \(0\) \(3\) \(0\) \(-5\) \(+\) \(q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4004.2.a.g \(6\) \(31.972\) 6.6.246302029.1 None \(0\) \(-2\) \(-3\) \(6\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4004.2.a.h \(9\) \(31.972\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(0\) \(9\) \(-\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
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