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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
272.1.g.a \(2\) \(0.136\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots\)
272.1.u.a \(4\) \(0.136\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{13}+\cdots\)
272.2.a.a \(1\) \(2.172\) \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-2q^{3}+q^{9}-2q^{11}-6q^{13}-q^{17}+\cdots\)
272.2.a.b \(1\) \(2.172\) \(\Q\) None None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(q-2q^{5}-4q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots\)
272.2.a.c \(1\) \(2.172\) \(\Q\) None None \(0\) \(2\) \(-2\) \(2\) \(-\) \(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
272.2.a.d \(1\) \(2.172\) \(\Q\) None None \(0\) \(2\) \(0\) \(4\) \(-\) \(q+2q^{3}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
272.2.a.e \(2\) \(2.172\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(2\) \(-\) \(q+(-1+\beta )q^{3}+2\beta q^{5}+(1-\beta )q^{7}+\cdots\)
272.2.a.f \(2\) \(2.172\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(4\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+2q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
272.2.b.a \(2\) \(2.172\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}+2q^{13}+\cdots\)
272.2.b.b \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+iq^{11}-2q^{13}+\cdots\)
272.2.b.c \(2\) \(2.172\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
272.2.b.d \(2\) \(2.172\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-\beta q^{7}+3q^{9}+2\beta q^{11}+2q^{13}+\cdots\)
272.2.j.a \(68\) \(2.172\) None None \(0\) \(0\) \(-4\) \(0\)
272.2.l.a \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(2\) \(0\) \(q+(-1-i)q^{2}+(1-i)q^{3}+2iq^{4}+\cdots\)
272.2.l.b \(30\) \(2.172\) None None \(2\) \(-2\) \(-2\) \(0\)
272.2.l.c \(32\) \(2.172\) None None \(0\) \(0\) \(0\) \(0\)
272.2.o.a \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-2\) \(-4\) \(q+(-2-2i)q^{3}+(-1-i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
272.2.o.b \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(2\) \(q+(-1-i)q^{3}+(1+i)q^{5}+(1-i)q^{7}+\cdots\)
272.2.o.c \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-3iq^{9}+(4-4i)q^{11}+\cdots\)
272.2.o.d \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-6\) \(6\) \(q+(1+i)q^{3}+(-3-3i)q^{5}+(3-3i)q^{7}+\cdots\)
272.2.o.e \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(-4\) \(q+(1+i)q^{3}+(2+2i)q^{5}+(-2+2i)q^{7}+\cdots\)
272.2.o.f \(2\) \(2.172\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(4\) \(q+(1+i)q^{3}+(2+2i)q^{5}+(2-2i)q^{7}+\cdots\)
272.2.o.g \(4\) \(2.172\) \(\Q(i, \sqrt{13})\) None None \(0\) \(2\) \(-4\) \(-2\) \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+\cdots\)
272.2.r.a \(68\) \(2.172\) None None \(-4\) \(0\) \(0\) \(0\)
272.2.s.a \(68\) \(2.172\) None None \(0\) \(-4\) \(0\) \(0\)
272.2.v.a \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(-8\) \(-4\) \(q+(-1-\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots\)
272.2.v.b \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-8\) \(0\) \(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8})q^{5}+\cdots\)
272.2.v.c \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(1-\zeta_{8})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
272.2.v.d \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(4\) \(q+(1+\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
272.2.v.e \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(4\) \(4\) \(q+(1+\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(1+2\zeta_{8}+\cdots)q^{7}+\cdots\)
272.2.v.f \(12\) \(2.172\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{2}q^{3}+\beta _{8}q^{5}+(-1+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
272.2.w.a \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(4\) \(8\) \(q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}+\zeta_{8}^{2})q^{3}+2\zeta_{8}^{2}q^{4}+\cdots\)
272.2.w.b \(132\) \(2.172\) None None \(-8\) \(-4\) \(-8\) \(-8\)
272.2.y.a \(4\) \(2.172\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(0\) \(-8\) \(q+(-1-\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}^{3})q^{3}+\cdots\)
272.2.y.b \(132\) \(2.172\) None None \(0\) \(0\) \(-4\) \(8\)
272.2.bd.a \(272\) \(2.172\) None None \(-8\) \(-8\) \(-8\) \(-16\)
272.2.bf.a \(8\) \(2.172\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}^{2}+\zeta_{16}^{3}-2\zeta_{16}^{6}+2\zeta_{16}^{7})q^{5}+\cdots\)
272.2.bf.b \(16\) \(2.172\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{10}+\cdots)q^{5}+\cdots\)
272.2.bf.c \(48\) \(2.172\) None None \(0\) \(0\) \(0\) \(0\)
272.2.bj.a \(272\) \(2.172\) None None \(-8\) \(-8\) \(-8\) \(-16\)
272.3.d.a \(4\) \(7.411\) 4.0.2312.1 None None \(0\) \(0\) \(12\) \(0\) \(q-\beta _{1}q^{3}+(3+\beta _{2})q^{5}+\beta _{3}q^{7}+(-5+\cdots)q^{9}+\cdots\)
272.3.d.b \(12\) \(7.411\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-12\) \(0\) \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots\)
272.3.g.a \(2\) \(7.411\) \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-17}) \) None \(0\) \(-2\) \(0\) \(-18\) \(q+(-1-\beta )q^{3}+(-9-\beta )q^{7}+(9+2\beta )q^{9}+\cdots\)
272.3.g.b \(2\) \(7.411\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-9q^{9}-10q^{13}+(-15-i)q^{17}+\cdots\)
272.3.g.c \(2\) \(7.411\) \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-17}) \) None \(0\) \(2\) \(0\) \(18\) \(q+(1+\beta )q^{3}+(9+\beta )q^{7}+(9+2\beta )q^{9}+\cdots\)
272.3.g.d \(12\) \(7.411\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{7}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+\cdots\)
272.3.i.a \(140\) \(7.411\) None None \(0\) \(0\) \(0\) \(-4\)
272.3.k.a \(140\) \(7.411\) None None \(-4\) \(0\) \(0\) \(0\)
272.3.p.a \(2\) \(7.411\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+9iq^{9}+24q^{13}+(15+\cdots)q^{17}+\cdots\)
272.3.p.b \(2\) \(7.411\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(14\) \(0\) \(q+(7+7i)q^{5}+9iq^{9}-24q^{13}+(15+\cdots)q^{17}+\cdots\)
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