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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1288.1.c.a \(1\) \(0.643\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-322}) \) \(\Q(\sqrt{46}) \) \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots\)
1288.1.c.b \(1\) \(0.643\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-322}) \) \(\Q(\sqrt{46}) \) \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{14}+\cdots\)
1288.1.bi.a \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-14}) \) None \(-1\) \(-9\) \(2\) \(-1\) \(q-\zeta_{22}^{3}q^{2}+(-1-\zeta_{22}^{4})q^{3}+\zeta_{22}^{6}q^{4}+\cdots\)
1288.1.bi.b \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-14}) \) None \(-1\) \(9\) \(-2\) \(-1\) \(q-\zeta_{22}^{3}q^{2}+(1+\zeta_{22}^{4})q^{3}+\zeta_{22}^{6}q^{4}+\cdots\)
1288.1.bi.c \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q+\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+\zeta_{22}q^{7}+\zeta_{22}^{5}q^{8}+\cdots\)
1288.1.bi.d \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}+\zeta_{22}q^{7}-\zeta_{22}^{2}q^{8}+\cdots\)
1288.1.bi.e \(20\) \(0.643\) \(\Q(\zeta_{44})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(2\) \(q+\zeta_{44}^{18}q^{2}+(\zeta_{44}^{11}+\zeta_{44}^{13})q^{3}+\cdots\)
1288.1.bu.a \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{10}q^{4}-\zeta_{22}^{3}q^{7}+\cdots\)
1288.1.bu.b \(10\) \(0.643\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{22}^{2}q^{2}+\zeta_{22}^{4}q^{4}+\zeta_{22}^{3}q^{7}+\cdots\)
1288.2.a.a \(1\) \(10.285\) \(\Q\) None None \(0\) \(-3\) \(-4\) \(-1\) \(+\) \(q-3q^{3}-4q^{5}-q^{7}+6q^{9}+2q^{11}+\cdots\)
1288.2.a.b \(1\) \(10.285\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) \(-\) \(q-3q^{3}-q^{7}+6q^{9}-6q^{11}+q^{13}+\cdots\)
1288.2.a.c \(1\) \(10.285\) \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) \(+\) \(q-2q^{3}+q^{7}+q^{9}-6q^{17}+6q^{19}+\cdots\)
1288.2.a.d \(1\) \(10.285\) \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) \(+\) \(q+2q^{5}-q^{7}-3q^{9}-4q^{13}-4q^{17}+\cdots\)
1288.2.a.e \(1\) \(10.285\) \(\Q\) None None \(0\) \(1\) \(0\) \(1\) \(+\) \(q+q^{3}+q^{7}-2q^{9}-6q^{11}-3q^{13}+\cdots\)
1288.2.a.f \(1\) \(10.285\) \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) \(-\) \(q+2q^{3}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1288.2.a.g \(1\) \(10.285\) \(\Q\) None None \(0\) \(2\) \(2\) \(1\) \(-\) \(q+2q^{3}+2q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
1288.2.a.h \(1\) \(10.285\) \(\Q\) None None \(0\) \(2\) \(4\) \(1\) \(-\) \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+4q^{11}+\cdots\)
1288.2.a.i \(1\) \(10.285\) \(\Q\) None None \(0\) \(3\) \(2\) \(-1\) \(-\) \(q+3q^{3}+2q^{5}-q^{7}+6q^{9}+2q^{11}+\cdots\)
1288.2.a.j \(2\) \(10.285\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(-4\) \(-2\) \(+\) \(q-\beta q^{3}-2q^{5}-q^{7}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
1288.2.a.k \(2\) \(10.285\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-4\) \(-2\) \(-\) \(q+\beta q^{3}+(-2-\beta )q^{5}-q^{7}-q^{9}+2q^{11}+\cdots\)
1288.2.a.l \(3\) \(10.285\) 3.3.148.1 None None \(0\) \(0\) \(4\) \(-3\) \(-\) \(q-\beta _{2}q^{3}+(2-2\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
1288.2.a.m \(3\) \(10.285\) 3.3.568.1 None None \(0\) \(1\) \(0\) \(3\) \(-\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1288.2.a.n \(4\) \(10.285\) 4.4.8468.1 None None \(0\) \(-3\) \(0\) \(4\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
1288.2.a.o \(4\) \(10.285\) 4.4.34196.1 None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q-\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1288.2.a.p \(5\) \(10.285\) 5.5.3385684.1 None None \(0\) \(-3\) \(2\) \(5\) \(-\) \(q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+q^{7}+(3-\beta _{4})q^{9}+\cdots\)
1288.2.f.a \(24\) \(10.285\) None None \(0\) \(0\) \(0\) \(0\)
1288.2.f.b \(24\) \(10.285\) None None \(0\) \(0\) \(0\) \(0\)
1288.2.q.a \(22\) \(10.285\) None None \(0\) \(-4\) \(-1\) \(1\)
1288.2.q.b \(22\) \(10.285\) None None \(0\) \(2\) \(-9\) \(-1\)
1288.2.q.c \(22\) \(10.285\) None None \(0\) \(2\) \(7\) \(-1\)
1288.2.q.d \(22\) \(10.285\) None None \(0\) \(4\) \(3\) \(1\)
1288.2.ba.a \(48\) \(10.285\) None None \(0\) \(-6\) \(0\) \(0\)
1288.2.ba.b \(48\) \(10.285\) None None \(0\) \(6\) \(0\) \(0\)
1288.3.d.a \(88\) \(35.095\) None None \(0\) \(0\) \(0\) \(-8\)
1288.3.k.a \(72\) \(35.095\) None None \(0\) \(0\) \(0\) \(0\)
1288.4.a.a \(11\) \(75.994\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(0\) \(-3\) \(-24\) \(77\) \(-\) \(q-\beta _{1}q^{3}+(-2-\beta _{7})q^{5}+7q^{7}+(5+\cdots)q^{9}+\cdots\)
1288.4.a.b \(11\) \(75.994\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(0\) \(11\) \(12\) \(-77\) \(+\) \(q+(1-\beta _{1})q^{3}+(1+\beta _{4})q^{5}-7q^{7}+(8+\cdots)q^{9}+\cdots\)
1288.4.a.c \(12\) \(75.994\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-7\) \(-18\) \(84\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{5})q^{5}+7q^{7}+\cdots\)
1288.4.a.d \(12\) \(75.994\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(-14\) \(-84\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}-7q^{7}+(7+\cdots)q^{9}+\cdots\)
1288.4.a.e \(12\) \(75.994\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(11\) \(-8\) \(84\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+7q^{7}+\cdots\)
1288.4.a.f \(13\) \(75.994\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(-7\) \(2\) \(-91\) \(-\) \(q+(-1+\beta _{1})q^{3}+\beta _{6}q^{5}-7q^{7}+(11+\cdots)q^{9}+\cdots\)
1288.4.a.g \(14\) \(75.994\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-3\) \(16\) \(-98\) \(+\) \(q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}-7q^{7}+(10+\beta _{2}+\cdots)q^{9}+\cdots\)
1288.4.a.h \(15\) \(75.994\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(0\) \(-3\) \(6\) \(105\) \(+\) \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+7q^{7}+(13+\beta _{2}+\cdots)q^{9}+\cdots\)
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