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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2548.1.c.a 2548.c 52.b $1$ $1.272$ \(\Q\) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}-q^{13}+\cdots\)
2548.1.c.b 2548.c 52.b $1$ $1.272$ \(\Q\) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}+q^{13}+\cdots\)
2548.1.c.c 2548.c 52.b $1$ $1.272$ \(\Q\) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}-q^{13}+\cdots\)
2548.1.c.d 2548.c 52.b $1$ $1.272$ \(\Q\) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}+q^{13}+\cdots\)
2548.1.c.e 2548.c 52.b $4$ $1.272$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None 2548.1.c.e \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
2548.1.o.a 2548.o 13.d $4$ $1.272$ \(\Q(\zeta_{8})\) None None 2548.1.o.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{3}q^{5}+q^{9}+\zeta_{8}^{3}q^{13}+\cdots\)
2548.1.p.a 2548.p 364.p $8$ $1.272$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None 2548.1.p.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+(\zeta_{16}-\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
2548.1.q.a 2548.q 364.q $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(-1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots\)
2548.1.q.b 2548.q 364.q $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots\)
2548.1.q.c 2548.q 364.q $4$ $1.272$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 2548.1.bn.b \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
2548.1.s.a 2548.s 364.s $8$ $1.272$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None 2548.1.bd.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{9}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots\)
2548.1.bd.a 2548.bd 52.i $8$ $1.272$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None 2548.1.bd.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(\zeta_{24}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots\)
2548.1.bg.a 2548.bg 91.s $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-91}) \) None 364.1.d.a \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}-q^{13}+\zeta_{6}^{2}q^{19}+\cdots\)
2548.1.bg.b 2548.bg 91.s $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-91}) \) None 364.1.d.a \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+q^{13}-\zeta_{6}^{2}q^{19}+\cdots\)
2548.1.bi.a 2548.bi 364.ai $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(2\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}+\zeta_{6}^{2}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
2548.1.bi.b 2548.bi 364.ai $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(2\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
2548.1.bi.c 2548.bi 364.ai $4$ $1.272$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 2548.1.bn.b \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(\zeta_{12}+\zeta_{12}^{3})q^{5}-q^{8}+\cdots\)
2548.1.bk.a 2548.bk 364.ak $8$ $1.272$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None 2548.1.bd.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}-q^{4}+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{5}+\cdots\)
2548.1.bl.a 2548.bl 364.al $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
2548.1.bl.b 2548.bl 364.al $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
2548.1.bl.c 2548.bl 364.al $8$ $1.272$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None 2548.1.c.e \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(\zeta_{24}-\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)
2548.1.bn.a 2548.bn 52.j $2$ $1.272$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(-1\) \(0\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
2548.1.bn.b 2548.bn 52.j $4$ $1.272$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 2548.1.bn.b \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
2548.1.bw.a 2548.bw 364.av $16$ $1.272$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None 2548.1.bw.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{22}q^{2}-\zeta_{48}^{20}q^{4}+(-\zeta_{48}^{17}+\cdots)q^{5}+\cdots\)
2548.1.bx.a 2548.bx 364.aw $16$ $1.272$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None 2548.1.p.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{22}q^{2}-\zeta_{48}^{20}q^{4}+(-\zeta_{48}+\cdots)q^{5}+\cdots\)
2548.1.bz.a 2548.bz 91.z $8$ $1.272$ \(\Q(\zeta_{24})\) None None 2548.1.o.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{8}q^{9}+\cdots\)
