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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
507.1.c.a \(1\) \(0.253\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots\)
507.1.h.a \(2\) \(0.253\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots\)
507.1.i.a \(2\) \(0.253\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots\)
507.1.n.a \(12\) \(0.253\) \(\Q(\zeta_{26})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{26}^{7}q^{3}-\zeta_{26}^{2}q^{4}+(\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots\)
507.1.o.a \(12\) \(0.253\) \(\Q(\zeta_{26})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{2}q^{4}+(-\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots\)
507.2.a.a \(1\) \(4.048\) \(\Q\) None None \(-1\) \(-1\) \(-2\) \(4\) \(+\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots\)
507.2.a.b \(1\) \(4.048\) \(\Q\) None None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
507.2.a.c \(1\) \(4.048\) \(\Q\) None None \(1\) \(-1\) \(-1\) \(2\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
507.2.a.d \(2\) \(4.048\) \(\Q(\sqrt{17}) \) None None \(-1\) \(2\) \(3\) \(3\) \(-\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
507.2.a.e \(2\) \(4.048\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q-q^{3}-2q^{4}+2\beta q^{5}+\beta q^{7}+q^{9}+\cdots\)
507.2.a.f \(2\) \(4.048\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots\)
507.2.a.g \(2\) \(4.048\) \(\Q(\sqrt{17}) \) None None \(1\) \(2\) \(-3\) \(-3\) \(-\) \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
507.2.a.h \(2\) \(4.048\) \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(0\) \(0\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots\)
507.2.a.i \(3\) \(4.048\) \(\Q(\zeta_{14})^+\) None None \(-3\) \(-3\) \(-6\) \(-2\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
507.2.a.j \(3\) \(4.048\) \(\Q(\zeta_{14})^+\) None None \(-1\) \(3\) \(-4\) \(-10\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
507.2.a.k \(3\) \(4.048\) \(\Q(\zeta_{14})^+\) None None \(1\) \(3\) \(4\) \(10\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
507.2.a.l \(3\) \(4.048\) \(\Q(\zeta_{14})^+\) None None \(3\) \(-3\) \(6\) \(2\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(4-\beta _{1})q^{4}+\cdots\)
507.2.b.a \(2\) \(4.048\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
507.2.b.b \(2\) \(4.048\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}+q^{4}-iq^{5}-iq^{6}-2iq^{7}+\cdots\)
507.2.b.c \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}+q^{9}+\cdots\)
507.2.b.d \(4\) \(4.048\) \(\Q(i, \sqrt{17})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
507.2.b.e \(4\) \(4.048\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+q^{3}+(-1-\zeta_{8}^{3})q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
507.2.b.f \(6\) \(4.048\) 6.0.153664.1 None None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-3-\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.b.g \(6\) \(4.048\) 6.0.153664.1 None None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
507.2.e.a \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(4\) \(4\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
507.2.e.b \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(-4\) \(-4\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
507.2.e.c \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(2\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
507.2.e.d \(4\) \(4.048\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots\)
507.2.e.e \(4\) \(4.048\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
507.2.e.f \(4\) \(4.048\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(2-2\zeta_{12})q^{4}-2\zeta_{12}^{3}q^{5}+\cdots\)
507.2.e.g \(4\) \(4.048\) \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(1\) \(-2\) \(6\) \(-3\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.e.h \(4\) \(4.048\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(-2\) \(0\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots\)
507.2.e.i \(6\) \(4.048\) 6.0.64827.1 None None \(-3\) \(3\) \(12\) \(-2\) \(q+(-2+2\beta _{1}+\beta _{4}+2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots\)
507.2.e.j \(6\) \(4.048\) 6.0.64827.1 None None \(-1\) \(-3\) \(8\) \(-10\) \(q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.e.k \(6\) \(4.048\) 6.0.64827.1 None None \(1\) \(-3\) \(-8\) \(10\) \(q+\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.e.l \(6\) \(4.048\) 6.0.64827.1 None None \(3\) \(3\) \(-12\) \(2\) \(q+(2-2\beta _{1}-\beta _{4}-2\beta _{5})q^{2}+(1-\beta _{5})q^{3}+\cdots\)
507.2.f.a \(4\) \(4.048\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-4\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
507.2.f.b \(4\) \(4.048\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
507.2.f.c \(4\) \(4.048\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
507.2.f.d \(8\) \(4.048\) 8.0.56070144.2 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-2\beta _{2}-\beta _{5})q^{4}+\cdots\)
507.2.f.e \(8\) \(4.048\) 8.0.56070144.2 None None \(0\) \(4\) \(0\) \(-8\) \(q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(\beta _{4}+\beta _{5})q^{3}+\cdots\)
507.2.f.f \(8\) \(4.048\) 8.0.56070144.2 None None \(0\) \(4\) \(0\) \(8\) \(q+(\beta _{1}+\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
507.2.f.g \(48\) \(4.048\) None None \(0\) \(0\) \(0\) \(0\)
507.2.j.a \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(1\) \(0\) \(-6\) \(q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
507.2.j.b \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(3\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots\)
507.2.j.c \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None None \(3\) \(1\) \(0\) \(6\) \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
507.2.j.d \(4\) \(4.048\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
507.2.j.e \(4\) \(4.048\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
507.2.j.f \(8\) \(4.048\) \(\Q(\zeta_{24})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+(1-\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
507.2.j.g \(8\) \(4.048\) 8.0.1731891456.1 None None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+3\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
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