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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3675.1.c.a 3675.c 3.b $1$ $1.834$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
3675.1.c.b 3675.c 3.b $1$ $1.834$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
3675.1.c.c 3675.c 3.b $1$ $1.834$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
3675.1.c.d 3675.c 3.b $1$ $1.834$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
3675.1.c.e 3675.c 3.b $2$ $1.834$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots\)
3675.1.c.f 3675.c 3.b $4$ $1.834$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
3675.1.c.g 3675.c 3.b $4$ $1.834$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+\zeta_{8}^{2}q^{8}+\cdots\)
3675.1.c.h 3675.c 3.b $4$ $1.834$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}q^{6}+\zeta_{8}^{2}q^{8}+\cdots\)
3675.1.f.a 3675.f 15.d $2$ $1.834$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots\)
3675.1.f.b 3675.f 15.d $2$ $1.834$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots\)
3675.1.f.c 3675.f 15.d $4$ $1.834$ \(\Q(\zeta_{8})\) None None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{8}q^{3}+\zeta_{8}q^{6}+q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
3675.1.f.d 3675.f 15.d $4$ $1.834$ \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}-\zeta_{8}q^{3}-\zeta_{8}q^{6}-q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
3675.1.k.a 3675.k 105.k $8$ $1.834$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
3675.1.k.b 3675.k 105.k $8$ $1.834$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{3}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{6}q^{9}+\cdots\)
3675.1.k.c 3675.k 105.k $8$ $1.834$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
3675.1.p.a 3675.p 105.o $4$ $1.834$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{12}+\cdots\)
3675.1.p.b 3675.p 105.o $8$ $1.834$ \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{9}q^{6}+\cdots\)
3675.1.p.c 3675.p 105.o $8$ $1.834$ \(\Q(\zeta_{24})\) None None \(4\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{9}q^{6}+\cdots\)
3675.1.u.a 3675.u 21.h $2$ $1.834$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
3675.1.u.b 3675.u 21.h $2$ $1.834$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots\)
3675.1.u.c 3675.u 21.h $4$ $1.834$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{12}+\cdots\)
3675.1.u.d 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}+\zeta_{24}^{11}q^{3}-\zeta_{24}^{9}q^{6}+\cdots\)
3675.1.u.e 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{3}q^{6}+\cdots\)
3675.1.u.f 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{7})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
3675.1.bf.a 3675.bf 105.w $8$ $1.834$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{105}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots\)
3675.1.bf.b 3675.bf 105.w $8$ $1.834$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots\)
3675.1.bf.c 3675.bf 105.w $16$ $1.834$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{48}^{5}-\zeta_{48}^{23})q^{2}-\zeta_{48}^{10}q^{3}+\cdots\)
3675.1.bf.d 3675.bf 105.w $16$ $1.834$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{48}^{7}+\zeta_{48}^{13})q^{2}-\zeta_{48}^{2}q^{3}+(-\zeta_{48}^{2}+\cdots)q^{4}+\cdots\)
3675.1.bj.a 3675.bj 735.ab $12$ $1.834$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{5}q^{3}-\zeta_{28}^{8}q^{4}+\zeta_{28}^{11}q^{7}+\cdots\)
3675.1.bm.a 3675.bm 147.l $6$ $1.834$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{14}^{3}q^{3}+\zeta_{14}^{2}q^{4}+\zeta_{14}q^{7}+\zeta_{14}^{6}q^{9}+\cdots\)
3675.1.bx.a 3675.bx 735.ak $24$ $1.834$ \(\Q(\zeta_{56})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{56}^{5}q^{3}-\zeta_{56}^{22}q^{4}-\zeta_{56}^{11}q^{7}+\cdots\)
3675.1.cg.a 3675.cg 147.n $12$ $1.834$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}+\zeta_{42}^{17}q^{7}+\cdots\)
3675.1.cg.b 3675.cg 147.n $12$ $1.834$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}-\zeta_{42}^{17}q^{7}+\cdots\)
3675.1.cl.a 3675.cl 735.aq $24$ $1.834$ \(\Q(\zeta_{84})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{84}^{25}q^{3}-\zeta_{84}^{40}q^{4}-\zeta_{84}^{13}q^{7}+\cdots\)
3675.1.cy.a 3675.cy 735.as $48$ $1.834$ \(\Q(\zeta_{168})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{168}^{59}q^{3}-\zeta_{168}^{2}q^{4}+\zeta_{168}^{29}q^{7}+\cdots\)
3675.2.a.a 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-2\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-2q^{11}+\cdots\)
3675.2.a.b 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-2\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots\)
3675.2.a.c 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-2\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots\)
3675.2.a.d 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
3675.2.a.e 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
3675.2.a.f 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
3675.2.a.g 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(-1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
3675.2.a.h 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{9}+2q^{12}+q^{13}+\cdots\)
3675.2.a.i 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{9}-2q^{12}-q^{13}+\cdots\)
3675.2.a.j 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(1\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.k 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.l 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(1\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.m 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.n 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
3675.2.a.o 3675.a 1.a $1$ $29.345$ \(\Q\) None None \(2\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}-6q^{11}+\cdots\)
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