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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3528.1.d.a 3528.d 3.b $2$ $1.761$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{11}-q^{13}-q^{19}-q^{25}+\cdots\)
3528.1.d.b 3528.d 3.b $2$ $1.761$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-\beta q^{11}+q^{13}+q^{19}-q^{25}+\cdots\)
3528.1.g.a 3528.g 8.d $1$ $1.761$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+2q^{11}+q^{16}-2q^{22}+\cdots\)
3528.1.g.b 3528.g 8.d $2$ $1.761$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}-iq^{23}+\cdots\)
3528.1.g.c 3528.g 8.d $2$ $1.761$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}-\beta q^{17}+\beta q^{19}+\cdots\)
3528.1.l.a 3528.l 56.h $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
3528.1.n.a 3528.n 24.h $4$ $1.761$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
3528.1.u.a 3528.u 504.u $16$ $1.761$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{4}q^{2}-\zeta_{48}^{9}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
3528.1.ba.a 3528.ba 504.aa $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.b 3528.ba 504.aa $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(2\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.c 3528.ba 504.aa $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3528.1.ba.d 3528.ba 504.aa $4$ $1.761$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
3528.1.ba.e 3528.ba 504.aa $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.bd.a 3528.bd 168.s $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
3528.1.bg.a 3528.bg 72.j $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
3528.1.bi.a 3528.bi 504.ai $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}-\zeta_{24}^{7}q^{3}-q^{4}+(-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
3528.1.bp.a 3528.bp 504.ap $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(2\) \(-1\) \(1\) \(0\) \(q+q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{6}+\cdots\)
3528.1.bp.b 3528.bp 504.ap $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(2\) \(1\) \(-1\) \(0\) \(q+q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
3528.1.bp.c 3528.bp 504.ap $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{12}q^{3}+q^{4}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
3528.1.bw.a 3528.bw 56.j $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
3528.1.bw.b 3528.bw 56.j $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
3528.1.bw.c 3528.bw 56.j $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
3528.1.bx.a 3528.bx 56.k $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots\)
3528.1.bx.b 3528.bx 56.k $4$ $1.761$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+q^{8}+\beta _{2}q^{16}+\cdots\)
3528.1.bx.c 3528.bx 56.k $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots\)
3528.1.ce.a 3528.ce 504.be $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(-1\) \(0\) \(0\) \(q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.b 3528.ce 504.be $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(1\) \(0\) \(0\) \(q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.c 3528.ce 504.be $4$ $1.761$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+q^{3}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{6}+\cdots\)
3528.1.ce.d 3528.ce 504.be $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{12}^{5}q^{3}+q^{4}+\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.ce.e 3528.ce 504.be $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{24}^{7}q^{3}+q^{4}+\zeta_{24}^{7}q^{6}+\cdots\)
3528.1.cg.a 3528.cg 72.p $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\)
3528.1.cg.b 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.cg.c 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.d 3528.cg 72.p $4$ $1.761$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.e 3528.cg 72.p $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.cm.a 3528.cm 504.bm $16$ $1.761$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{12}q^{2}+\zeta_{48}^{5}q^{3}-q^{4}+\zeta_{48}^{17}q^{6}+\cdots\)
3528.1.co.a 3528.co 504.bo $16$ $1.761$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{20}q^{2}+\zeta_{48}^{5}q^{3}-\zeta_{48}^{16}q^{4}+\cdots\)
3528.1.ct.a 3528.ct 168.ae $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
3528.1.cu.a 3528.cu 21.h $4$ $1.761$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}+q^{13}+\cdots\)
3528.1.cw.a 3528.cw 504.bw $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(-1\) \(-2\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
3528.1.cw.b 3528.cw 504.bw $2$ $1.761$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(1\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
3528.1.cw.c 3528.cw 504.bw $4$ $1.761$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
3528.1.db.a 3528.db 504.cb $8$ $1.761$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.dh.a 3528.dh 392.r $12$ $1.761$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{28}q^{2}+\zeta_{28}^{2}q^{4}+(\zeta_{28}^{9}+\zeta_{28}^{11}+\cdots)q^{5}+\cdots\)
3528.1.fb.a 3528.fb 392.af $24$ $1.761$ \(\Q(\zeta_{84})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{84}^{31}q^{2}-\zeta_{84}^{20}q^{4}+(-\zeta_{84}^{33}+\cdots)q^{5}+\cdots\)
3528.2.a.a 3528.a 1.a $1$ $28.171$ \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots\)
3528.2.a.b 3528.a 1.a $1$ $28.171$ \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{17}+2q^{19}-8q^{23}+11q^{25}+\cdots\)
3528.2.a.c 3528.a 1.a $1$ $28.171$ \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots\)
3528.2.a.d 3528.a 1.a $1$ $28.171$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
3528.2.a.e 3528.a 1.a $1$ $28.171$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
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