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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
756.1.d.a \(2\) \(0.377\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-2\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+\cdots\)
756.1.d.b \(2\) \(0.377\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(\zeta_{6}+\cdots)q^{19}+\cdots\)
756.1.h.a \(1\) \(0.377\) \(\Q\) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
756.1.h.b \(1\) \(0.377\) \(\Q\) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
756.1.h.c \(1\) \(0.377\) \(\Q\) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
756.1.h.d \(1\) \(0.377\) \(\Q\) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
756.1.z.a \(2\) \(0.377\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+(1-\zeta_{6}^{2})q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
756.1.bk.a \(2\) \(0.377\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+q^{13}-\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots\)
756.2.a.a \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) \(-\) \(q-3q^{5}+q^{7}-3q^{11}+2q^{13}+6q^{17}+\cdots\)
756.2.a.b \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) \(+\) \(q-3q^{5}+q^{7}+2q^{13}-3q^{17}-4q^{19}+\cdots\)
756.2.a.c \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(q-q^{5}-q^{7}-2q^{11}-5q^{17}+2q^{19}+\cdots\)
756.2.a.d \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(-\) \(q+q^{5}-q^{7}+2q^{11}+5q^{17}+2q^{19}+\cdots\)
756.2.a.e \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q+3q^{5}+q^{7}+2q^{13}+3q^{17}-4q^{19}+\cdots\)
756.2.a.f \(1\) \(6.037\) \(\Q\) None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q+3q^{5}+q^{7}+3q^{11}+2q^{13}-6q^{17}+\cdots\)
756.2.a.g \(2\) \(6.037\) \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q-\beta q^{5}-q^{7}+\beta q^{11}+6q^{13}-2\beta q^{17}+\cdots\)
756.2.b.a \(4\) \(6.037\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots\)
756.2.b.b \(4\) \(6.037\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
756.2.b.c \(12\) \(6.037\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{7}q^{2}+(1+\beta _{11})q^{4}-\beta _{8}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.d \(12\) \(6.037\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
756.2.b.e \(16\) \(6.037\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{11}q^{5}+\beta _{6}q^{7}+\cdots\)
756.2.b.f \(16\) \(6.037\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{2}+\beta _{8}q^{4}+\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots\)
756.2.e.a \(24\) \(6.037\) None None \(0\) \(0\) \(0\) \(0\)
756.2.e.b \(24\) \(6.037\) None None \(0\) \(0\) \(0\) \(0\)
756.2.f.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-6\) \(4\) \(q-3q^{5}+(2-\zeta_{6})q^{7}+3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
756.2.f.b \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(-2-\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
756.2.f.c \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(6\) \(4\) \(q+3q^{5}+(2-\zeta_{6})q^{7}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
756.2.f.d \(4\) \(6.037\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)
756.2.i.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(-5\) \(q+(2-2\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+4\zeta_{6}q^{11}+\cdots\)
756.2.i.b \(14\) \(6.037\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(0\) \(2\) \(6\) \(q-\beta _{3}q^{5}+(\beta _{5}+\beta _{12})q^{7}+\beta _{13}q^{11}+\cdots\)
756.2.j.a \(6\) \(6.037\) 6.0.309123.1 None None \(0\) \(0\) \(-3\) \(-3\) \(q+(-1+\beta _{1}+\beta _{3})q^{5}-\beta _{3}q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
756.2.j.b \(6\) \(6.037\) 6.0.309123.1 None None \(0\) \(0\) \(1\) \(3\) \(q+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{4})q^{7}+(1-2\beta _{2}+\cdots)q^{11}+\cdots\)
756.2.k.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-3+2\zeta_{6})q^{7}-7q^{13}-8\zeta_{6}q^{19}+\cdots\)
756.2.k.b \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-1-2\zeta_{6})q^{7}+5q^{13}-8\zeta_{6}q^{19}+\cdots\)
756.2.k.c \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(3-\zeta_{6})q^{7}+2q^{13}+\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots\)
756.2.k.d \(4\) \(6.037\) \(\Q(\sqrt{-3}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{5}+(2+3\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
756.2.k.e \(6\) \(6.037\) 6.0.309123.1 None None \(0\) \(0\) \(-1\) \(2\) \(q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
756.2.k.f \(6\) \(6.037\) 6.0.309123.1 None None \(0\) \(0\) \(1\) \(2\) \(q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
756.2.l.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(4\) \(q-2q^{5}+(3-2\zeta_{6})q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
756.2.l.b \(14\) \(6.037\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(0\) \(-4\) \(-3\) \(q+(\beta _{3}-\beta _{7})q^{5}-\beta _{5}q^{7}+(\beta _{9}-\beta _{13})q^{11}+\cdots\)
756.2.n.a \(4\) \(6.037\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots\)
756.2.n.b \(84\) \(6.037\) None None \(1\) \(0\) \(0\) \(0\)
756.2.o.a \(88\) \(6.037\) None None \(3\) \(0\) \(0\) \(0\)
756.2.t.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(-3+\zeta_{6})q^{7}+(4-8\zeta_{6})q^{13}+(10+\cdots)q^{19}+\cdots\)
756.2.t.b \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+(1+2\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{13}+(-4+\cdots)q^{19}+\cdots\)
756.2.t.c \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+(3-2\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(4-2\zeta_{6})q^{19}+\cdots\)
756.2.t.d \(4\) \(6.037\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-10\) \(q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(2+4\beta _{2}+\cdots)q^{13}+\cdots\)
756.2.t.e \(12\) \(6.037\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{10}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots\)
756.2.w.a \(16\) \(6.037\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-1\) \(q+\beta _{9}q^{5}+(\beta _{4}-\beta _{10})q^{7}-\beta _{15}q^{11}+\cdots\)
756.2.x.a \(16\) \(6.037\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-1\) \(q+(\beta _{1}-\beta _{15})q^{5}+(-\beta _{6}+\beta _{13})q^{7}+\cdots\)
756.2.ba.a \(72\) \(6.037\) None None \(0\) \(0\) \(0\) \(0\)
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