2548.1.ca.a 2548.ca 364.az $16$ $1.272$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None 2548.1.bw.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{18}q^{2}-\zeta_{48}^{12}q^{4}+(\zeta_{48}^{9}+\zeta_{48}^{19}+\cdots)q^{5}+\cdots\)
2548.1.ch.a 2548.ch 364.bg $16$ $1.272$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None 2548.1.bw.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{22}q^{2}-\zeta_{48}^{20}q^{4}+(-\zeta_{48}^{9}+\cdots)q^{5}+\cdots\)
2548.1.co.a 2548.co 2548.bo $6$ $1.272$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-13}) \) None 2548.1.co.a \(-1\) \(0\) \(0\) \(-1\) \(q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}-\zeta_{14}q^{7}+\zeta_{14}^{2}q^{8}+\cdots\)
2548.1.co.b 2548.co 2548.bo $6$ $1.272$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-13}) \) None 2548.1.co.a \(1\) \(0\) \(0\) \(1\) \(q+\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+\zeta_{14}q^{7}-\zeta_{14}^{2}q^{8}+\cdots\)
2548.1.de.a 2548.de 2548.ce $12$ $1.272$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-13}) \) None 2548.1.de.a \(-1\) \(0\) \(0\) \(-1\) \(q+\zeta_{42}^{17}q^{2}-\zeta_{42}^{13}q^{4}-\zeta_{42}^{8}q^{7}+\cdots\)
2548.1.de.b 2548.de 2548.ce $12$ $1.272$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-13}) \) None 2548.1.de.a \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{42}^{17}q^{2}-\zeta_{42}^{13}q^{4}+\zeta_{42}^{8}q^{7}+\cdots\)
2548.2.a.a 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.d \(0\) \(-3\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-3q^{5}+6q^{9}-5q^{11}-q^{13}+\cdots\)
2548.2.a.b 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.c \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-3q^{11}+q^{13}+3q^{17}+\cdots\)
2548.2.a.c 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.a \(0\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-q^{11}-q^{13}+q^{15}+\cdots\)
2548.2.a.d 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.b \(0\) \(-1\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots\)
2548.2.a.e 2548.a 1.a $1$ $20.346$ \(\Q\) None None 52.2.a.a \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-3q^{9}-2q^{11}+q^{13}-6q^{17}+\cdots\)
2548.2.a.f 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.a.b \(0\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-3q^{9}-2q^{11}+q^{13}+4q^{17}+\cdots\)
2548.2.a.g 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.b \(0\) \(1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
2548.2.a.h 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.a \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}-q^{11}+q^{13}+q^{15}+\cdots\)
2548.2.a.i 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.a.a \(0\) \(2\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{9}-4q^{11}-q^{13}+\cdots\)
2548.2.a.j 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.c \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-3q^{11}-q^{13}-3q^{17}+\cdots\)
2548.2.a.k 2548.a 1.a $1$ $20.346$ \(\Q\) None None 364.2.j.d \(0\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}+6q^{9}-5q^{11}+q^{13}+\cdots\)
2548.2.a.l 2548.a 1.a $2$ $20.346$ \(\Q(\sqrt{3}) \) None None 364.2.a.d \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-\beta q^{5}+(1-2\beta )q^{9}+\cdots\)
2548.2.a.m 2548.a 1.a $2$ $20.346$ \(\Q(\sqrt{6}) \) None None 364.2.a.c \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+3q^{9}+(4+\beta )q^{11}+\cdots\)
2548.2.a.n 2548.a 1.a $3$ $20.346$ 3.3.756.1 None None 2548.2.a.n \(0\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
2548.2.a.o 2548.a 1.a $3$ $20.346$ 3.3.756.1 None None 2548.2.a.n \(0\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
2548.2.a.p 2548.a 1.a $4$ $20.346$ 4.4.29268.1 None None 364.2.j.e \(0\) \(-3\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-\beta _{3}q^{5}+(3-2\beta _{1}+\cdots)q^{9}+\cdots\)
2548.2.a.q 2548.a 1.a $4$ $20.346$ 4.4.29268.1 None None 364.2.j.e \(0\) \(3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(3-2\beta _{1}+\beta _{3})q^{9}+\cdots\)
2548.2.a.r 2548.a 1.a $6$ $20.346$ 6.6.39110656.1 None None 2548.2.a.r \(0\) \(0\) \(-10\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{4})q^{3}+(-2+\beta _{3})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
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