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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
261.1.f.a \(4\) \(0.130\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
261.2.a.a \(2\) \(2.084\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-4\) \(0\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.b \(2\) \(2.084\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(-4\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
261.2.a.c \(2\) \(2.084\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(4\) \(0\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.a.d \(2\) \(2.084\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(2\) \(0\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-2\beta q^{7}+\cdots\)
261.2.a.e \(3\) \(2.084\) 3.3.229.1 None None \(-2\) \(0\) \(0\) \(4\) \(-\) \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots\)
261.2.c.a \(2\) \(2.084\) \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(6\) \(4\) \(q+\beta q^{2}-3q^{4}+3q^{5}+2q^{7}-\beta q^{8}+\cdots\)
261.2.c.b \(4\) \(2.084\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(-8\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+2\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.c.c \(6\) \(2.084\) 6.0.\(\cdots\).1 \(\Q(\sqrt{-87}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
261.2.e.a \(22\) \(2.084\) None None \(-1\) \(-2\) \(1\) \(7\)
261.2.e.b \(34\) \(2.084\) None None \(-1\) \(-2\) \(1\) \(-9\)
261.2.g.a \(4\) \(2.084\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(16\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
261.2.g.b \(8\) \(2.084\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}+(2\beta _{2}+\beta _{6})q^{4}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
261.2.g.c \(8\) \(2.084\) 8.0.1871773696.1 None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{5})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
261.2.i.a \(56\) \(2.084\) None None \(0\) \(0\) \(2\) \(-2\)
261.2.k.a \(6\) \(2.084\) \(\Q(\zeta_{14})\) None None \(2\) \(0\) \(-1\) \(1\) \(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
261.2.k.b \(18\) \(2.084\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(7\) \(-4\) \(q+\beta _{3}q^{2}+(-\beta _{10}-\beta _{16})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
261.2.k.c \(18\) \(2.084\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(4\) \(0\) \(1\) \(-4\) \(q+(\beta _{3}-\beta _{9})q^{2}+(2\beta _{1}+\beta _{5}-\beta _{6}+2\beta _{12}+\cdots)q^{4}+\cdots\)
261.2.k.d \(24\) \(2.084\) None None \(0\) \(0\) \(0\) \(0\)
261.2.l.a \(112\) \(2.084\) None None \(-6\) \(-4\) \(0\) \(-4\)
261.2.o.a \(12\) \(2.084\) 12.0.\(\cdots\).1 None None \(7\) \(0\) \(1\) \(-11\) \(q+(1-\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
261.2.o.b \(24\) \(2.084\) None None \(0\) \(0\) \(4\) \(8\)
261.2.o.c \(36\) \(2.084\) None None \(0\) \(0\) \(0\) \(0\)
261.2.q.a \(336\) \(2.084\) None None \(-5\) \(-10\) \(-9\) \(-5\)
261.2.r.a \(120\) \(2.084\) None None \(0\) \(0\) \(0\) \(0\)
261.2.u.a \(336\) \(2.084\) None None \(-7\) \(-14\) \(-9\) \(-5\)
261.2.x.a \(672\) \(2.084\) None None \(-36\) \(-24\) \(-42\) \(-10\)
261.3.b.a \(20\) \(7.112\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
261.3.d.a \(20\) \(7.112\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{10}q^{2}+(2+\beta _{1})q^{4}-\beta _{13}q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.3.f.a \(8\) \(7.112\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(-2\) \(0\) \(0\) \(-4\) \(q-\beta _{5}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{4}+\cdots\)
261.3.f.b \(8\) \(7.112\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(8\) \(0\) \(0\) \(12\) \(q+(1+\beta _{2}-\beta _{3})q^{2}+(\beta _{2}-2\beta _{3}-2\beta _{4}+\cdots)q^{4}+\cdots\)
261.3.f.c \(12\) \(7.112\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) \(q+(\beta _{1}-\beta _{9})q^{2}+(-\beta _{2}-\beta _{6}+3\beta _{7}+\cdots)q^{4}+\cdots\)
261.3.f.d \(20\) \(7.112\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2\beta _{10}+\beta _{13})q^{4}-\beta _{16}q^{5}+\cdots\)
261.3.h.a \(116\) \(7.112\) None None \(0\) \(0\) \(-6\) \(-2\)
261.3.j.a \(112\) \(7.112\) None None \(0\) \(2\) \(-18\) \(2\)
261.3.m.a \(232\) \(7.112\) None None \(-2\) \(-4\) \(0\) \(-4\)
261.3.n.a \(120\) \(7.112\) None None \(0\) \(0\) \(0\) \(16\)
261.3.p.a \(120\) \(7.112\) None None \(0\) \(0\) \(0\) \(-16\)
261.3.s.a \(48\) \(7.112\) None None \(16\) \(0\) \(14\) \(-10\)
261.3.s.b \(120\) \(7.112\) None None \(-8\) \(0\) \(0\) \(0\)
261.3.s.c \(120\) \(7.112\) None None \(0\) \(0\) \(0\) \(0\)
261.3.t.a \(696\) \(7.112\) None None \(-15\) \(-10\) \(-15\) \(-5\)
261.3.v.a \(696\) \(7.112\) None None \(-21\) \(-14\) \(-15\) \(-5\)
261.3.w.a \(1392\) \(7.112\) None None \(-12\) \(-24\) \(-14\) \(-10\)
261.4.a.a \(2\) \(15.399\) \(\Q(\sqrt{41}) \) None None \(1\) \(0\) \(1\) \(-24\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+(2-3\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
261.4.a.b \(2\) \(15.399\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(10\) \(-16\) \(-\) \(q+(1+\beta )q^{2}+(-5+2\beta )q^{4}+(5+4\beta )q^{5}+\cdots\)
261.4.a.c \(2\) \(15.399\) \(\Q(\sqrt{17}) \) None None \(5\) \(0\) \(11\) \(-24\) \(+\) \(q+(3-\beta )q^{2}+(5-5\beta )q^{4}+(7-3\beta )q^{5}+\cdots\)
261.4.a.d \(5\) \(15.399\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-3\) \(0\) \(-29\) \(4\) \(-\) \(q+(-1+\beta _{1})q^{2}+(6+\beta _{2}+\beta _{3})q^{4}+\cdots\)
261.4.a.e \(5\) \(15.399\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-3\) \(0\) \(1\) \(4\) \(+\) \(q+(-1+\beta _{1})q^{2}+(6-2\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
261.4.a.f \(5\) \(15.399\) 5.5.13458092.1 None None \(0\) \(0\) \(-10\) \(40\) \(+\) \(q+\beta _{1}q^{2}+(6+2\beta _{1}+2\beta _{3}+\beta _{4})q^{4}+\cdots\)
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