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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2480.1.k.a 2480.k 155.c $1$ $1.238$ \(\Q\) \(\Q(\sqrt{-155}) \) None 620.1.f.a \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}-2q^{13}-q^{15}+q^{17}+\cdots\)
2480.1.k.b 2480.k 155.c $1$ $1.238$ \(\Q\) \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) 155.1.c.a \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+2q^{19}+q^{25}+q^{31}+\cdots\)
2480.1.k.c 2480.k 155.c $1$ $1.238$ \(\Q\) \(\Q(\sqrt{-155}) \) None 620.1.f.a \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+2q^{13}+q^{15}-q^{17}+\cdots\)
2480.1.k.d 2480.k 155.c $2$ $1.238$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-155}) \) None 620.1.f.c \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{15}-\beta q^{17}+\cdots\)
2480.1.k.e 2480.k 155.c $2$ $1.238$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-31}) \) None 155.1.c.b \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-q^{9}+\cdots\)
2480.1.t.a 2480.t 2480.t $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.t.a \(0\) \(0\) \(-2\) \(2\) \(q-iq^{2}-q^{4}-q^{5}+(1-i)q^{7}+iq^{8}+\cdots\)
2480.1.t.b 2480.t 2480.t $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.t.b \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}+q^{4}-iq^{5}+(-1+i)q^{7}+q^{8}+\cdots\)
2480.1.t.c 2480.t 2480.t $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.t.c \(-2\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
2480.1.t.d 2480.t 2480.t $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.t.d \(0\) \(0\) \(2\) \(-2\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
2480.1.bj.a 2480.bj 2480.aj $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.bj.a \(-2\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-iq^{9}+q^{10}+\cdots\)
2480.1.bj.b 2480.bj 2480.aj $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.bj.a \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{5}+q^{8}-iq^{9}+iq^{10}+\cdots\)
2480.1.bj.c 2480.bj 2480.aj $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.bj.c \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
2480.1.bj.d 2480.bj 2480.aj $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.bj.c \(2\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
2480.1.bm.a 2480.bm 2480.am $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.t.b \(0\) \(0\) \(2\) \(-2\) \(q-iq^{2}-q^{4}+q^{5}+(-1+i)q^{7}+iq^{8}+\cdots\)
2480.1.bm.b 2480.bm 2480.am $2$ $1.238$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-31}) \) None 2480.1.t.a \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}-iq^{5}+(1-i)q^{7}+q^{8}+\cdots\)
2480.1.bm.c 2480.bm 2480.am $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.t.d \(-2\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
2480.1.bm.d 2480.bm 2480.am $4$ $1.238$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-31}) \) None 2480.1.t.c \(0\) \(0\) \(-2\) \(2\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
2480.1.bs.a 2480.bs 620.o $2$ $1.238$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) 2480.1.bs.a \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+(-1+\zeta_{6}^{2})q^{11}+\cdots\)
2480.1.bs.b 2480.bs 620.o $2$ $1.238$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) 2480.1.bs.a \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+(1-\zeta_{6}^{2})q^{11}+\zeta_{6}^{2}q^{25}+\cdots\)
2480.1.bv.a 2480.bv 155.i $2$ $1.238$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) 620.1.q.a \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+(1-\zeta_{6}^{2})q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
2480.1.de.a 2480.de 155.o $4$ $1.238$ \(\Q(\zeta_{12})\) None None 1240.1.cg.b \(0\) \(-2\) \(2\) \(-2\) \(q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}-\zeta_{12}^{4}q^{5}+\cdots\)
2480.1.de.b 2480.de 155.o $4$ $1.238$ \(\Q(\zeta_{12})\) None None 1240.1.cg.a \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+\zeta_{12}q^{9}+\cdots\)
2480.2.a.a 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.g \(0\) \(-3\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}-2q^{7}+6q^{9}+2q^{11}+\cdots\)
2480.2.a.b 2480.a 1.a $1$ $19.803$ \(\Q\) None None 155.2.a.b \(0\) \(-2\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2480.2.a.c 2480.a 1.a $1$ $19.803$ \(\Q\) None None 310.2.a.b \(0\) \(-2\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
2480.2.a.d 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.f \(0\) \(-2\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}+4q^{13}+2q^{15}+\cdots\)
2480.2.a.e 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.e \(0\) \(-2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
2480.2.a.f 2480.a 1.a $1$ $19.803$ \(\Q\) None None 620.2.a.c \(0\) \(-1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}-2q^{9}+2q^{13}+\cdots\)
2480.2.a.g 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.c \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-2q^{11}+2q^{13}+8q^{19}+\cdots\)
2480.2.a.h 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.d \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
2480.2.a.i 2480.a 1.a $1$ $19.803$ \(\Q\) None None 620.2.a.b \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots\)
2480.2.a.j 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.a \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-2q^{13}-q^{15}+\cdots\)
2480.2.a.k 2480.a 1.a $1$ $19.803$ \(\Q\) None None 155.2.a.c \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+4q^{11}-6q^{13}+\cdots\)
2480.2.a.l 2480.a 1.a $1$ $19.803$ \(\Q\) None None 1240.2.a.b \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}-2q^{9}+2q^{11}+\cdots\)
2480.2.a.m 2480.a 1.a $1$ $19.803$ \(\Q\) None None 155.2.a.a \(0\) \(1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-2q^{11}+\cdots\)
2480.2.a.n 2480.a 1.a $1$ $19.803$ \(\Q\) None None 310.2.a.a \(0\) \(2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{13}+\cdots\)
2480.2.a.o 2480.a 1.a $1$ $19.803$ \(\Q\) None None 620.2.a.a \(0\) \(3\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+2q^{7}+6q^{9}-2q^{11}+\cdots\)
2480.2.a.p 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{2}) \) None None 1240.2.a.i \(0\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-2q^{7}-q^{9}+(-2+\beta )q^{11}+\cdots\)
2480.2.a.q 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{6}) \) None None 310.2.a.d \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots\)
2480.2.a.r 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{17}) \) None None 1240.2.a.h \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+(2-2\beta )q^{11}+\cdots\)
2480.2.a.s 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{3}) \) None None 310.2.a.c \(0\) \(2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
2480.2.a.t 2480.a 1.a $3$ $19.803$ 3.3.756.1 None None 620.2.a.d \(0\) \(-3\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+\beta _{2}q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
2480.2.a.u 2480.a 1.a $3$ $19.803$ 3.3.148.1 None None 310.2.a.e \(0\) \(-2\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2480.2.a.v 2480.a 1.a $3$ $19.803$ 3.3.148.1 None None 1240.2.a.j \(0\) \(3\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2480.2.a.w 2480.a 1.a $4$ $19.803$ 4.4.25492.1 None None 620.2.a.e \(0\) \(-3\) \(4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2480.2.a.x 2480.a 1.a $4$ $19.803$ 4.4.8468.1 None None 155.2.a.e \(0\) \(-1\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
2480.2.a.y 2480.a 1.a $4$ $19.803$ 4.4.112820.1 None None 1240.2.a.k \(0\) \(1\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
2480.2.a.z 2480.a 1.a $4$ $19.803$ 4.4.20308.1 None None 155.2.a.d \(0\) \(1\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
2480.2.a.ba 2480.a 1.a $6$ $19.803$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None 1240.2.a.m \(0\) \(1\) \(6\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(4-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
2480.2.a.bb 2480.a 1.a $6$ $19.803$ 6.6.473125168.1 None None 1240.2.a.l \(0\) \(3\) \(-6\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
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