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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
671.1.d.a \(1\) \(0.335\) \(\Q\) \(\Q(\sqrt{-671}) \) None \(-1\) \(-1\) \(2\) \(-1\) \(q-q^{2}-q^{3}+2q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
671.1.d.b \(1\) \(0.335\) \(\Q\) \(\Q(\sqrt{-671}) \) None \(1\) \(-1\) \(2\) \(1\) \(q+q^{2}-q^{3}+2q^{5}-q^{6}+q^{7}-q^{8}+\cdots\)
671.1.d.c \(2\) \(0.335\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-671}) \) None \(-1\) \(-1\) \(-1\) \(4\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
671.1.d.d \(2\) \(0.335\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-671}) \) None \(1\) \(-1\) \(-1\) \(-4\) \(q+(1-\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
671.1.d.e \(4\) \(0.335\) \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-671}) \) None \(-1\) \(1\) \(-2\) \(4\) \(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
671.1.d.f \(4\) \(0.335\) \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-671}) \) None \(1\) \(1\) \(-2\) \(-4\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
671.1.p.a \(4\) \(0.335\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{5}-\zeta_{12}q^{7}+\zeta_{12}^{3}q^{8}+\cdots\)
671.2.a.a \(5\) \(5.358\) 5.5.24217.1 None None \(-2\) \(0\) \(-2\) \(-1\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
671.2.a.b \(6\) \(5.358\) 6.6.2661761.1 None None \(0\) \(-1\) \(-1\) \(-5\) \(+\) \(q+\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
671.2.a.c \(19\) \(5.358\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(5\) \(0\) \(0\) \(9\) \(-\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
671.2.a.d \(21\) \(5.358\) None None \(0\) \(3\) \(7\) \(5\) \(-\)
671.2.c.a \(52\) \(5.358\) None None \(0\) \(4\) \(0\) \(0\)
671.2.e.a \(52\) \(5.358\) None None \(-2\) \(2\) \(0\) \(-7\)
671.2.e.b \(52\) \(5.358\) None None \(0\) \(2\) \(0\) \(5\)
671.2.f.a \(120\) \(5.358\) None None \(0\) \(0\) \(0\) \(0\)
671.2.h.a \(4\) \(5.358\) \(\Q(\zeta_{10})\) None None \(-3\) \(1\) \(4\) \(2\) \(q+(-1+\zeta_{10})q^{2}+\zeta_{10}q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots\)
671.2.h.b \(236\) \(5.358\) None None \(2\) \(-2\) \(-6\) \(1\)
671.2.i.a \(108\) \(5.358\) None None \(-2\) \(-2\) \(4\) \(8\)
671.2.i.b \(108\) \(5.358\) None None \(0\) \(-2\) \(4\) \(10\)
671.2.j.a \(4\) \(5.358\) \(\Q(\zeta_{10})\) None None \(2\) \(6\) \(-1\) \(-3\) \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
671.2.j.b \(108\) \(5.358\) None None \(-3\) \(5\) \(7\) \(-6\)
671.2.j.c \(128\) \(5.358\) None None \(-5\) \(-17\) \(-8\) \(-3\)
671.2.k.a \(4\) \(5.358\) \(\Q(\zeta_{10})\) None None \(2\) \(5\) \(4\) \(2\) \(q+(\zeta_{10}+\zeta_{10}^{3})q^{2}+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
671.2.k.b \(236\) \(5.358\) None None \(-3\) \(-6\) \(-16\) \(1\)
671.2.l.a \(4\) \(5.358\) \(\Q(\zeta_{10})\) None None \(-3\) \(0\) \(-1\) \(2\) \(q+(-1-\zeta_{10}^{2})q^{2}+(1+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots\)
671.2.l.b \(236\) \(5.358\) None None \(2\) \(-6\) \(4\) \(-4\)
671.2.m.a \(4\) \(5.358\) \(\Q(\zeta_{10})\) None None \(2\) \(1\) \(-6\) \(2\) \(q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
671.2.m.b \(236\) \(5.358\) None None \(-8\) \(-2\) \(4\) \(-9\)
671.2.o.a \(100\) \(5.358\) None None \(0\) \(4\) \(-6\) \(6\)
671.2.q.a \(240\) \(5.358\) None None \(0\) \(-1\) \(0\) \(-5\)
671.2.x.a \(240\) \(5.358\) None None \(0\) \(-6\) \(-10\) \(0\)
671.2.ba.a \(240\) \(5.358\) None None \(-5\) \(-1\) \(0\) \(-5\)
671.2.bc.a \(208\) \(5.358\) None None \(0\) \(-4\) \(-10\) \(-30\)
671.2.bd.a \(240\) \(5.358\) None None \(-5\) \(-1\) \(0\) \(-5\)
671.2.bf.a \(240\) \(5.358\) None None \(-5\) \(-6\) \(-5\) \(0\)
671.2.bj.a \(240\) \(5.358\) None None \(0\) \(0\) \(-12\) \(0\)
671.2.bk.a \(480\) \(5.358\) None None \(-3\) \(-2\) \(-16\) \(-11\)
671.2.bl.a \(480\) \(5.358\) None None \(-8\) \(-2\) \(-6\) \(-6\)
671.2.bm.a \(480\) \(5.358\) None None \(-3\) \(-12\) \(-1\) \(-6\)
671.2.bn.a \(208\) \(5.358\) None None \(0\) \(-2\) \(-10\) \(-10\)
671.2.bn.b \(208\) \(5.358\) None None \(2\) \(-2\) \(-10\) \(-8\)
671.2.bo.a \(480\) \(5.358\) None None \(-8\) \(-2\) \(-1\) \(-6\)
671.2.bp.a \(480\) \(5.358\) None None \(-8\) \(-12\) \(-6\) \(-1\)
671.2.br.a \(480\) \(5.358\) None None \(-10\) \(0\) \(-10\) \(-10\)
671.2.bt.a \(480\) \(5.358\) None None \(-10\) \(-10\) \(-10\) \(-20\)
671.2.bv.a \(480\) \(5.358\) None None \(-10\) \(-10\) \(0\) \(-10\)
671.2.bw.a \(480\) \(5.358\) None None \(0\) \(-20\) \(-20\) \(0\)
671.2.by.a \(480\) \(5.358\) None None \(-10\) \(-10\) \(-10\) \(-10\)
671.2.cb.a \(480\) \(5.358\) None None \(-10\) \(0\) \(0\) \(0\)
671.2.ce.a \(480\) \(5.358\) None None \(-4\) \(-2\) \(0\) \(2\)
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