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Results (43 matches)

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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 17
8568.2.a.a 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.j \(0\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}-5q^{11}-3q^{13}-q^{17}+\cdots\)
8568.2.a.b 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.i \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-6q^{11}+4q^{13}+q^{17}+\cdots\)
8568.2.a.c 8568.a 1.a $1$ $68.416$ \(\Q\) None 8568.2.a.c \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{11}+2q^{13}+q^{17}+\cdots\)
8568.2.a.d 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.b \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+4q^{11}+2q^{13}+q^{17}+\cdots\)
8568.2.a.e 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.h \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
8568.2.a.f 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.f \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+3q^{11}+q^{13}-q^{17}+\cdots\)
8568.2.a.g 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.g \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-q^{11}-3q^{13}-q^{17}+\cdots\)
8568.2.a.h 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.a \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}-q^{13}+q^{17}+5q^{19}+\cdots\)
8568.2.a.i 8568.a 1.a $1$ $68.416$ \(\Q\) None 8568.2.a.c \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-6q^{11}+2q^{13}-q^{17}+\cdots\)
8568.2.a.j 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.c \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{13}-q^{17}-q^{25}+\cdots\)
8568.2.a.k 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.e \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-6q^{11}-4q^{13}-q^{17}+\cdots\)
8568.2.a.l 8568.a 1.a $1$ $68.416$ \(\Q\) None 2856.2.a.d \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}+6q^{13}-q^{17}+\cdots\)
8568.2.a.m 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{201}) \) None 2856.2.a.p \(0\) \(0\) \(-6\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-q^{11}+q^{13}-q^{17}+\cdots\)
8568.2.a.n 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{17}) \) None 8568.2.a.n \(0\) \(0\) \(-3\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.o 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{15}) \) None 2856.2.a.n \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+5q^{11}+(2-\beta )q^{13}+\cdots\)
8568.2.a.p 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{3}) \) None 2856.2.a.o \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(3-2\beta )q^{11}+(-4+\beta )q^{13}+\cdots\)
8568.2.a.q 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{17}) \) None 2856.2.a.l \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(1-2\beta )q^{11}+(-1+2\beta )q^{13}+\cdots\)
8568.2.a.r 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{17}) \) None 2856.2.a.m \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.s 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{17}) \) None 2856.2.a.k \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.t 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{13}) \) None 952.2.a.b \(0\) \(0\) \(3\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-2+2\beta )q^{11}+\cdots\)
8568.2.a.u 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{17}) \) None 8568.2.a.n \(0\) \(0\) \(3\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.v 8568.a 1.a $2$ $68.416$ \(\Q(\sqrt{5}) \) None 952.2.a.a \(0\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(2-4\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
8568.2.a.w 8568.a 1.a $3$ $68.416$ 3.3.1229.1 None 952.2.a.e \(0\) \(0\) \(-3\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}-q^{7}-2q^{11}+2q^{13}+\cdots\)
8568.2.a.x 8568.a 1.a $3$ $68.416$ 3.3.229.1 None 952.2.a.f \(0\) \(0\) \(-3\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+q^{7}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots\)
8568.2.a.y 8568.a 1.a $3$ $68.416$ 3.3.961.1 None 2856.2.a.r \(0\) \(0\) \(-2\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
8568.2.a.z 8568.a 1.a $3$ $68.416$ 3.3.229.1 None 952.2.a.d \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}-q^{7}+2q^{11}+(2-2\beta _{1}+2\beta _{2})q^{13}+\cdots\)
8568.2.a.ba 8568.a 1.a $3$ $68.416$ 3.3.148.1 None 8568.2.a.ba \(0\) \(0\) \(-1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+(-1-2\beta _{2})q^{11}+(1+\cdots)q^{13}+\cdots\)
8568.2.a.bb 8568.a 1.a $3$ $68.416$ 3.3.148.1 None 8568.2.a.ba \(0\) \(0\) \(1\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(1+2\beta _{2})q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots\)
8568.2.a.bc 8568.a 1.a $3$ $68.416$ 3.3.316.1 None 2856.2.a.s \(0\) \(0\) \(2\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}-q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\)
8568.2.a.bd 8568.a 1.a $3$ $68.416$ 3.3.568.1 None 2856.2.a.q \(0\) \(0\) \(4\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+q^{7}+(1-\beta _{2})q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.be 8568.a 1.a $3$ $68.416$ 3.3.229.1 None 952.2.a.c \(0\) \(0\) \(5\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{5}+q^{7}-2\beta _{1}q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
8568.2.a.bf 8568.a 1.a $4$ $68.416$ 4.4.183064.1 None 2856.2.a.v \(0\) \(0\) \(-5\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}-q^{7}-\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
8568.2.a.bg 8568.a 1.a $4$ $68.416$ 4.4.13448.1 None 952.2.a.h \(0\) \(0\) \(-5\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{5}+q^{7}-\beta _{1}q^{11}+2q^{13}+\cdots\)
8568.2.a.bh 8568.a 1.a $4$ $68.416$ 4.4.67348.1 None 8568.2.a.bh \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
8568.2.a.bi 8568.a 1.a $4$ $68.416$ 4.4.7232.1 None 2856.2.a.u \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{5}-q^{7}+(1-\beta _{2})q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
8568.2.a.bj 8568.a 1.a $4$ $68.416$ 4.4.5225.1 None 952.2.a.g \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{5}-q^{7}+(-1+\beta _{2})q^{11}+\cdots\)
8568.2.a.bk 8568.a 1.a $4$ $68.416$ 4.4.81416.1 None 2856.2.a.t \(0\) \(0\) \(1\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(-1+\beta _{3})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8568.2.a.bl 8568.a 1.a $4$ $68.416$ 4.4.67348.1 None 8568.2.a.bh \(0\) \(0\) \(2\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}-q^{7}+q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
8568.2.a.bm 8568.a 1.a $5$ $68.416$ 5.5.14050576.1 None 2856.2.a.w \(0\) \(0\) \(-1\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+q^{7}+(-\beta _{2}-\beta _{4})q^{11}-\beta _{3}q^{13}+\cdots\)
8568.2.a.bn 8568.a 1.a $7$ $68.416$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 8568.2.a.bn \(0\) \(0\) \(-4\) \(-7\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}+(1+\beta _{6})q^{11}+\cdots\)
8568.2.a.bo 8568.a 1.a $7$ $68.416$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 8568.2.a.bo \(0\) \(0\) \(-2\) \(7\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}-\beta _{5}q^{11}+(1-\beta _{2}-\beta _{5}+\cdots)q^{13}+\cdots\)
8568.2.a.bp 8568.a 1.a $7$ $68.416$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 8568.2.a.bo \(0\) \(0\) \(2\) \(7\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+\beta _{5}q^{11}+(1-\beta _{2}-\beta _{5}+\cdots)q^{13}+\cdots\)
8568.2.a.bq 8568.a 1.a $7$ $68.416$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 8568.2.a.bn \(0\) \(0\) \(4\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}-q^{7}+(-1-\beta _{6})q^{11}+\cdots\)
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