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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1521.1.j.a \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \) None \(-2\) \(0\) \(2\) \(0\) \(q+(-1-i)q^{2}+iq^{4}+(1+i)q^{5}-q^{8}+\cdots\)
1521.1.j.b \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{4}+(1-i)q^{7}-q^{16}+(1+i)q^{19}+\cdots\)
1521.1.j.c \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+(1+i)q^{2}+iq^{4}+(-1-i)q^{5}+q^{8}+\cdots\)
1521.1.bd.a \(4\) \(0.759\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-39}) \) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1521.1.bd.b \(4\) \(0.759\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{4}+(\zeta_{12}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\)
1521.1.bd.c \(4\) \(0.759\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{16}+\cdots\)
1521.1.bd.d \(4\) \(0.759\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-39}) \) None \(2\) \(0\) \(4\) \(0\) \(q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(1+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
1521.1.bm.a \(24\) \(0.759\) \(\Q(\zeta_{52})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{52}^{17}q^{4}+(-\zeta_{52}^{5}-\zeta_{52}^{20})q^{7}+\cdots\)
1521.2.a.a \(1\) \(12.145\) \(\Q\) None None \(-1\) \(0\) \(1\) \(2\) \(-\) \(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
1521.2.a.b \(1\) \(12.145\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-2q^{4}-q^{7}+4q^{16}+8q^{19}-5q^{25}+\cdots\)
1521.2.a.c \(1\) \(12.145\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q-2q^{4}+q^{7}+4q^{16}-8q^{19}-5q^{25}+\cdots\)
1521.2.a.d \(1\) \(12.145\) \(\Q\) None None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-q^{10}+\cdots\)
1521.2.a.e \(1\) \(12.145\) \(\Q\) None None \(1\) \(0\) \(2\) \(4\) \(-\) \(q+q^{2}-q^{4}+2q^{5}+4q^{7}-3q^{8}+2q^{10}+\cdots\)
1521.2.a.f \(2\) \(12.145\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
1521.2.a.g \(2\) \(12.145\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(3\) \(-3\) \(-\) \(q-\beta q^{2}+(2+\beta )q^{4}+(2-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
1521.2.a.h \(2\) \(12.145\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-2q^{4}+2\beta q^{5}-\beta q^{7}-2\beta q^{11}+4q^{16}+\cdots\)
1521.2.a.i \(2\) \(12.145\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-2q^{4}-3\beta q^{7}+4q^{16}-2\beta q^{19}+\cdots\)
1521.2.a.j \(2\) \(12.145\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}-2\beta q^{11}+\cdots\)
1521.2.a.k \(2\) \(12.145\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots\)
1521.2.a.l \(2\) \(12.145\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{2}+q^{4}-2\beta q^{7}-\beta q^{8}+2\beta q^{11}+\cdots\)
1521.2.a.m \(2\) \(12.145\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(-3\) \(3\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+(-2+\beta )q^{5}+(1+\cdots)q^{7}+\cdots\)
1521.2.a.n \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(-3\) \(0\) \(-6\) \(2\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
1521.2.a.o \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(-2\) \(0\) \(-4\) \(3\) \(+\) \(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1521.2.a.p \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(-1\) \(0\) \(-4\) \(10\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
1521.2.a.q \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(1\) \(0\) \(4\) \(-10\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1521.2.a.r \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(2\) \(0\) \(4\) \(-3\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1521.2.a.s \(3\) \(12.145\) \(\Q(\zeta_{14})^+\) None None \(3\) \(0\) \(6\) \(-2\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots\)
1521.2.a.t \(4\) \(12.145\) 4.4.8112.1 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
1521.2.a.u \(4\) \(12.145\) \(\Q(\sqrt{3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{3}q^{2}+3q^{4}+\beta _{3}q^{5}+2\beta _{1}q^{7}+\cdots\)
1521.2.a.v \(6\) \(12.145\) 6.6.1997632.1 None None \(0\) \(0\) \(0\) \(-12\) \(+\) \(q+\beta _{5}q^{2}+(-2\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
1521.2.a.w \(6\) \(12.145\) 6.6.1997632.1 None None \(0\) \(0\) \(0\) \(12\) \(-\) \(q+\beta _{5}q^{2}+(-2\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
1521.2.b.a \(2\) \(12.145\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}-q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{8}+3q^{10}+\cdots\)
1521.2.b.b \(2\) \(12.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+2iq^{5}-4iq^{7}+3iq^{8}+\cdots\)
1521.2.b.c \(2\) \(12.145\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}-iq^{5}+2iq^{7}+3iq^{8}+\cdots\)
1521.2.b.d \(2\) \(12.145\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+3\zeta_{6}q^{7}+4q^{16}-2\zeta_{6}q^{19}+\cdots\)
1521.2.b.e \(2\) \(12.145\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+iq^{7}+4q^{16}+8iq^{19}+5q^{25}+\cdots\)
1521.2.b.f \(2\) \(12.145\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{11}+\cdots\)
1521.2.b.g \(4\) \(12.145\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{5}-2\beta _{2}q^{7}+\cdots\)
1521.2.b.h \(4\) \(12.145\) \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1521.2.b.i \(4\) \(12.145\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
1521.2.b.j \(4\) \(12.145\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1521.2.b.k \(6\) \(12.145\) 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-3-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
1521.2.b.l \(6\) \(12.145\) 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+(1-2\beta _{2}-\beta _{4})q^{4}+\cdots\)
1521.2.b.m \(6\) \(12.145\) 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1521.2.b.n \(12\) \(12.145\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(-2-\beta _{2}+2\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1521.2.i.a \(4\) \(12.145\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1521.2.i.b \(4\) \(12.145\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(12\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(3+3\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1521.2.i.c \(8\) \(12.145\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{4}+(2\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
1521.2.i.d \(8\) \(12.145\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+2\zeta_{24}^{3}q^{4}+\cdots\)
1521.2.i.e \(8\) \(12.145\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(4\) \(q+(-\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+2\zeta_{24}^{3}q^{4}+\cdots\)
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