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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1575.1.e.a \(2\) \(0.786\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{7}-iq^{8}+q^{11}-q^{14}+\cdots\)
1575.1.e.b \(2\) \(0.786\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-iq^{7}+q^{16}-iq^{28}-iq^{37}+\cdots\)
1575.1.e.c \(4\) \(0.786\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1575.1.h.a \(1\) \(0.786\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}-q^{7}+q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.b \(1\) \(0.786\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(1\) \(q-q^{4}+q^{7}+q^{16}-q^{28}+2q^{37}+\cdots\)
1575.1.h.c \(1\) \(0.786\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.d \(2\) \(0.786\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}-\beta q^{11}+\cdots\)
1575.1.h.e \(2\) \(0.786\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{2}+2q^{4}+q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
1575.1.n.a \(4\) \(0.786\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots\)
1575.1.n.b \(4\) \(0.786\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\cdots\)
1575.1.n.c \(8\) \(0.786\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{8}+\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1575.1.n.d \(8\) \(0.786\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{8}-\zeta_{24}^{10})q^{2}+(-\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
1575.1.x.a \(2\) \(0.786\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}q^{4}-\zeta_{6}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\cdots\)
1575.1.x.b \(2\) \(0.786\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{4}+\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)
1575.1.y.a \(4\) \(0.786\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-q^{9}+\cdots\)
1575.1.bj.a \(4\) \(0.786\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{13}+\cdots\)
1575.1.cb.a \(8\) \(0.786\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots\)
1575.1.ci.a \(8\) \(0.786\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{13}+\cdots\)
1575.1.cn.a \(8\) \(0.786\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{7}+\cdots\)
1575.1.cp.a \(8\) \(0.786\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{6}+\cdots\)
1575.2.a.a \(1\) \(12.576\) \(\Q\) None None \(-2\) \(0\) \(0\) \(-1\) \(+\) \(q-2q^{2}+2q^{4}-q^{7}+3q^{11}+q^{13}+\cdots\)
1575.2.a.b \(1\) \(12.576\) \(\Q\) None None \(-1\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{2}-q^{4}-q^{7}+3q^{8}+4q^{13}+q^{14}+\cdots\)
1575.2.a.c \(1\) \(12.576\) \(\Q\) None None \(-1\) \(0\) \(0\) \(1\) \(+\) \(q-q^{2}-q^{4}+q^{7}+3q^{8}-4q^{11}+2q^{13}+\cdots\)
1575.2.a.d \(1\) \(12.576\) \(\Q\) None None \(-1\) \(0\) \(0\) \(1\) \(+\) \(q-q^{2}-q^{4}+q^{7}+3q^{8}-4q^{13}-q^{14}+\cdots\)
1575.2.a.e \(1\) \(12.576\) \(\Q\) None None \(-1\) \(0\) \(0\) \(1\) \(-\) \(q-q^{2}-q^{4}+q^{7}+3q^{8}+6q^{11}+2q^{13}+\cdots\)
1575.2.a.f \(1\) \(12.576\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-2q^{4}-q^{7}+3q^{11}-5q^{13}+4q^{16}+\cdots\)
1575.2.a.g \(1\) \(12.576\) \(\Q\) None None \(1\) \(0\) \(0\) \(-1\) \(-\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}+4q^{13}-q^{14}+\cdots\)
1575.2.a.h \(1\) \(12.576\) \(\Q\) None None \(1\) \(0\) \(0\) \(-1\) \(-\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}+6q^{13}-q^{14}+\cdots\)
1575.2.a.i \(1\) \(12.576\) \(\Q\) None None \(1\) \(0\) \(0\) \(-1\) \(+\) \(q+q^{2}-q^{4}-q^{7}-3q^{8}+6q^{11}-2q^{13}+\cdots\)
1575.2.a.j \(1\) \(12.576\) \(\Q\) None None \(1\) \(0\) \(0\) \(1\) \(+\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}-4q^{13}+q^{14}+\cdots\)
1575.2.a.k \(1\) \(12.576\) \(\Q\) None None \(2\) \(0\) \(0\) \(1\) \(-\) \(q+2q^{2}+2q^{4}+q^{7}+3q^{11}-q^{13}+\cdots\)
1575.2.a.l \(2\) \(12.576\) \(\Q(\sqrt{5}) \) None None \(-3\) \(0\) \(0\) \(-2\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
1575.2.a.m \(2\) \(12.576\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(2\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots\)
1575.2.a.n \(2\) \(12.576\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(0\) \(2\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
1575.2.a.o \(2\) \(12.576\) \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(2\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+q^{7}-3q^{8}+3q^{11}+\cdots\)
1575.2.a.p \(2\) \(12.576\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(0\) \(2\) \(+\) \(q-\beta q^{2}+(2+\beta )q^{4}+q^{7}+(-4-\beta )q^{8}+\cdots\)
1575.2.a.q \(2\) \(12.576\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}-2\beta q^{11}+\cdots\)
1575.2.a.r \(2\) \(12.576\) \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q-\beta q^{2}+3q^{4}-q^{7}-\beta q^{8}+(-2-2\beta )q^{11}+\cdots\)
1575.2.a.s \(2\) \(12.576\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-2\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{7}+(1-2\beta )q^{8}+\cdots\)
1575.2.a.t \(2\) \(12.576\) \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(-2\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}+3q^{11}+\cdots\)
1575.2.a.u \(2\) \(12.576\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{7}+(3+\beta )q^{8}+\cdots\)
1575.2.a.v \(2\) \(12.576\) \(\Q(\sqrt{5}) \) None None \(3\) \(0\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+q^{7}+(1+4\beta )q^{8}+\cdots\)
1575.2.a.w \(3\) \(12.576\) 3.3.148.1 None None \(-1\) \(0\) \(0\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{7}+(-2+\cdots)q^{8}+\cdots\)
1575.2.a.x \(3\) \(12.576\) 3.3.148.1 None None \(1\) \(0\) \(0\) \(3\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{7}+(2+\cdots)q^{8}+\cdots\)
1575.2.a.y \(4\) \(12.576\) 4.4.174928.1 None None \(0\) \(0\) \(0\) \(-4\) \(-\) \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{7}+(2\beta _{1}+\beta _{3})q^{8}+\cdots\)
1575.2.a.z \(4\) \(12.576\) 4.4.174928.1 None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+q^{7}+(2\beta _{1}+\beta _{3})q^{8}+\cdots\)
1575.2.b.a \(4\) \(12.576\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.b.b \(4\) \(12.576\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
1575.2.b.c \(4\) \(12.576\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
1575.2.b.d \(4\) \(12.576\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{1}q^{2}-\beta _{2}q^{7}-2\beta _{1}q^{8}-\beta _{1}q^{11}+\cdots\)
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