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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.1.p.a \(4\) \(0.201\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{4}q^{7}+\cdots\)
403.2.a.a \(2\) \(3.218\) \(\Q(\sqrt{5}) \) None None \(3\) \(-4\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}-2q^{3}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
403.2.a.b \(6\) \(3.218\) 6.6.5748973.1 None None \(-2\) \(-5\) \(-9\) \(0\) \(+\) \(q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
403.2.a.c \(7\) \(3.218\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(2\) \(5\) \(11\) \(4\) \(-\) \(q+\beta _{3}q^{2}+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
403.2.a.d \(8\) \(3.218\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-5\) \(-3\) \(-15\) \(-4\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
403.2.a.e \(8\) \(3.218\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-1\) \(7\) \(11\) \(-2\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
403.2.c.a \(2\) \(3.218\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(0\) \(q+2q^{3}+2q^{4}+4iq^{5}-2iq^{7}+q^{9}+\cdots\)
403.2.c.b \(32\) \(3.218\) None None \(0\) \(-4\) \(0\) \(0\)
403.2.e.a \(70\) \(3.218\) None None \(-2\) \(4\) \(-2\) \(8\)
403.2.f.a \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-6\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-3q^{5}-2\zeta_{6}q^{7}+\cdots\)
403.2.f.b \(34\) \(3.218\) None None \(4\) \(0\) \(-14\) \(6\)
403.2.f.c \(36\) \(3.218\) None None \(-5\) \(0\) \(12\) \(-4\)
403.2.g.a \(70\) \(3.218\) None None \(-2\) \(-8\) \(-2\) \(-4\)
403.2.h.a \(30\) \(3.218\) None None \(-6\) \(-2\) \(7\) \(6\)
403.2.h.b \(34\) \(3.218\) None None \(6\) \(-2\) \(-5\) \(-2\)
403.2.i.a \(68\) \(3.218\) None None \(-4\) \(0\) \(-4\) \(8\)
403.2.k.a \(4\) \(3.218\) \(\Q(\zeta_{10})\) None None \(-2\) \(-1\) \(-6\) \(-7\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots\)
403.2.k.b \(4\) \(3.218\) \(\Q(\zeta_{10})\) None None \(-1\) \(-2\) \(-4\) \(1\) \(q-\zeta_{10}q^{2}+(-2+2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
403.2.k.c \(4\) \(3.218\) \(\Q(\zeta_{10})\) None None \(-1\) \(3\) \(6\) \(-9\) \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}^{3})q^{3}+\cdots\)
403.2.k.d \(48\) \(3.218\) None None \(7\) \(-2\) \(-12\) \(25\)
403.2.k.e \(68\) \(3.218\) None None \(-3\) \(-2\) \(12\) \(2\)
403.2.l.a \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(-3\) \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
403.2.l.b \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(3\) \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots\)
403.2.l.c \(68\) \(3.218\) None None \(0\) \(-6\) \(0\) \(0\)
403.2.r.a \(68\) \(3.218\) None None \(0\) \(0\) \(0\) \(0\)
403.2.s.a \(70\) \(3.218\) None None \(-6\) \(-2\) \(0\) \(0\)
403.2.v.a \(70\) \(3.218\) None None \(-6\) \(4\) \(0\) \(-12\)
403.2.y.a \(136\) \(3.218\) None None \(0\) \(-10\) \(0\) \(0\)
403.2.ba.a \(140\) \(3.218\) None None \(-8\) \(0\) \(-2\) \(12\)
403.2.be.a \(4\) \(3.218\) \(\Q(\zeta_{12})\) None None \(-2\) \(6\) \(-2\) \(-10\) \(q+(-1+\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+\cdots\)
403.2.be.b \(4\) \(3.218\) \(\Q(\zeta_{12})\) None None \(-2\) \(6\) \(-2\) \(8\) \(q+(-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
403.2.be.c \(136\) \(3.218\) None None \(-4\) \(-24\) \(2\) \(-2\)
403.2.bf.a \(140\) \(3.218\) None None \(-8\) \(-6\) \(-2\) \(-12\)
403.2.bg.a \(144\) \(3.218\) None None \(-8\) \(0\) \(-8\) \(-16\)
403.2.bi.a \(120\) \(3.218\) None None \(6\) \(2\) \(13\) \(-16\)
403.2.bi.b \(136\) \(3.218\) None None \(-6\) \(2\) \(-15\) \(-8\)
403.2.bj.a \(280\) \(3.218\) None None \(-3\) \(3\) \(-8\) \(-1\)
403.2.bk.a \(280\) \(3.218\) None None \(-3\) \(-9\) \(-8\) \(-13\)
403.2.bl.a \(8\) \(3.218\) \(\Q(\zeta_{15})\) None None \(-4\) \(-5\) \(-24\) \(-3\) \(q+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{2}+\cdots\)
403.2.bl.b \(280\) \(3.218\) None None \(1\) \(0\) \(-8\) \(-2\)
403.2.bn.a \(272\) \(3.218\) None None \(-6\) \(-20\) \(-16\) \(-18\)
403.2.bp.a \(280\) \(3.218\) None None \(-9\) \(-9\) \(0\) \(-3\)
403.2.bs.a \(288\) \(3.218\) None None \(-9\) \(-1\) \(0\) \(-15\)
403.2.bt.a \(280\) \(3.218\) None None \(-9\) \(-3\) \(0\) \(-15\)
403.2.bz.a \(288\) \(3.218\) None None \(0\) \(-16\) \(0\) \(0\)
403.2.cb.a \(576\) \(3.218\) None None \(-12\) \(-10\) \(-32\) \(-4\)
403.2.cc.a \(560\) \(3.218\) None None \(-12\) \(-4\) \(-8\) \(-8\)
403.2.cd.a \(576\) \(3.218\) None None \(-12\) \(-28\) \(-8\) \(-16\)
403.2.ch.a \(560\) \(3.218\) None None \(-12\) \(-10\) \(-8\) \(-32\)
403.3.b.a \(1\) \(10.981\) \(\Q\) \(\Q(\sqrt{-403}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{4}+9q^{9}-9q^{11}+13q^{13}+2^{4}q^{16}+\cdots\)
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