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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
231.1.h.a \(1\) \(0.115\) \(\Q\) \(\Q(\sqrt{-231}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
231.1.h.b \(1\) \(0.115\) \(\Q\) \(\Q(\sqrt{-231}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q-q^{2}+q^{3}-q^{5}-q^{6}+q^{7}+q^{8}+\cdots\)
231.1.h.c \(1\) \(0.115\) \(\Q\) \(\Q(\sqrt{-231}) \) None \(1\) \(-1\) \(1\) \(1\) \(q+q^{2}-q^{3}+q^{5}-q^{6}+q^{7}-q^{8}+\cdots\)
231.1.h.d \(1\) \(0.115\) \(\Q\) \(\Q(\sqrt{-231}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+q^{2}+q^{3}-q^{5}+q^{6}-q^{7}-q^{8}+\cdots\)
231.2.a.a \(1\) \(1.845\) \(\Q\) None None \(-1\) \(-1\) \(-2\) \(1\) \(-\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
231.2.a.b \(2\) \(1.845\) \(\Q(\sqrt{21}) \) None None \(-1\) \(-2\) \(6\) \(2\) \(-\) \(q-\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}+\beta q^{6}+\cdots\)
231.2.a.c \(2\) \(1.845\) \(\Q(\sqrt{5}) \) None None \(1\) \(2\) \(2\) \(2\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
231.2.a.d \(3\) \(1.845\) 3.3.837.1 None None \(0\) \(-3\) \(0\) \(-3\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
231.2.a.e \(3\) \(1.845\) 3.3.229.1 None None \(2\) \(3\) \(4\) \(-3\) \(-\) \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots\)
231.2.c.a \(16\) \(1.845\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
231.2.e.a \(28\) \(1.845\) None None \(0\) \(0\) \(0\) \(-8\)
231.2.g.a \(24\) \(1.845\) None None \(0\) \(-6\) \(0\) \(0\)
231.2.i.a \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.b \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(-4\) \(-4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.c \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(0\) \(5\) \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
231.2.i.d \(4\) \(1.845\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(-2\) \(4\) \(4\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.e \(8\) \(1.845\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(-4\) \(-4\) \(2\) \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.f \(10\) \(1.845\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(-2\) \(5\) \(4\) \(-1\) \(q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.j.a \(4\) \(1.845\) \(\Q(\zeta_{10})\) None None \(-4\) \(1\) \(-3\) \(-1\) \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
231.2.j.b \(4\) \(1.845\) \(\Q(\zeta_{10})\) None None \(-2\) \(1\) \(3\) \(1\) \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.c \(4\) \(1.845\) \(\Q(\zeta_{10})\) None None \(1\) \(1\) \(7\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.d \(4\) \(1.845\) \(\Q(\zeta_{10})\) None None \(2\) \(-1\) \(-1\) \(-1\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.e \(4\) \(1.845\) \(\Q(\zeta_{10})\) None None \(5\) \(1\) \(-3\) \(-1\) \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.f \(8\) \(1.845\) 8.0.13140625.1 None None \(2\) \(2\) \(2\) \(2\) \(q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
231.2.j.g \(20\) \(1.845\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-5\) \(-5\) \(5\) \(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)
231.2.l.a \(8\) \(1.845\) 8.0.\(\cdots\).5 None None \(0\) \(4\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
231.2.l.b \(48\) \(1.845\) None None \(0\) \(-6\) \(0\) \(0\)
231.2.n.a \(52\) \(1.845\) None None \(0\) \(0\) \(0\) \(-6\)
231.2.p.a \(32\) \(1.845\) None None \(0\) \(0\) \(-12\) \(0\)
231.2.s.a \(96\) \(1.845\) None None \(0\) \(6\) \(0\) \(0\)
231.2.u.a \(112\) \(1.845\) None None \(0\) \(0\) \(0\) \(-2\)
231.2.w.a \(64\) \(1.845\) None None \(0\) \(0\) \(0\) \(10\)
231.2.y.a \(64\) \(1.845\) None None \(0\) \(-8\) \(0\) \(-1\)
231.2.y.b \(64\) \(1.845\) None None \(4\) \(8\) \(-4\) \(-1\)
231.2.ba.a \(128\) \(1.845\) None None \(0\) \(0\) \(12\) \(-10\)
231.2.bc.a \(224\) \(1.845\) None None \(0\) \(-9\) \(0\) \(-16\)
231.2.be.a \(224\) \(1.845\) None None \(0\) \(-3\) \(0\) \(-20\)
231.3.b.a \(40\) \(6.294\) None None \(0\) \(-2\) \(0\) \(0\)
231.3.d.a \(24\) \(6.294\) None None \(0\) \(0\) \(0\) \(0\)
231.3.f.a \(28\) \(6.294\) None None \(0\) \(0\) \(0\) \(-8\)
231.3.h.a \(3\) \(6.294\) 3.3.6237.1 \(\Q(\sqrt{-231}) \) None \(0\) \(-9\) \(0\) \(-21\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.b \(3\) \(6.294\) 3.3.6237.1 \(\Q(\sqrt{-231}) \) None \(0\) \(-9\) \(0\) \(21\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.c \(3\) \(6.294\) 3.3.6237.1 \(\Q(\sqrt{-231}) \) None \(0\) \(9\) \(0\) \(-21\) \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.d \(3\) \(6.294\) 3.3.6237.1 \(\Q(\sqrt{-231}) \) None \(0\) \(9\) \(0\) \(21\) \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
231.3.h.e \(48\) \(6.294\) None None \(0\) \(0\) \(0\) \(0\)
231.3.k.a \(120\) \(6.294\) None None \(0\) \(-6\) \(0\) \(0\)
231.3.m.a \(24\) \(6.294\) None None \(0\) \(-36\) \(0\) \(-10\)
231.3.m.b \(28\) \(6.294\) None None \(0\) \(42\) \(0\) \(16\)
231.3.o.a \(64\) \(6.294\) None None \(0\) \(0\) \(4\) \(0\)
231.3.q.a \(108\) \(6.294\) None None \(0\) \(0\) \(0\) \(-2\)
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