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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
4032.2.a.a 4032.a 1.a $1$ $32.196$ \(\Q\) None 56.2.a.b \(0\) \(0\) \(-4\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}+2q^{17}-2q^{19}+8q^{23}+\cdots\)
4032.2.a.b 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.a \(0\) \(0\) \(-4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}+2q^{11}+2q^{13}-4q^{19}+\cdots\)
4032.2.a.c 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.a \(0\) \(0\) \(-4\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}-2q^{11}+2q^{13}+4q^{19}+\cdots\)
4032.2.a.d 4032.a 1.a $1$ $32.196$ \(\Q\) None 56.2.a.b \(0\) \(0\) \(-4\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}+2q^{17}+2q^{19}-8q^{23}+\cdots\)
4032.2.a.e 4032.a 1.a $1$ $32.196$ \(\Q\) None 42.2.a.a \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
4032.2.a.f 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.b \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.g 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.a \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-2q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.h 4032.a 1.a $1$ $32.196$ \(\Q\) None 21.2.a.a \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
4032.2.a.i 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.d \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{11}+6q^{13}-2q^{17}+\cdots\)
4032.2.a.j 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.d \(0\) \(0\) \(-2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-6q^{11}+6q^{13}-2q^{17}+\cdots\)
4032.2.a.k 4032.a 1.a $1$ $32.196$ \(\Q\) None 21.2.a.a \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
4032.2.a.l 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.a \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.m 4032.a 1.a $1$ $32.196$ \(\Q\) None 42.2.a.a \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
4032.2.a.n 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.b \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+4q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.o 4032.a 1.a $1$ $32.196$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}-2q^{13}-4q^{17}+4q^{23}+\cdots\)
4032.2.a.p 4032.a 1.a $1$ $32.196$ \(\Q\) None 224.2.a.a \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}+4q^{13}+2q^{17}+6q^{19}+\cdots\)
4032.2.a.q 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.c \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{11}+2q^{13}-4q^{17}+4q^{19}+\cdots\)
4032.2.a.r 4032.a 1.a $1$ $32.196$ \(\Q\) None 14.2.a.a \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{13}-6q^{17}+2q^{19}-5q^{25}+\cdots\)
4032.2.a.s 4032.a 1.a $1$ $32.196$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}-2q^{13}+4q^{17}-4q^{23}+\cdots\)
4032.2.a.t 4032.a 1.a $1$ $32.196$ \(\Q\) None 84.2.a.b \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
4032.2.a.u 4032.a 1.a $1$ $32.196$ \(\Q\) None 84.2.a.b \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\)
4032.2.a.v 4032.a 1.a $1$ $32.196$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}-2q^{13}+4q^{17}+4q^{23}+\cdots\)
4032.2.a.w 4032.a 1.a $1$ $32.196$ \(\Q\) None 14.2.a.a \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{13}-6q^{17}-2q^{19}-5q^{25}+\cdots\)
4032.2.a.x 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.c \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}+2q^{13}-4q^{17}-4q^{19}+\cdots\)
4032.2.a.y 4032.a 1.a $1$ $32.196$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-2q^{13}-4q^{17}-4q^{23}+\cdots\)
4032.2.a.z 4032.a 1.a $1$ $32.196$ \(\Q\) None 224.2.a.a \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+4q^{13}+2q^{17}-6q^{19}+\cdots\)
4032.2.a.ba 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.d \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-6q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.bb 4032.a 1.a $1$ $32.196$ \(\Q\) None 56.2.a.a \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.bc 4032.a 1.a $1$ $32.196$ \(\Q\) None 168.2.a.a \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
4032.2.a.bd 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.d \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
4032.2.a.be 4032.a 1.a $1$ $32.196$ \(\Q\) None 168.2.a.b \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
4032.2.a.bf 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.a \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
4032.2.a.bg 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.a \(0\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
4032.2.a.bh 4032.a 1.a $1$ $32.196$ \(\Q\) None 168.2.a.a \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
4032.2.a.bi 4032.a 1.a $1$ $32.196$ \(\Q\) None 672.2.a.d \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
4032.2.a.bj 4032.a 1.a $1$ $32.196$ \(\Q\) None 168.2.a.b \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
4032.2.a.bk 4032.a 1.a $1$ $32.196$ \(\Q\) None 56.2.a.a \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
4032.2.a.bl 4032.a 1.a $1$ $32.196$ \(\Q\) None 504.2.a.d \(0\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+6q^{11}+6q^{13}+2q^{17}+\cdots\)
4032.2.a.bm 4032.a 1.a $1$ $32.196$ \(\Q\) None 84.2.a.a \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}+2q^{11}+6q^{13}+4q^{17}+\cdots\)
4032.2.a.bn 4032.a 1.a $1$ $32.196$ \(\Q\) None 84.2.a.a \(0\) \(0\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-2q^{11}+6q^{13}+4q^{17}+\cdots\)
4032.2.a.bo 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
4032.2.a.bp 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots\)
4032.2.a.bq 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{3}) \) None 63.2.a.b \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+\beta q^{11}-2q^{13}+\beta q^{17}+\cdots\)
4032.2.a.br 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(2-\beta )q^{11}-2q^{13}+\cdots\)
4032.2.a.bs 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(-2+\beta )q^{11}-2q^{13}+\cdots\)
4032.2.a.bt 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{3}) \) None 63.2.a.b \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}-\beta q^{11}-2q^{13}+\beta q^{17}+\cdots\)
4032.2.a.bu 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}-2\beta q^{13}+\cdots\)
4032.2.a.bv 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(2+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
4032.2.a.bw 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(-2-2\beta )q^{11}+\cdots\)
4032.2.a.bx 4032.a 1.a $2$ $32.196$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
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