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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1512.1.e.a \(1\) \(0.755\) \(\Q\) \(\Q(\sqrt{-42}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
1512.1.e.b \(1\) \(0.755\) \(\Q\) \(\Q(\sqrt{-42}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
1512.1.e.c \(1\) \(0.755\) \(\Q\) \(\Q(\sqrt{-42}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
1512.1.e.d \(1\) \(0.755\) \(\Q\) \(\Q(\sqrt{-42}) \) None \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
1512.1.l.a \(4\) \(0.755\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+(\zeta_{12}-\zeta_{12}^{5})q^{5}+\cdots\)
1512.1.ba.a \(4\) \(0.755\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1512.1.bd.a \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(-2\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
1512.1.bd.b \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(0\) \(1\) \(2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.c \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(-1\) \(2\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
1512.1.bd.d \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(0\) \(2\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
1512.1.bn.a \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.b \(2\) \(0.755\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.c \(4\) \(0.755\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(-2\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
1512.1.bw.a \(4\) \(0.755\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{7}+\cdots\)
1512.1.bw.b \(4\) \(0.755\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
1512.1.ce.a \(4\) \(0.755\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1512.1.cu.a \(4\) \(0.755\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{17}+(-1+\cdots)q^{19}+\cdots\)
1512.1.ef.a \(6\) \(0.755\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None \(0\) \(-3\) \(6\) \(0\) \(q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(1+\cdots)q^{5}+\cdots\)
1512.1.ef.b \(6\) \(0.755\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None \(0\) \(3\) \(-6\) \(0\) \(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1512.1.ef.c \(12\) \(0.755\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{10}q^{2}+\zeta_{36}^{3}q^{3}-\zeta_{36}^{2}q^{4}+\cdots\)
1512.2.a.a \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-4\) \(-1\) \(-\) \(q-4q^{5}-q^{7}-4q^{11}-q^{13}-3q^{17}+\cdots\)
1512.2.a.b \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{5}-q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots\)
1512.2.a.c \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{5}-q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
1512.2.a.d \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(q-q^{5}-q^{7}+2q^{11}-4q^{13}+3q^{17}+\cdots\)
1512.2.a.e \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) \(+\) \(q-q^{5}+q^{7}-3q^{11}-2q^{17}+q^{19}+\cdots\)
1512.2.a.f \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) \(+\) \(q-q^{5}+q^{7}-6q^{13}+7q^{17}-8q^{19}+\cdots\)
1512.2.a.g \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(+\) \(q+q^{5}-q^{7}-2q^{11}-4q^{13}-3q^{17}+\cdots\)
1512.2.a.h \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(+\) \(q+q^{5}-q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots\)
1512.2.a.i \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(-\) \(q+q^{5}-q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots\)
1512.2.a.j \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(1\) \(1\) \(+\) \(q+q^{5}+q^{7}-6q^{13}-7q^{17}-8q^{19}+\cdots\)
1512.2.a.k \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(1\) \(1\) \(-\) \(q+q^{5}+q^{7}+3q^{11}+2q^{17}+q^{19}+\cdots\)
1512.2.a.l \(1\) \(12.073\) \(\Q\) None None \(0\) \(0\) \(4\) \(-1\) \(-\) \(q+4q^{5}-q^{7}+4q^{11}-q^{13}+3q^{17}+\cdots\)
1512.2.a.m \(2\) \(12.073\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-4\) \(2\) \(+\) \(q+(-2+\beta )q^{5}+q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.n \(2\) \(12.073\) \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(-1\) \(2\) \(-\) \(q-\beta q^{5}+q^{7}+(1+\beta )q^{13}-q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.o \(2\) \(12.073\) \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}-2\beta q^{13}+\cdots\)
1512.2.a.p \(2\) \(12.073\) \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q+\beta q^{5}-q^{7}+(2-\beta )q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.q \(2\) \(12.073\) \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(1\) \(2\) \(-\) \(q+\beta q^{5}+q^{7}+(1+\beta )q^{13}+q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.r \(2\) \(12.073\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(4\) \(2\) \(-\) \(q+(2+\beta )q^{5}+q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots\)
1512.2.c.a \(2\) \(12.073\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-2\) \(q+(-1-i)q^{2}+2iq^{4}+2iq^{5}-q^{7}+\cdots\)
1512.2.c.b \(2\) \(12.073\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-2\) \(q+(1-i)q^{2}-2iq^{4}+2iq^{5}-q^{7}+\cdots\)
1512.2.c.c \(8\) \(12.073\) 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
1512.2.c.d \(16\) \(12.073\) \(\Q(\zeta_{40})\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\zeta_{40}^{11}q^{2}-\zeta_{40}q^{4}+(\zeta_{40}^{10}+\zeta_{40}^{11}+\cdots)q^{5}+\cdots\)
1512.2.c.e \(20\) \(12.073\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots\)
1512.2.c.f \(24\) \(12.073\) None None \(0\) \(0\) \(0\) \(24\)
1512.2.c.g \(24\) \(12.073\) None None \(0\) \(0\) \(0\) \(24\)
1512.2.j.a \(8\) \(12.073\) 8.0.56070144.2 None None \(-4\) \(0\) \(-8\) \(0\) \(q+(-1-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
1512.2.j.b \(8\) \(12.073\) 8.0.56070144.2 None None \(4\) \(0\) \(8\) \(0\) \(q+(1+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1512.2.j.c \(32\) \(12.073\) None None \(0\) \(0\) \(0\) \(0\)
1512.2.j.d \(48\) \(12.073\) None None \(0\) \(0\) \(0\) \(0\)
1512.2.k.a \(16\) \(12.073\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\)
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