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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3584.1.c.a $4$ $1.789$ 4.0.2048.2 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+\beta _{3}q^{3}-\beta _{1}q^{5}-q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3584.1.c.b $4$ $1.789$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{14}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+q^{9}+\cdots\)
3584.1.c.c $4$ $1.789$ 4.0.2048.2 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(4\) $-$ \(q-\beta _{3}q^{3}-\beta _{1}q^{5}+q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3584.1.h.a $4$ $1.789$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ \(q-\beta _{3}q^{3}-\beta _{1}q^{5}-q^{7}+(1-\beta _{2})q^{9}+\cdots\)
3584.1.h.b $4$ $1.789$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{14}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
3584.1.h.c $4$ $1.789$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(4\) $-$ \(q+\beta _{3}q^{3}-\beta _{1}q^{5}+q^{7}+(1-\beta _{2})q^{9}+\cdots\)
3584.1.v.a $4$ $1.789$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-1-\zeta_{8}^{3})q^{11}+\cdots\)
3584.1.v.b $4$ $1.789$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-1-\zeta_{8}^{3})q^{11}+\cdots\)
3584.1.v.c $4$ $1.789$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(1+\zeta_{8}^{3})q^{11}+\cdots\)
3584.1.v.d $4$ $1.789$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(1+\zeta_{8}^{3})q^{11}+\cdots\)
3584.1.bf.a $8$ $1.789$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(\zeta_{16}^{3}+\zeta_{16}^{6}+\cdots)q^{11}+\cdots\)
3584.1.bf.b $8$ $1.789$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(-\zeta_{16}^{3}-\zeta_{16}^{6}+\cdots)q^{11}+\cdots\)
3584.1.bm.a $16$ $1.789$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{32}^{5}q^{7}+\zeta_{32}^{3}q^{9}+(\zeta_{32}^{6}+\zeta_{32}^{15}+\cdots)q^{11}+\cdots\)
3584.1.cd.a $64$ $1.789$ \(\Q(\zeta_{128})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{128}^{59}q^{2}-\zeta_{128}^{54}q^{4}+\zeta_{128}^{63}q^{7}+\cdots\)
3584.2.a.a $2$ $28.618$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q+\beta q^{3}-q^{7}-q^{9}-\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.a.b $2$ $28.618$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(2\) $+$ \(q+\beta q^{3}+q^{7}-q^{9}-\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.a.c $4$ $28.618$ \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.d $4$ $28.618$ \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(4\) $+$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.e $6$ $28.618$ 6.6.18857984.1 None None \(0\) \(-4\) \(0\) \(-6\) $+$ \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.f $6$ $28.618$ 6.6.18857984.1 None None \(0\) \(-4\) \(0\) \(6\) $+$ \(q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.g $6$ $28.618$ 6.6.12836864.1 None None \(0\) \(0\) \(-4\) \(-6\) $+$ \(q-\beta _{1}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.h $6$ $28.618$ 6.6.12836864.1 None None \(0\) \(0\) \(-4\) \(6\) $+$ \(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.i $6$ $28.618$ 6.6.12836864.1 None None \(0\) \(0\) \(4\) \(-6\) $-$ \(q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.j $6$ $28.618$ 6.6.12836864.1 None None \(0\) \(0\) \(4\) \(6\) $-$ \(q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.k $6$ $28.618$ 6.6.18857984.1 None None \(0\) \(4\) \(0\) \(-6\) $-$ \(q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.l $6$ $28.618$ 6.6.18857984.1 None None \(0\) \(4\) \(0\) \(6\) $-$ \(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.m $8$ $28.618$ 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-8\) $+$ \(q+\beta _{7}q^{3}+(-\beta _{3}-\beta _{7})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
3584.2.a.n $8$ $28.618$ 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(8\) $-$ \(q+\beta _{7}q^{3}+(\beta _{3}+\beta _{7})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.o $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(0\) \(-10\) $-$ \(q-\beta _{5}q^{3}-\beta _{3}q^{5}-q^{7}+(2+\beta _{6})q^{9}+\cdots\)
3584.2.a.p $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(0\) \(10\) $-$ \(q-\beta _{5}q^{3}+\beta _{3}q^{5}+q^{7}+(2+\beta _{6})q^{9}+\cdots\)
3584.2.b.a $2$ $28.618$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) $-$ \(q+\beta q^{3}-q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.b.b $2$ $28.618$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ \(q+\beta q^{3}+q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.b.c $4$ $28.618$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3584.2.b.d $4$ $28.618$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(4\) $-$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3584.2.b.e $8$ $28.618$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(-8\) $-$ \(q+\beta _{7}q^{3}+(\beta _{5}-\beta _{7})q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
3584.2.b.f $8$ $28.618$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(8\) $-$ \(q+\beta _{7}q^{3}+(-\beta _{5}+\beta _{7})q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
3584.2.b.g $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(0\) \(-10\) $-$ \(q-\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.h $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(0\) \(10\) $-$ \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.i $12$ $28.618$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $-$ \(q-\beta _{6}q^{3}+\beta _{7}q^{5}-q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.j $12$ $28.618$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $-$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-q^{7}-\beta _{2}q^{9}+\beta _{7}q^{11}+\cdots\)
3584.2.b.k $12$ $28.618$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $-$ \(q-\beta _{6}q^{3}-\beta _{7}q^{5}+q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)
3584.2.b.l $12$ $28.618$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $-$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}-\beta _{2}q^{9}+\beta _{7}q^{11}+\cdots\)
3584.2.m.a $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-2\) \(0\) $-$ \(q+(-2+2i)q^{3}+(-1-i)q^{5}+iq^{7}+\cdots\)
3584.2.m.b $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(2\) \(0\) $-$ \(q+(-2+2i)q^{3}+(1+i)q^{5}-iq^{7}+\cdots\)
3584.2.m.c $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(0\) $-$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.d $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(0\) $-$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(0\) $-$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.f $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(0\) $-$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.g $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+(-1+i)q^{3}+iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
3584.2.m.h $2$ $28.618$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+(-1+i)q^{3}-iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
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