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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1020.1.o.a \(4\) \(0.509\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)
1020.1.cl.a \(16\) \(0.509\) \(\Q(\zeta_{32})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{11}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{6}q^{4}+\cdots\)
1020.1.cl.b \(16\) \(0.509\) \(\Q(\zeta_{32})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{9}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{2}q^{4}+\cdots\)
1020.2.a.a \(1\) \(8.145\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots\)
1020.2.a.b \(1\) \(8.145\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
1020.2.a.c \(1\) \(8.145\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(+\) \(q-q^{3}+q^{5}+q^{9}-6q^{11}+2q^{13}+\cdots\)
1020.2.a.d \(1\) \(8.145\) \(\Q\) None None \(0\) \(-1\) \(1\) \(3\) \(-\) \(q-q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
1020.2.a.e \(1\) \(8.145\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
1020.2.a.f \(1\) \(8.145\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{3}-q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1020.2.a.g \(1\) \(8.145\) \(\Q\) None None \(0\) \(1\) \(-1\) \(5\) \(-\) \(q+q^{3}-q^{5}+5q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
1020.2.a.h \(1\) \(8.145\) \(\Q\) None None \(0\) \(1\) \(1\) \(-5\) \(+\) \(q+q^{3}+q^{5}-5q^{7}+q^{9}-5q^{11}+q^{15}+\cdots\)
1020.2.a.i \(2\) \(8.145\) \(\Q(\sqrt{33}) \) None None \(0\) \(-2\) \(-2\) \(1\) \(+\) \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1020.2.a.j \(2\) \(8.145\) \(\Q(\sqrt{33}) \) None None \(0\) \(2\) \(2\) \(1\) \(-\) \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
1020.2.e.a \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}+2iq^{11}-6q^{13}+\cdots\)
1020.2.e.b \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}+3iq^{7}-q^{9}-3iq^{11}+\cdots\)
1020.2.e.c \(4\) \(8.145\) \(\Q(i, \sqrt{33})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1020.2.e.d \(4\) \(8.145\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}-\zeta_{8}q^{5}+(\zeta_{8}+\zeta_{8}^{2})q^{7}-q^{9}+\cdots\)
1020.2.g.a \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}-q^{9}+(1-2i)q^{15}+\cdots\)
1020.2.g.b \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}-5q^{11}+\cdots\)
1020.2.g.c \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}+3iq^{7}-q^{9}+\cdots\)
1020.2.g.d \(10\) \(8.145\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}+\beta _{6}q^{5}+\beta _{9}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1020.2.k.a \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(2\) \(q-q^{3}+(-2-i)q^{5}+q^{7}+q^{9}+3iq^{11}+\cdots\)
1020.2.k.b \(2\) \(8.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(-2\) \(q+q^{3}+(2+i)q^{5}-q^{7}+q^{9}-3iq^{11}+\cdots\)
1020.2.k.c \(8\) \(8.145\) 8.0.\(\cdots\).1 None None \(0\) \(-8\) \(3\) \(-6\) \(q-q^{3}+\beta _{5}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots\)
1020.2.k.d \(8\) \(8.145\) 8.0.\(\cdots\).1 None None \(0\) \(8\) \(-3\) \(6\) \(q+q^{3}-\beta _{5}q^{5}+(1-\beta _{2})q^{7}+q^{9}+\beta _{6}q^{11}+\cdots\)
1020.2.s.a \(72\) \(8.145\) None None \(0\) \(0\) \(0\) \(0\)
1020.2.v.a \(64\) \(8.145\) None None \(0\) \(-4\) \(0\) \(8\)
1020.2.y.a \(40\) \(8.145\) None None \(0\) \(0\) \(4\) \(0\)
1020.2.bd.a \(12\) \(8.145\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}-\beta _{3}q^{9}+\cdots\)
1020.2.bd.b \(12\) \(8.145\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}-\beta _{9}q^{7}-\beta _{3}q^{9}+\cdots\)
1020.2.bg.a \(16\) \(8.145\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{3}-\beta _{12}q^{5}-3\beta _{10}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1020.2.bg.b \(56\) \(8.145\) None None \(0\) \(0\) \(0\) \(0\)
1020.2.bn.a \(72\) \(8.145\) None None \(0\) \(0\) \(0\) \(0\)
1020.2.bp.a \(24\) \(8.145\) None None \(0\) \(0\) \(0\) \(-8\)
1020.2.bp.b \(24\) \(8.145\) None None \(0\) \(0\) \(0\) \(8\)
1020.2.cc.a \(64\) \(8.145\) None None \(0\) \(0\) \(-8\) \(0\)
1020.3.c.a \(64\) \(27.793\) None None \(0\) \(0\) \(0\) \(0\)
1020.3.i.a \(48\) \(27.793\) None None \(0\) \(0\) \(0\) \(0\)
1020.3.m.a \(44\) \(27.793\) None None \(0\) \(0\) \(0\) \(-8\)
1020.3.o.a \(8\) \(27.793\) 8.0.1731891456.1 \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta _{3}q^{3}+(-2\beta _{3}-\beta _{4})q^{5}-9q^{9}+\cdots\)
1020.3.o.b \(64\) \(27.793\) None None \(0\) \(0\) \(0\) \(0\)
1020.3.t.a \(72\) \(27.793\) None None \(0\) \(0\) \(0\) \(0\)
1020.3.u.a \(72\) \(27.793\) None None \(0\) \(0\) \(0\) \(0\)
1020.3.bc.a \(96\) \(27.793\) None None \(0\) \(-8\) \(0\) \(0\)
1020.3.bh.a \(64\) \(27.793\) None None \(0\) \(0\) \(0\) \(-16\)
1020.3.bm.a \(72\) \(27.793\) None None \(0\) \(0\) \(-8\) \(-24\)
1020.4.a.a \(1\) \(60.182\) \(\Q\) None None \(0\) \(3\) \(-5\) \(20\) \(-\) \(q+3q^{3}-5q^{5}+20q^{7}+9q^{9}-20q^{11}+\cdots\)
1020.4.a.b \(1\) \(60.182\) \(\Q\) None None \(0\) \(3\) \(5\) \(-8\) \(+\) \(q+3q^{3}+5q^{5}-8q^{7}+9q^{9}+20q^{11}+\cdots\)
1020.4.a.c \(2\) \(60.182\) \(\Q(\sqrt{19}) \) None None \(0\) \(-6\) \(-10\) \(-24\) \(-\) \(q-3q^{3}-5q^{5}+(-12+\beta )q^{7}+9q^{9}+\cdots\)
1020.4.a.d \(2\) \(60.182\) \(\Q(\sqrt{389}) \) None None \(0\) \(-6\) \(-10\) \(32\) \(-\) \(q-3q^{3}-5q^{5}+(2^{4}-\beta )q^{7}+9q^{9}+\cdots\)
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