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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2583.1.f.a \(3\) \(1.289\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(1\) \(0\) \(0\) \(-3\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{4}-q^{7}+(\beta _{1}-\beta _{2})q^{8}+\cdots\)
2583.1.f.b \(3\) \(1.289\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(1\) \(0\) \(0\) \(3\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(1+\beta _{2})q^{8}+\cdots\)
2583.1.ba.a \(2\) \(1.289\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-287}) \) None \(1\) \(-2\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{2}-q^{3}+\zeta_{6}^{2}q^{6}-\zeta_{6}^{2}q^{7}+\cdots\)
2583.1.ba.b \(2\) \(1.289\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-287}) \) None \(1\) \(2\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}^{2}q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
2583.1.ba.c \(12\) \(1.289\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-287}) \) None \(-1\) \(-2\) \(0\) \(-6\) \(q+(-\zeta_{42}^{5}-\zeta_{42}^{9})q^{2}-\zeta_{42}^{3}q^{3}+\cdots\)
2583.1.ba.d \(12\) \(1.289\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-287}) \) None \(-1\) \(2\) \(0\) \(6\) \(q+(\zeta_{42}^{6}+\zeta_{42}^{8})q^{2}+\zeta_{42}^{9}q^{3}+(\zeta_{42}^{12}+\cdots)q^{4}+\cdots\)
2583.2.a.a \(1\) \(20.625\) \(\Q\) None None \(-1\) \(0\) \(1\) \(-1\) \(-\) \(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
2583.2.a.b \(1\) \(20.625\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q-2q^{4}+q^{7}-3q^{11}+2q^{13}+4q^{16}+\cdots\)
2583.2.a.c \(1\) \(20.625\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(-\) \(q-2q^{4}+q^{7}+3q^{11}+2q^{13}+4q^{16}+\cdots\)
2583.2.a.d \(1\) \(20.625\) \(\Q\) None None \(1\) \(0\) \(-3\) \(-1\) \(-\) \(q+q^{2}-q^{4}-3q^{5}-q^{7}-3q^{8}-3q^{10}+\cdots\)
2583.2.a.e \(1\) \(20.625\) \(\Q\) None None \(1\) \(0\) \(-2\) \(1\) \(-\) \(q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots\)
2583.2.a.f \(1\) \(20.625\) \(\Q\) None None \(1\) \(0\) \(3\) \(1\) \(-\) \(q+q^{2}-q^{4}+3q^{5}+q^{7}-3q^{8}+3q^{10}+\cdots\)
2583.2.a.g \(2\) \(20.625\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(-1\) \(-2\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2583.2.a.h \(2\) \(20.625\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(1\) \(2\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots\)
2583.2.a.i \(2\) \(20.625\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(-4\) \(2\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}-2q^{5}+q^{7}+(4+\cdots)q^{8}+\cdots\)
2583.2.a.j \(2\) \(20.625\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(3\) \(-2\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+(2-\beta )q^{5}-q^{7}+\cdots\)
2583.2.a.k \(2\) \(20.625\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(2\) \(2\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+q^{7}+\cdots\)
2583.2.a.l \(3\) \(20.625\) \(\Q(\zeta_{14})^+\) None None \(-4\) \(0\) \(-2\) \(-3\) \(-\) \(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
2583.2.a.m \(3\) \(20.625\) 3.3.257.1 None None \(-1\) \(0\) \(-6\) \(3\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-2q^{5}+q^{7}+\cdots\)
2583.2.a.n \(3\) \(20.625\) 3.3.148.1 None None \(1\) \(0\) \(-1\) \(3\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2583.2.a.o \(4\) \(20.625\) 4.4.8468.1 None None \(-1\) \(0\) \(3\) \(-4\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
2583.2.a.p \(5\) \(20.625\) 5.5.626512.1 None None \(-3\) \(0\) \(-3\) \(-5\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
2583.2.a.q \(5\) \(20.625\) 5.5.1197392.1 None None \(-3\) \(0\) \(9\) \(5\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
2583.2.a.r \(5\) \(20.625\) 5.5.633117.1 None None \(1\) \(0\) \(5\) \(5\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
2583.2.a.s \(5\) \(20.625\) 5.5.981328.1 None None \(3\) \(0\) \(-1\) \(-5\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2583.2.a.t \(6\) \(20.625\) 6.6.185257757.1 None None \(1\) \(0\) \(1\) \(-6\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
2583.2.a.u \(7\) \(20.625\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-4\) \(0\) \(-1\) \(7\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2583.2.a.v \(8\) \(20.625\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-4\) \(0\) \(-8\) \(8\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2583.2.a.w \(8\) \(20.625\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(4\) \(0\) \(8\) \(8\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
2583.2.a.x \(11\) \(20.625\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-4\) \(0\) \(0\) \(-11\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}-q^{7}+\cdots\)
2583.2.a.y \(11\) \(20.625\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(4\) \(0\) \(0\) \(-11\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots\)


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