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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2268.1.h.a \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)
2268.1.m.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots\)
2268.1.m.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots\)
2268.1.p.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(1+\zeta_{6})q^{19}+q^{25}+(1+\zeta_{6}+\cdots)q^{31}+\cdots\)
2268.1.p.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots\)
2268.1.s.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.c \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.d \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-21}) \) None \(1\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.e \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.f \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.g \(8\) \(1.132\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.bc.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(-3\) \(1\) \(q+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
2268.1.bc.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(1-\zeta_{6}^{2})q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.c \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bc.d \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{21}) \) \(0\) \(0\) \(3\) \(1\) \(q+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\)
2268.1.bd.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+(-1+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bd.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{19}-\zeta_{6}q^{25}+\cdots\)
2268.1.bh.a \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
2268.1.bh.b \(2\) \(1.132\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
2268.2.a.a \(1\) \(18.110\) \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(q-2q^{5}-q^{7}-q^{11}+2q^{17}+2q^{19}+\cdots\)
2268.2.a.b \(1\) \(18.110\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
2268.2.a.c \(1\) \(18.110\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}+3q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
2268.2.a.d \(1\) \(18.110\) \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) \(-\) \(q+2q^{5}-q^{7}+q^{11}-2q^{17}+2q^{19}+\cdots\)
2268.2.a.e \(2\) \(18.110\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+2\beta q^{5}+q^{7}+\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots\)
2268.2.a.f \(2\) \(18.110\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+\beta q^{5}+q^{7}+2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots\)
2268.2.a.g \(3\) \(18.110\) 3.3.321.1 None None \(0\) \(0\) \(-3\) \(3\) \(+\) \(q+(-1+\beta _{1})q^{5}+q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
2268.2.a.h \(3\) \(18.110\) 3.3.321.1 None None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(q-\beta _{1}q^{5}-q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
2268.2.a.i \(3\) \(18.110\) 3.3.321.1 None None \(0\) \(0\) \(1\) \(-3\) \(-\) \(q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2268.2.a.j \(3\) \(18.110\) 3.3.321.1 None None \(0\) \(0\) \(3\) \(3\) \(-\) \(q+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
2268.2.a.k \(4\) \(18.110\) \(\Q(\sqrt{3}, \sqrt{19})\) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
2268.2.f.a \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{3}q^{5}+\beta _{10}q^{7}-\beta _{4}q^{11}+\beta _{13}q^{13}+\cdots\)
2268.2.f.b \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{15}q^{5}+\beta _{9}q^{7}+\beta _{1}q^{11}+\beta _{7}q^{13}+\cdots\)
2268.2.i.a \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) \(q+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
2268.2.i.b \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(4\) \(q+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
2268.2.i.c \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.d \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+(-2+3\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.e \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+(1-3\zeta_{6})q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.f \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(3-\zeta_{6})q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.g \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(4\) \(q+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
2268.2.i.h \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) \(q+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
2268.2.i.i \(4\) \(18.110\) \(\Q(\sqrt{-3}, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-10\) \(q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
2268.2.i.j \(6\) \(18.110\) 6.0.309123.1 None None \(0\) \(0\) \(-1\) \(2\) \(q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.k \(6\) \(18.110\) 6.0.309123.1 None None \(0\) \(0\) \(1\) \(2\) \(q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.l \(8\) \(18.110\) 8.0.310217769.2 None None \(0\) \(0\) \(-2\) \(1\) \(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{5}q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2268.2.i.m \(8\) \(18.110\) 8.0.310217769.2 None None \(0\) \(0\) \(2\) \(1\) \(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{5}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2268.2.i.n \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{13}q^{5}+\beta _{3}q^{7}-\beta _{12}q^{11}+(2-2\beta _{4}+\cdots)q^{13}+\cdots\)
2268.2.j.a \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(1\) \(q-4\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2268.2.j.b \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2268.2.j.c \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
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